ChemWiki - User contributions [en]

Rep:Dy815

2018-02-28T11:12:56Z

Dy815: /* Calculation file list */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' product is the thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' product is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction. As shown in the IRC gif, '''the six-member ring''' became the '''aromatic system''' during the reactions processing.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

Log file for CHELETROPIC IRC:[[Media:DY815-CHELETROPIC-IRC.LOG]]

Log file for CHELETROPIC PRODUCT:[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

Log file for CHELETROPIC TS:[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

Log file for DIELS-ALDER ENDO IRC:[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

Log file for DIELS-ALDER ENDO PRODUCT:[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

Log file for DIELS-ALDER ENDO TS:[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

Log file for DA EXO IRC:[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

Log file for DA EXO PRODUCT:[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

Log file for DA EXO TS:[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

Log file for SECOND DA IRC (ENDO):[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

Log file for SECOND DA IRC (EXO):[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

Log file for SECOND DA PRODUCT (ENDO):[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

Log file for SECOND DA PRODUCT (EXO):[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

Log file for SECOND DA TS (ENDO):[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

Log file for SECOND DA TS (EXO):[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T11:07:10Z

Dy815: /* IRC calculation */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' product is the thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' product is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction. As shown in the IRC gif, '''the six-member ring''' became the '''aromatic system''' during the reactions processing.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T11:04:29Z

Dy815: /* IRC calculation */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' product is the thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' product is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction. As shown in the IRC gif, the six-member ring became the aromatic system during the reactions processing.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T11:02:48Z

Dy815: /* IRC calculation */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' product is the thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' product is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction. As shown in the IRC gif, the '''aromatic transition state''' is formed during these reactions.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T11:00:08Z

Dy815: /* Steric clashes between bridging and terminal hydrogens */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' product is the thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' product is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:59:43Z

Dy815: /* Secondary molecular orbital overlap */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' product is a thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' product is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:59:02Z

Dy815: /* Steric clashes between bridging and terminal hydrogens */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' product is a thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:57:26Z

Dy815: /* calculation of reaction energies */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and free energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:50:33Z

Dy815: /* Molecular orbital at transition states for the endo and exo reaction */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen. '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*'''). '''Note''': all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies.

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:48:17Z

Dy815: /* Molecular Orbital (MO) diagram */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented because GaussView is not able to give very accurate energies. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:10:58Z

Dy815: /* Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*The obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:08:32Z

Dy815: /* Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figures below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:08:08Z

Dy815: /* Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in figure below).
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:07:29Z

Dy815: /* Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table ('''table 5''') above, the difference between '''exo TS''' and '''endo TS''' is not clearly seen. If we calculate these two transition states (endo and exo) in the '''same PES''' together, we can see clearly from the table below ('''table 6''') that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for '''Exo TS''' are lower than these energy levels of '''Endo MO''', while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with two transition states only is smaller than 8M, the Jmol pictures are able to be uploaded to wiki file and tabulated ('''table 6''').

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T10:00:55Z

Dy815: /* Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct for the Endo MO diagram, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T09:59:51Z

Dy815: /* Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like as exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T09:59:06Z

Dy815: /* Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

This MO diagram was '''not what we expected''' because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T09:57:37Z

Dy815: /* Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T09:54:48Z

Dy815: /* Measurements of C-C bond lengths involved in Diels-Alder Reaction */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all other C-C bond lengths (except C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub>) are greater than the literature value of C=C(sp<sup>2</sup>), and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T09:51:55Z

Dy815: /* Exercise 1 */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond lengths for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T09:46:49Z

Dy815: /* Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO diagrams''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T09:45:26Z

Dy815: /* Correct the MO for Endo and Exo, with calculating combined endo and exo transition states and reactants */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO diagrams for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T09:44:16Z

Dy815: /* Vibration analysis for the Diels-Alder reaction */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

Additionally, IRC energy graph for this vibrational analysis is plotted as well ('''figure 7*''').

[[File:DY815 EX1 IRC ENERGY.PNG|thumb|centre|Figure 7* IRC energy graph| 600px]]

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

File:DY815 EX1 IRC ENERGY.PNG

2018-02-28T09:41:52Z

Dy815:

Rep:Dy815

2018-02-28T09:37:17Z

Dy815: /* Correct Endo and Exo MO, with calculating combined endo and exo transition states and reactants */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct the MO for Endo and Exo, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:DY815 CORRECT MO CHEMDRAW.PNG|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

File:DY815 CORRECT MO CHEMDRAW.PNG

2018-02-28T09:36:38Z

Dy815:

Rep:Dy815

2018-02-28T02:31:22Z

Dy815: /* Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction) */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct Endo and Exo MO, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T02:30:50Z

Dy815: /* Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction) */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct Endo and Exo MO, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways.

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T02:17:48Z

Dy815: /* Vibration analysis for the Diels-Alder reaction */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their π orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct Endo and Exo MO, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive value indicates that the second diels-Alder reactions are not spontaneous reaction and are not favourable compared with the normal Diels-Alder reaction and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised. And this is also reflected by the activation energies of '''endo''' and '''exo''' '''side reaction''' pathways (the activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways).

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T02:16:58Z

Dy815: /* Vibration analysis for the Diels-Alder reaction */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

In the gif, we can also see that these two reactants approach each other with their pi orbitals parallel head to head, p orbitals for the ends of both reactants dis-rotated to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which states a [4+2] cycloadditon reaction is thermally allowed.

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct Endo and Exo MO, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive value indicates that the second diels-Alder reactions are not spontaneous reaction and are not favourable compared with the normal Diels-Alder reaction and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised. And this is also reflected by the activation energies of '''endo''' and '''exo''' '''side reaction''' pathways (the activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways).

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T02:15:50Z

Dy815: /* Frontier Molecular Orbital (FMO) */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct Endo and Exo MO, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive value indicates that the second diels-Alder reactions are not spontaneous reaction and are not favourable compared with the normal Diels-Alder reaction and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised. And this is also reflected by the activation energies of '''endo''' and '''exo''' '''side reaction''' pathways (the activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways).

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T02:08:10Z

Dy815: /* Measurements of C-C bond lengths involved in Diels-Alder Reaction */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and corresponding dynamic pictures calculated by GaussView are also shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct Endo and Exo MO, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive value indicates that the second diels-Alder reactions are not spontaneous reaction and are not favourable compared with the normal Diels-Alder reaction and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised. And this is also reflected by the activation energies of '''endo''' and '''exo''' '''side reaction''' pathways (the activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways).

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Dy815

2018-02-28T02:06:58Z

Dy815: /* Requirements for successful Diels-Alder reactions */

==Introduction==

===Potential Energy Surface (PES)===
The Potential energy surface (PES) is a central concept in computational chemistry, and PES can allow chemists to work out mathematical or graphical results of some specific chemical reactions. <ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The concept of PES is based on Born-Oppenheimer approximation - in a molecule the nuclei are essentially stationary compared with the electrons motion, which makes molecular shapes meaningful.<ref># E. Lewars, Computational Chemistry, Springer US, Boston, MA, 2004, DOI: https://doi.org/10.1007/0-306-48391-2_2</ref>

The potential energy surface can be plotted by potential energy against any combination of degrees of freedom or reaction coordinates; therefore, geometric coordinates, <math chem>q</math>, should be applied here to describe a reacting system. For example, as like '''Second Year''' molecular reaction dynamics lab ('''triatomic reacting system: HOF'''), geometric coordinate (<math chem>q_1</math>) can be set as O-H bond length, and another geometric coordinate (<math chem>q_2</math>) can be set as O-F bond length. However, as the complexity of molecules increases, more dimensions of geometric parameters such as bond angle or dihedral need to be included to describe these complex reacting systems. In this computational lab, <math chem>q</math> is in the basis of the normal modes which are a linear combination of all bond rotations, stretches and bends, and looks a bit like a vibration.

===Transition State===
Transition state is normally considered as a point with the highest potential energy in a specific chemical reaction. More precisely, for reaction coordinate, transition state is a stationary point ('''zero first derivative''') with '''negative second derivative''' along the minimal-energy reaction pathway(<math>\frac{dV}{dq}=0</math> and <math>\frac{d^2V}{dq^2}<0</math>). <math chem>V</math> indicates the potential energy, and <math chem>q</math> here represents an geometric parameter, in the basis of normal modes at transition state, which is a linear combination of all bond rotations, streches and bends, and hence looks like a vibration.

In computational chemistry, along the geometric coordinates (<math chem>q</math>), one lowest-energy pathway can be found, as the most likely reaction pathway for the reaction, which connects the reactant and the product. The maximum point along the lowest-energy path is considered as the transition state of the chemical reaction.

===Computational Method===
As Schrödinger equation states, <math> \lang {\Psi} |\mathbf{H}|\Psi\rang = \lang {\Psi} |\mathbf{E}|\Psi\rang,</math> a linear combination of atomic orbitals can sum to the molecular orbital: <math>\sum_{i}^N {c_i}| \Phi \rangle = |\psi\rangle. </math> If the whole linear equation expands, a simple matrix representation can be written:
:<math> {E} =
\begin{pmatrix} c_1 & c_2 & \cdots & \ c_i \end{pmatrix}
\begin{pmatrix}
\lang {\Psi_1} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_1} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_1} |\mathbf{H}|\Psi_i\rang \\
\lang {\Psi_2} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_2} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_2} |\mathbf{H}|\Psi_i\rang \\
\vdots & \vdots & \ddots & \vdots \\
\lang {\Psi_i} |\mathbf{H}|\Psi_1\rang & \lang {\Psi_i} |\mathbf{H}|\Psi_2\rang & \cdots & \lang {\Psi_i} |\mathbf{H}|\Psi_i\rang \\ \end{pmatrix}
\begin{pmatrix} c_1 \\ c_2 \\ \vdots \\ c_i \end{pmatrix},
</math>

where the middle part is called Hessian matrix.

Therefore, according to '''variation principle''' in quantum mechanics, this equation can be solve into the form of <math chem>H_c</math> = <math chem>E_c</math>.

In this lab, GaussView is an useful tool to calculate molecular energy and optimize molecular structures, based on different methods of solving the Hessian matrix part (<math chem>H_c</math> bit in the simple equation above). '''PM6''' and '''B3LYP''' are used in this computational lab, and main difference between '''PM6''' and '''B3LYP''' is that these two methods use different algorithms in calculating the Hessian matrix part. '''PM6''' uses a Hartree–Fock formalism which plugs some empirically experimental-determined parameters into the Hessian matrix to simplify the molecular calculations. While, '''B3LYP''' is one of the most popular methods of '''density functional theory''' ('''DFT'''), which is also a so-called 'hybrid exchange-correlation functional' method. Therefore, in this computational lab, the calculation done by parameterized '''PM6''' method is always faster and less-expensive than '''B3LYP''' method.

==Exercise 1==

In this exercise, very classic Diels-Alder reaction between butadiene and ethene has been investigated. In the reaction, an acceptable transition state has been calculated. The molecular orbitals, comparison of bond length for different C-C and the requirements for this reaction will be discussed below. (The classic Diels-Alder reaction is shown in '''figure 1'''.)

'''Note''' : all the calculations were at '''PM6''' level.

[[File:DY815 EX1 REACTION SCHEME.PNG|thumb|centre|Figure 1. Reaction Scheme of Diels Alder reaction between butadiene and ethene|700x600px]]

===Molecular Orbital (MO) Analysis===

====Molecular Orbital (MO) diagram====

The molecular orbitals of Diels-Alder reaction between butadiene and ethene is presented below ('''Fig 2'''):

[[File:Ex1-dy815-MO.PNG|thumb|centre|Figure 2. MO diagram of Diels Alder reaction between butadiene and ethene|700x600px]]

In '''figure 2''', all the energy levels are not quantitatively presented. It is worth noticing that the energy level of '''ethene LUMO''' is the highest among all MOs, while the energy level of '''ethene HOMO''' is the lowest one. To confirm the correct order of energy levels of MO presented in the diagram, '''energy calculations''' at '''PM6 level''' have been done, and Jmol pictures of MOs have been shown in '''table 1''' (from low energy level to high energy level):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 1: Table for energy levels of MOs in the order of energy(from low to high)
! '''ethene''' HOMO - MO 31
! '''butadiene''' HOMO - MO 32
! '''transition state''' HOMO-1 - MO 33
! '''transition state''' HOMO - MO 34
! '''butadiene''' LUMO - MO 35
! '''transition state''' LUMO - MO 36
! '''transition state''' LUMO+1 - MO 37
! '''ethene''' LUMO - MO 38
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 35; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 36; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 37; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 38; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 SM VS TS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

In '''table 1''', all the calculations are done by putting the reactants and the optimized transition state in the same PES. TO achieve this, all the components (each reactant and the optimized transition state) are set a far-enough distances to avoid any presence of interactions in this system (the distance usually set up greater than 6 Å, which is greater than 2 × Van der Waals radius of atoms). The pictures of calculation method and molecular buildup are presented below:

[[File:DY815 EX1 Calculation Method of energy calculation.PNG|thumb|centre|Figure 3. energy calculation method for MOs|700x600px]]

[[File:DY815 Molecular drawing for energy calculation.PNG|thumb|centre|Figure 4. molecular buildup for MO energy calculation|700x600px]]

====Frontier Molecular Orbital (FMO)====

The '''table 2''' below contains the Jmol pictures of frontier MOs - HOMO and LUMO of two reactants (ethene and butadiene) and HOMO-1, HOMO, LUMO and LUMO+1 of calculated transition state are tabulated.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 2: Table of HOMO and LUMO of butadiene and ethene, and the four MOs produced for the TS
! Molecular orbital of ethene (HOMO)
! Molecular orbital of ethene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of butadiene (HOMO)
! Molecular orbital of butadiene (LUMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (HOMO-1)
! Molecular orbital of TS (HOMO)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Molecular orbital of TS (LUMO)
! Molecular orbital of TS (LUMO+1)
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Requirements for successful Diels-Alder reactions====

Combining with '''figure 2''' and '''table 2''', it can be concluded that the '''requirements for successful reaction''' are direct orbital overlap of the reactants and correct symmetry. Correct direct orbital overlap leads to a successful reaction of reactants with the same symmetry (only '''symmetric/ symmetric''' and '''antisymmetric/ antisymmetric''' are 'reaction-allowed', otherwise, the interactions are 'reaction-forbidden'). As a result, the orbital overlap integral for symmetric-symmetric and antisymmetric-antisymmetric interactions is '''non-zero''', while the orbital overlap integral for the antisymmetric-symmetric interaction is '''zero'''.

=== Measurements of C-C bond lengths involved in Diels-Alder Reaction===

Measurements of 4 C-C bond lengths of two reactants and bond lengths of both the transition state and the product gives the information of reaction. A summary of all bond lengths involving in this Diels-Alder reaction has been shown in the '''figure 5''' and a table of dynamic pictures calculated by GaussView has also been shown below ('''figure 6'''):

[[File:DY815 EX1 BL2.PNG|thumb|centre|Figure 5. Summary of bond lengths involving in Diels Alder reaction between butadiene and ethene|700x600px]]

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>EX1 SM1 JMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4]; label display; color label red; frank off</script>
<name>DY815EX1ETHENE</name>
</jmolApplet>
<jmolbutton>
<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
<target>DY815EX1ETHENE</target>
</jmolbutton>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 DIENE.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 4 6 8]; label display; color label red; frank off</script>
<name>DY815EX1DIENE</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1DIENE</target>
<item>
<script>frame 2; measure off; measure 1 4 </script>
<text>C1-C4 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 4 6 </script>
<text>C4-C6 Distances</text>
</item>
<item>
<script>frame 2; measure off; measure 6 8 </script>
<text>C6-C8 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>DY815 EX1 TSJMOL.LOG</uploadedFileContents>
<script>frame 2; select atomno=[1 2 14 11 5 8]; label display; color label red; frank off</script>
<name>DY815EX1TS</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1TS</target>
<item>
<script>frame 2; measure off; measure 1 2 </script>
<text>C1-C2 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C8-C1 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

<jmol>
<jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>PRO1-PM6(FREQUENCY).LOG</uploadedFileContents>
<script>frame 2; select atomno=[5 11 14 2 1 8]; label display; color label red; select atomno=[1 2]; connect double; frank off</script>
<name>DY815EX1PRO</name>
</jmolApplet>
<jmolMenu>
<target>DY815EX1PRO</target>
<item>
<script>frame 2; measure off; measure 11 5 </script>
<text>C5-C11 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 5 8 </script>
<text>C5-C8 Distances</text>
</item>
<item>
<script>frame 2; measure off;measure 8 1 </script>
<text>C1-C8 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 1 2 </script>
<text>C1-C2 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 2 14 </script>
<text>C2-C14 Distances</text>

</item>
<item>
<script>frame 2; measure off;measure 14 11 </script>
<text>C11-C14 Distances</text>
</item>
</jmolMenu>
</jmol>

'''Figure 6.''' Corresponding (to '''figure 5''') dynamic Jmol pictures for C-C bond lengths involving in Diels Alder reaction

The change of bond lengths can be clearly seen in '''figure 5''', in first step, the double bonds in ethene (C<sub>1</sub>-C<sub>2</sub>) and butadiene (C<sub>3</sub>-C<sub>4</sub> and C<sub>5</sub>-C<sub>6</sub>) increase from about 1.33Å to about 1.38Å, while the only single bond in butadiene (C<sub>4</sub>-C<sub>5</sub>) is seen a decrease from 1.47Å to 1.41Å. Compared to the literature values<ref># L.Pauling and L. O. Brockway, Journal of the American Chemical Society, 1937, Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref> of C-C (sp<sup>3</sup>:1.54Å), C=C (sp<sup>2</sup>:1.33Å) and Van der Waals radius of carbon (1.70Å), the changes of bond lengths indicate that C=C(sp<sup>2</sup>) changes into C-C(sp<sup>3</sup>), and C-C(sp<sup>3</sup>) changes into C=C(sp<sup>2</sup>) at the meantime. As well, since the C<sub>1</sub>-C<sub>6</sub> and C<sub>2</sub>-C<sub>3</sub> is less than twice fold of Van der Waals radius of carbon (~2.11Å < 3.4Å), the orbital interaction occurs in this step as well. Because all the C-C bond lengths here are greater than the literature value of C=C(sp<sup>2</sup>) and less than the literature value of C-C(sp<sup>3</sup>), all the C-C bonds can possess the properties of partial double bonds do.

After the second step, all the bond lengths in the product (cyclohexene) go to approximately literature bond lengths which they should be.

===Vibration analysis for the Diels-Alder reaction===

The vibrational gif picture which shows the formation of cyclohexene picture is presented below ('''figure 7'''):

[[File:DY815 EX1 Irc-PM6-22222222.gif|thumb|centre|Figure 7. gif picture for the process of the Diels-Alder reaction|700x600px]]

In this gif, it can also be seen a '''synchronous''' process according to this '''vibrational analysis'''. So, GaussView tells us that Diels-Alder reaction between ethane and butadiene is a concerted pericyclic reaction as expected. Another explanation of a '''synchronous''' process is that in '''molecular distance analysis''' at transition state, C<sub>1</sub>-C<sub>6</sub> = C<sub>2</sub>-C<sub>3</sub> = 2.11 Å.

===Calculation files list===

optimized reactant: [[Media:EX1 SM1 JMOL.LOG]] [[Media:DY815 EX1 DIENE.LOG]]

optimized product: [[Media:PRO1-PM6(FREQUENCY).LOG]]

otimized/frequency calculated transition state:[[Media:DY815 EX1 TSJMOL.LOG]]

IRC to confirm the transition state: [[Media:DY815-EX1-IRC-PM6.LOG]]

Energy calculation to confirm the frontier MO: [[Media:DY815 EX1 SM VS TS ENERGYCAL.LOG]]

==Exercise 2==

[[File:DY815 EX2 Reaction Scheme.PNG|thumb|centre|Figure 8. Reaction scheme for Diels-Alder reaction between cyclohexadiene and 1,3-dioxole|700x600px]]

The reaction scheme ('''figure 8''') shows the exo and endo reaction happened between cyclohexadiene and 1,3-dioxole. In this section, MO and FMO are analyzed to characterize this Diels-Alder reaction and energy calculations will be presented as well.

'''Note''':All the calculations in this lab were done by '''B3LYP''' method on GaussView.

===Molecular orbital at transition states for the endo and exo reaction===

====Correct MOs of the Exo Diels-Alder reaction, generated by energy calculation====

The energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES'''. The distance between the transition state and the reactants are set far away to avoid interaction between each reactants and the transition state. The calculation follows the same energy calculation method mentioned in '''fig 3''' and '''fig 4''', except from '''B3LYP''' method being applied here. '''Table 3''' includes all the MOs needed to know to construct a MO diagram.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 3: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''cyclohexadiene''' HOMO - MO 79
! '''EXO TS''' HOMO-1 - MO 80
! '''1,3-dioxole''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''EXO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''1,3-dioxole''' LUMO - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 EXO MO 2222.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Dy815 ex2 EXO MMMMMMO.PNG|thumb|centre|Figure 9. MO for exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

Therefore, the MO diagram can be constructed as above ('''figure 9''').

====Incorrect MO diagram of the Endo Diels-Alder reaction, genereated by energy calculation====

The determination of '''endo''' MO here follows the exactly same procedures as mentioned in construction '''exo''' MO, except substituting the '''endo''' transition into '''exo''' transition state. '''Table 4''' shows the information needed to construct '''endo''' MO.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 4: Table for Endo energy levels of TS MO (energy from low to high)
! '''1,3-dioxole''' HOMO - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''cyclohexadiene''' HOMO - MO 82
! '''cyclohexadiene''' LUMO - MO 83
! '''1,3-dioxole''' LUMO - MO 84
! '''ENDO TS''' LUMO - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDO MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the table above, the MO diagram for '''endo''' can be generated ('''figure 10''') because all the relative energy levels are clearly seen.

[[File:DY815 EX2-ENDO MMMMMMO.PNG|thumb|centre|Figure 10. Wrong MO for endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole |700x600px]]

THIS MO diagram was not what we expected because the LUMO of dienophile should be higher than the unoccupied orbitals of endo transition state as like in exo MO. This is '''not correct'''. Therefore, a new method to determine '''endo''' transition state was done.

====Correct Endo and Exo MO, with calculating combined endo and exo transition states and reactants====

The new comparison method follows:

*Putting two transition states (endo and exo) in a single Guassview window with far enough distance to avoid any interaction. Far enough means '''the distance > 2 * VDW radius of carbon'''.

*Putting 1,3-dioxole and cyclohexadiene in the same Guassview window with far enough distance to avoid any interaction.

*Make sure these '''four''' components have no interaction with each other. Putting these four components in one GaussView window is to make sure these components being calculated on the same '''PES'''.(The final setup shown below)
[[File:DY815 SET1 FOR FINAL MO.PNG|thumb|centre|Putting the four components together|600px]]

*Calculate '''energy''' at '''B3LYP''' level (as shown in '''fig ''').
[[File:DY815 SET2 FOR FINAL MO.PNG|thumb|centre|energy calculation for the system|600px]]
[[File:DY815 SET3 FOR FINAL MO.PNG|thumb|centre|B3LYP calculation method being appiled|600px]]

*See the obtained MO is shown below:
[[File:DY815 Final MO GUASSIAN WINDOW.PNG|thumb|centre|12 desired MOs generated to obtain the correct MO|700x600px]]

Although the relative molecular orbitals were obtained, the '''log file''' for the calculation is greater than '''8M''' (actually '''9367KB'''). Even though it was impossible to upload it in wiki file, a table ('''Table 5''') which shows relations for these MOs is presented below.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 5: Table for energy levels of transition states (Exo and Endo) MO and reactants MO
! MO-118
! MO-119
! MO-120
! MO-121
! MO-122
! MO-123
! MO-124
! MO-125
! MO-126
! MO-127
! MO-128
! MO-129
|-
! cyclohexadiene HOMO
! EXO TS HOMO-1
! ENDO TS HOMO-1
! 1,3-dioxole HOMO
! ENDO TS HOMO
! EXO TS HOMO
! cyclohexadiene LUMO
! EXO TS LUMO
! ENDO TS LUMO
! EXO TS LUMO+1
! ENDO TS LUMO+1
! 1,3-dioxole LUMO
|}

Therefore, the actually '''correct MO''', containing both endo and exo transition states molecular orbitals, was presented and shown below (shown in '''figure 10*''').

[[File:|thumb|centre|Figure 10*. Correct MO diagram for endo TS|700x600px]]

From table above, if we only put these two transition states (endo and exo) together, we can find that the energy levels of '''HOMO-1''', '''LUMO''' and '''LUMO+1''' for Exo TS are lower than the energy levels for Endo MO, while '''HOMO''' for '''Exo TS''' is higher comapared to '''HOMO''' for '''Endo TS'''. Because the '''log file''' with only two transition states being calculated is able to be uploaded to wiki file, the Jmol pictures for comparing these two TS are tabulated below ('''table 6'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 6: Table for Exo and Endo energy levels of TS MO in the order of energy(from low to high)
! '''EXO TS''' HOMO-1 - MO 79
! '''ENDO TS''' HOMO-1 - MO 80
! '''ENDO TS''' HOMO - MO 81
! '''EXO TS''' HOMO - MO 82
! '''EXO TS''' LUMO - MO 83
! '''ENDO TS''' LUMO - MO 84
! '''EXO TS''' LUMO+1 - MO 85
! '''ENDO TS''' LUMO+1 - MO 86
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 79; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 80; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 81; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 82; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 83; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 84; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 85; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 86; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Characterize the type of DA reaction by comparing dienophiles in EX1 and EX2 (ethene and 1,3-dioxole)====

This Diels Alder reaction can be characterized by analysing the difference between molecular orbitals for dienophiles, because the difference for two diene (butadiene vs cyclohexadiene) is not big and we cannot decide the type of DA reaction by comparing the dienes.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 7: Table for Exo energy levels of TS MO in the order of energy(from low to high)
! '''ethene''' HOMO - MO 26
! '''1,3-dioxole''' HOMO - MO 27
! '''ethene''' LUMO - MO 28
! '''1,3-dioxole''' LUMO - MO 29
|-
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 26; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 27; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 28; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

To confirm the which type of Diels-Alder reaction it is, we need to put the two reactants on the same PES to compare the absolute energy, which can be done by GaussView '''energy calculation'''. The procedures are very similar to exercise 1 ('''figure 3, figure 4''') - put two reactants in the same window, setting a far enough distance to avoid any interaction, and then use '''energy''' calculation at '''B3LYP''' level.

{| class="wikitable" style="border: none; background: none;"
|+|Table 8: table of energy calculation resulted in this DA reaction
!
! HOMO
! LUMO
! Energy difference (absolute value)
|-
!standard
!cyclohexadiene
!1,3-dioxole
!0.24476 a.u.
|-
!inverse
!1,3-dioxole
!cyclohexadiene
!0.17774 a.u
|}

It can be concluded from the table that it is an inverse electron demand Diels-Alder reaction, because energy difference for inverse electron demand is lower than the standard one. This is caused by the oxygens donating into the double bond raising the HOMO and LUMO of the 1,3-dioxole. Due to the extra donation of electrons, the dienophile 1,3-dioxole, has increased the energy levels of its '''HOMO''' and '''LUMO'''.

=== Reaction energy analysis===

====calculation of reaction energies====

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 9. thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! exo-transition state!! endo-product!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.324374 || -267.068643 || -500.332150 || -500.329165 || -500.418692 || -500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (KJ/mol)
| -612593.1906 || -701188.77561 || -1313622.1599 || -1313614.3228 || -1313849.3759 || -1313845.7764
|}

The reaction barrier of a reaction is the energy difference between the transition state and the reactant. If the reaction barrier is smaller, the reaction goes faster, which also means it is kinetically favoured. And if the energy difference between the reactant and the final product is large, it means that this reaction is thermodynamically favoured.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 10. Reaction energy and activation energy for endo and exo DA reaction
!
! reaction energy (KJ/mol)
! activation energy (KJ/mol)
|-
! EXO
! -63.81
! 167.64
|-
! ENDO
! -67.41
! 159.81
|}

We can see, from the table above, that '''endo''' pathway is not only preferred thermodynamically but also preferred kinetically. The reasons why it is not only thermodynamic product but also a kinetic product will be discussed later.

====Steric clashes between bridging and terminal hydrogens====

The reason why the '''endo''' is thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive value indicates that the second diels-Alder reactions are not spontaneous reaction and are not favourable compared with the normal Diels-Alder reaction and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised. And this is also reflected by the activation energies of '''endo''' and '''exo''' '''side reaction''' pathways (the activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways).

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

===Calculation file list===

[[Media:DY815-CHELETROPIC-IRC.LOG]]

[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.