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Rep:CP2215TransitionStructureLab

2018-04-07T11:39:59Z

Fv611: /* Reaction of Butadiene with Ethylene */

= Transition States Lab - Calum Patel =

=== Introduction ===

'''Background'''

Pericyclic reactions are a cornerstone in organic chemistry and their outcomes are underpinned by both steric effects and stereoelectronic effects, as elucidated by Woodward and Hoffman in the late 1900's. '''<ref name="one"/>''' These effects are fundamental when predicting the transition state (TS) of which the pericyclic reaction traverses going from reactants to product. A potential energy surface (PES) represents the potential energy of a given system as a function of a changing degree of freedom in a molecule, as shown in Figure 1 where the reactants and products are represented as minima on the surface and the TS is found at the saddle point on the PES. '''<ref name="two"/>''' In the simple case, such as a trimolecular reaction, A + BC → AB + C, the degree of freedoms are subjectively chosen to simply be the distances between 'A' and 'B' and between 'B' and 'C'. However, complexity is encountered when many degrees of freedom are considered, such as in the case of pericyclic reactions.

[[File:CP2215_PES2.png|x300px|thumb|'''Figure 1.'''Example PES of the trimolecular reaction A + BC → AB + C, where V is potential energy. Image adapted from '''<ref name="two"/>''' ]]

In this work, TSs of four different pericyclic reactions will be located at two different levels of theory summarized as PM6 (parameterization method 6) and B3LYP/6-31G(d), which uses density functional theory (DFT) and an orbital basis set for the atoms known as 6-31G(d). A basis set is a set of functions, known as basis vectors (Gaussian functions) that typically mimic atomic orbitals, which can be combined linearly (linear combination of atomic orbitals, LCAO) to generate molecular orbitals (MOs), as illustrated in Equation 1. This LCAO can be represented in a matrix form and is used to solve the Hamiltonian, through evaluation of the Hamiltonian integrals contained in the Hamiltonian matrix, allowing for the determination of the total energy of the respective system and of all the MO's involved. The Hamiltonian matrix is diagonalised before evaluation using either of the two methods described above.

[[File:CP2215_LCAO.png|x300px|thumb|right|'''Equation 1.''' Equation for the energy of a molecular system, where N=N number of atoms, φn and φm = basis vectors, Ĥ = Hamiltonian operator and C = coefficients for each basis vector. This equation can be represented by a matrix (Hamiltonian matrix) to solve for the Hamiltonian integrals]]

[[File:CP2215_DFTequation.png|x200px|thumb|right|'''Equation 2.'''Underlying mathematics of DFT, where the first three components correspond to Coulomb attractive energy among nuclei and electrons, kinetic energy and Coulomb repulsive energy, respectively. The E<sub>xc</sub> is the exchange correlation energy (evaluated by Hartree-Fock in B3LYP calculation)]]

'''Computational Methods'''

PM6 is a semi-empirical method which uses empirical data to reduce the computational cost and processing power required to solve the Hamiltonian. Reducing the number of iterations when solving the Hamiltonian matrix is necessary for larger systems, some of which will be explored in this work. '''<ref name="three"/>''' One disadvantage of PM6 calculations is that are limited in accuracy as they solve the Hamiltonian using empirically fitted parameters found from experimental data. '''<ref name="four"/>''' The B3LYP method employs a hybrid function of Hartree-Fock (HF) and DFT. DFT is an electron density operator which solves for each Hamiltonian integral within the Hamiltonian matrix, evaluating a 6-31G(d) basis set. As a consequence a much longer processing time is required for B3LYP/6-31(d) calculations. DFT is exact in principle, but in practice it requires an approximation of electron exchange and correlation terms, formally known as an exchange-correlation term (''xc''). '''<ref name="five"/>''' The underlying mathematics of the DFT is shown in Equation 2. The ''xc'' term can be calculated using a local-density approximation (LDA) or generalized gradient approximation (GGA). In this work, PM6 and B3LYP/6-31G(d) calculations will be undertaken using GaussView 5.0.9. Due to having an extensive processing time, B3LYP will be used to optimise calculations that were produced using PM6, to gain results of greater accuracy. There are three different methods that may be employed in this work, using PM6 and/or B3LYP/6-31G(d) calculations and they are summarised below.

Method 1 - ''Draw a guess TS in GaussView and run a TS(Berny) calculation using a PM6 calculation followed by an optimisation at the B3LYP/6-31G(d) level.The TS structure must be known prior to the calculation.''

Method 2 - ''Draw a guess TS in GaussView and set the atoms involved in bond making at distances based on empirical data and freeze them in space. An optimisation is run at the PM6 level, the atoms are unfrozen and a TS(Berny) calculation is then run. By optimising the guess TS first GaussView is provided with a better guess structure (unlike in method 1) resulting in a more reliable TS structure after the final calculation.''

Method 3 - ''Similar to method 2, however, rather than a guess TS an optimized product (or reactant) is used as the starting point. This structure is optimized at the PM6 level, bonds between reactant fragments are broken and atoms are frozen in space (as carried out in method 2) to provide a guess TS. This guess TS is optimized at the PM6 level before a final TS(Berny) calculation is run to provide the final optimized TS. In this method we determine a correct guess structure before attempting to find the actual TS, which is overall more reliable than methods 1 or 2.''

The methods employed for each reaction studied in this work are summarized in Table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1. Computational methods followed for each reaction studied'''
! Reaction
! Method
! Reason
|-
| Reaction of Butadiene with Ethylene
| 2 (PM6 only)
|Good understanding of the TS
|-
| Reaction of Cyclohexadiene and 1,3-Dioxole
| 2 (PM6 and B3LYP/6-31G(d))
| Good understanding of the TS
|-
| Diels-Alder vs Cheletropic of O-Xylylene and SO<sub>2</sub>
| 3 (PM6 only)
| TS not as well defined compare to other two reactions, however, product predictions are more reliable
|-
| [1,1']bicyclohexyl-1,1'-diene Photochemical 4π Electrocyclisation
| 3 (PM6 only)
| TS not as well defined compare to other two reactions, however, product predictions are more reliable
|}

'''Exploring the Potential Energy Surface'''

[[File:CP2215_hessian.png|x150px|thumb|left|'''Figure 2.''' Hessian Matrix containing force constants, k (second derivatives) for 3N<sub>atoms</sub>-6 degrees of freedom]]

Energies obtained through employment of these methods will allow for the exploration of the PES of each molecular system studied in which there are 3N<sub>atoms</sub>-6 degrees of freedom. In this regard, the PES explored is for 3N atoms, where only the internal motions of the molecule result in a change in potential energy and not the external motions such as translations and rotations, hence the subtraction of 6. '''<ref name="four"/>''' . In particular, this work is primarily focused on locating stationary points on the surface (first derivatives or gradients) and then determining the curvature at these points to elucidate whether they are minima or saddle points , which is indicated by the second derivative at these points. This second derivative value is equated to the force constant, k, of the system at this point. The second derivative at each point (minima, saddle point etc.) on the PES is evaluated using a Hessian matrix and the force constants are obtained through diagonalisation of the Hessian matrix, as illustrated in figure 2, in addition to the contributions to each degree of freedom, i.e. normal modes. A minimum on the PES corresponds to reactants or products and is a point from which a small displacement in any direction increases the energy, thus the second derivative is positive. A saddle point corresponds to the TS as is located between two minima. Murrell and Laidler defined a TS as a stationary point with a single negative Hessian eigenvalue, which corresponds to a negative force constant and thus a single imaginary normal mode frequency. '''<ref name="two"/>'''

Reactions will explore the PES in search of the minimum energy pathway going from reactants to products. In doing so the system must traverse through the TS, the highest point of potential energy along the minimum energy pathway. In this lab, reaction pathways and more specifically minima and TS structures will be located through intrinsic reaction coordinate (IRC) calculations. Energy barriers and reaction energies will be calculated using the appropriate frames from the IRC. Structures from these frames will be optimised according to the methods described above to provide energies in Hartrees (unless otherwise quoted). Reactant structures will be drawn out separately and optimised accordingly to determine energy barriers, unless otherwise stated.

== Reaction of Butadiene with Ethylene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Great job - good work across this whole section.)
===Reaction Scheme===

[[File:CP2215_butadiene_rxn.png|x100px|thumb|center|'''Scheme 1.''' Cycloaddition between ethylene and butadiene]]

===MO diagram and Jmols===

[[File:CP2215 butadiene ethylene filled.png|x650px|thumb|'''Figure 4.''' Transition state MO diagram for the cycloaddition between ethylene and butadiene]]

{| class="wikitable"
|+ '''Table 2. FOs for butadiene and ethylene and MOs for the TS (S=symmetric, AS=anti symmetric)'''
! Ethylene MO's
! Butadiene MO's
! colspan="2"|Transition State Orbitals
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>HOMO (1a{S}), E = -0.39224</title>
<script>frame 1.10; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>HOMO (2a{AS}), E = -0.35900</title>
<script>frame 1.22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>(1 {AS}), E = -0.32755</title>
<script>frame 1.26; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_CYCLOHEXENE_OPTIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>(2 {S}), E = -0.32534</title>
<script>frame 1.26; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_CYCLOHEXENE_OPTIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>LUMO (1b{AS}), E = 0.04252</title>
<script>frame 1.10; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>LUMO (2b{S}), E = 0.01944</title>
<script>frame 1.22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>(3 {S}), E = 0.01731</title>
<script>frame 1.26; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_CYCLOHEXENE_OPTIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>(4 {AS}), E = 0.03067</title>
<script>frame 1.26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_CYCLOHEXENE_OPTIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Cycloaddition Transition State MOs'''

The 4 + 2 cycloaddition reaction between ethylene and butadiene (S-cis conformer) is shown in scheme 1. Reactant fragment orbitals (FO) and TS MO's can be described as being '''symmetric (S)''' or '''anti-symmetric (AS)'''. As shown in Table 2 and illustrated in figure 4, only orbitals of the same symmetry can combine, either constructively or destructively. Relative energies for each MO have been presented in Hartrees and correlate to the fully optimised (PM6 level), lowest energy structures.

The S HOMO '''(1a)''' of ethylene combines constructively and destructively with the S LUMO of butadiene '''(2b)''' to form the two S TS MO's; MO '''2''' (HOMO) by constructive interference and MO '''3''' (LUMO) by destructive interference. MO '''2''' is closer in energy to the HOMO of ethylene '''(1a)''', indicating that MO '''2''' for the TS has a greater contribution from the HOMO of ethylene. The opposite is true for the TS MO '''3''' which is closer in energy to the LUMO of butadiene '''(2b)''' and thus has a greater orbital contribution from this FO.

The AS HOMO '''(2a)''' of butadiene combines constructively and destructively with the AS LUMO of ethylene '''(1b)''' to form the two AS TS MO's; MO '''1''' (HOMO-1) by constructive interference and MO '''4''' (LUMO+1) by destructive interference. MO '''1''' is closer in energy to the HOMO of butadiene '''(2a)''', indicating that MO '''1''' for the TS has a greater contribution from the HOMO of butadiene. The contra is true for the TS MO '''4''' which is closer in energy to the LUMO of ethylene '''(1b)''' and thus exhibits a greater orbital contribution from this FO.

It is clear from the MO's generated (Table 2) that only orbitals that share the same symmetry can interact to form TS MO's. In this sense, a S-AS interaction will results in zero orbital overlap whilst S-S or AS-AS interactions will result in a non-zero orbital overall, as long as the energies of the respective FOs are close enough in energy to interact.

We would expect the MOs generated for the final product to ultimately lower the energy of the whole system. Here only the energies of the TS structures are shown.

'''Bond Lengths and TS Vibration'''

{| class="wikitable" border="1" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3. C-C Bond Lengths of butadiene, ethylene, TS and cyclohexadiene product
! Structure!!C-C Length (Å) !! Butadiene !! Ethylene !! TS !! Cyclohexene
|-
|rowspan="6"|[[File:CP2215 structure.png|thumb]]
| C1-C2 || 1.333 || - || 1.380 || 1.501
|-
| C2-C3 || 1.471 || - || 1.411 || 1.337
|-
| C3-C4 || 1.333 || - || 1.380 || 1.501
|-
| C4-C5 || - || - || 2.115 || 1.537
|-
| C5-C6 || - || 1.328 || 1.382 || 1.535
|-
| C1-C6 || - || - || 2.115 || 1.537
|}

From Table 3 it can be seen that as the reaction proceeds from reactants to products, the C5-C6 bond (ethylene) increases from 1.328 Å to 1.382 Å, corresponding to a change in hybridisation at these carbons from sp<sup>2</sup> to sp<sup>3</sup> and thus a change in bond order. This is also the case for C1-C2 and C3-C4 (sp<sup>2</sup>- sp<sup>2</sup> double bonds in butadiene). As expected the bond length of 1.471 Å for C2-C3 is shorter then a typical single C-C bond length (1.54 Å) ,'''<ref name="six"/>''' this is due to C2 and C3 being both sp<sup>2</sup> hybridised and not both sp<sup>3</sup> hybridised. This C2-C3 bond length shortens as the reaction proceeds, decreasing from 1.471 Å to 1.411 Å in the TS and then further to 1.337 Å in the product. This value lies in parallel to a typical C=C bond length (1.33 Å) , '''<ref name="six"/>''' which is expected as the C2-C3 bond changes from a C-C single bond to a C=C double bond (with both carbons remaining sp<sup>2</sup> hybridised.

In the reaction two new bond are formed between C1-C6 and C4-C5, in the TS these distances are equal at 2.115 Å, which lies as an intermediate value between a single C-C bond length and twice the Van der Waals radius of the C atom (1.7 Å). '''<ref name="seven"/>''' These observations fit with theory, where the TS is an intermediate structure between the two reactants when bond breaking/forming occurs. From observing the IRC for this reaction, figure 5, it can be seen that the TS is closer in energy to the reactants than products indicating an early stage TS. '''<ref name="eight"/>''' The bonds formed are both sp<sup>3</sup> hybridised C-C single bonds of 1.537 Å, which lies in excellent agreement with literature (1.54 Å for C-C single bond).
In the TS both distances (C1-C6 and C4-C5) are equal which indicates synchronous bond formation. This is further supported by the reaction path vibration in the TS (negative vibration), as shown in Figure 6 where the termini of each reactant move towards each other simultaneously.

[[File:CP2215 butadiene irc.png|x250px|thumb|right|'''Figure 5.'''IRC for the cycloaddition between ethylene and butadiene, showing early stage TS]]

<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>Figure 6. Negative Vibration of TS</title>
<script>frame 1.27;vibration on; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>CP2215_CYCLOHEXENE_OPTIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=== LOG Files ===

[[Media:CP2215 BUTADIENE.LOG|Log file PM6 Optimisation Butadiene]]

[[Media:CP2215 ETHENE.LOG|Log file PM6 Optimisation Ethylene]]

[[Media:CP2215_CYCLOHEXENE_OPTIMISEDTS.LOG|Log file PM6 Optimisation TS]]

[[Media:CP2215_CYCLOADDITIONPRODUCT.LOG|Log file PM6 Optimisation Cyclohexene]]

== Reaction of Cyclohexadiene and 1,3-Dioxole ==

===Reaction Scheme and MO diagrams===

[[File:CP2215_cyclohexadiene_rxn.png|x250px|thumb|center|'''Scheme 2.''' Cycloaddition between Cyclohexadiene and 1,3-Dioxole]]

The 4 + 2 cycloaddition reaction between cyclohexadiene and 1,3-dioxole can take one of two pathways through an ENDO or EXO TS, as shown in scheme 2, giving rise to two stereoisomer products. MO's for each reaction pathway are shown in figure 7. Note that the energies provided for the reactant molecules in figure 7 have been determined through individual optimizations of each starting reactant at the B3LYP/6-31G(d) level.TS MO's for both ENDO/EXO pathways have been provided in Table 4 (corresponding MO's can be seen in figure 7). Again, the aforementioned symmetry rules have been obeyed (S-S or AS-AS = non zero overlap and AS-S = zero overlap). The energy splitting between the HOMO-LUMO TS MOs for each the ENDO and EXO case is 0.1859 Hartrees and 0.1787 Hartrees, respectively. The energy splitting between the HOMO-1 - LUMO+1 TS MOs for each the ENDO and EXO case is 0.2219 Hartrees and 0.2082 Hartrees, respectively . Interestingly, the ENDO HOMO (S) TS MOs is lower in energy than the equivalent EXO TS MO. There is marginal difference between the energies of the HOMO-1 TS MOs of each ENDO and EXO pathway. These results imply that the ENDO TS is the lower energy structure. This will be confirmed through compuational thermochemical analysis (see below).

[[File:CP2215_dioxoleMOdiagram.png|x700px|thumb|center|'''Figure 7.''' MO's involved in the cycloaddition between Cyclohexadiene and 1,3-Dioxole via either an ENDO or EXO TS]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 4. FOs for cyclohexadiene and 1,3-dioxole MOs for the TS (S=symmetric, AS=anti symmetric)'''
! colspan="2"|ENDO Transition State Orbitals
! colspan="2"|EXO Transition State Orbitals
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title> ENDO TS HOMO-1 (AS), E = -0.1965</title>
<script>frame 1.32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>GUNNY ENDO B3LYP TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>ENDO TS HOMO (S), E = -0.1905</title>
<script>frame 1.32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>GUNNY ENDO B3LYP TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>EXO TS HOMO-1(AS), E = -0.1980</title>
<script>frame 1.20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>GUNNY EXO B3LYP TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>EXO TS HOMO(S), E = -0.1856</title>
<script>frame 1.20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>GUNNY EXO B3LYP TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>ENDO LUMO (S), E = -0.0046</title>
<script>frame 1.32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>GUNNY ENDO B3LYP TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>ENDO LUMO+1 (AS), E = 0.0154</title>
<script>frame 1.32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>GUNNY ENDO B3LYP TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>EXO TS LUMO (S), E = -0.0069</title>
<script>frame 1.20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>GUNNY EXO B3LYP TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title>EXO TS LUMO+1 (AS), E = 0.0102</title>
<script>frame 1.20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; MO cutoff 0.01</script>
<uploadedFileContents>GUNNY EXO B3LYP TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Inverse Or Normal Electron Demand===

Single point energy calculations have been carried out at the B3LYP/6-31G(d) level on the reactant molecules in the same frame (from the relevant IRC calculation) level to qualitatively determine the electron demand of the cycloaddition reaction. The energies of the interacting reactant MO’s differ marginally between the ENDO and EXO case; -0.1860 (ENDO) and -0.1914 (EXO) Hartrees for the filled interacting orbital and -0.0174 (ENDO) and -0.0165 (EXO) Hartrees for the unfilled interacting orbital. These energies correspond to the filled interacting orbital being the HOMO of the dienophile (1,3-Dioxole) and the unfilled interacting orbital being the LUMO of the diene (Cyclohexadiene), these MOs are shown in Table 5. Interestingly, these energies differ slightly from those determined through optimisations of the individual starting reactants (figure 7).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 5. HOMO of 1,3-dioxole and LUMO of cyclohexadiene (reactants in ENDO orientation)'''
!HOMO of 1,3-dioxole
!LUMO of cyclohexadiene
|-
|<jmol>
<jmolApplet>
<color>Black</color>
<size>250</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>CP2215 ENDO REACTANTS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>Black</color>
<size>250</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>CP2215 ENDO REACTANTS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Normal electron demand Diels Alder (4 + 2 cycloaddition) reactions are described by the dienophile being electron deficient and diene being electron rich, thus the LUMO of the dienophile interacts with the HOMO of the diene. The opposite case is true for inverse electron demand alternative. '''<ref name="six"/>'''

In this reaction the HOMO of the dienophile and LUMO of the diene are closest in energy and thus the interaction is stronger than that between the LUMO of the dieneophile and the HOMO of the diene, strongly indicating that this reaction is governed by inverse-electron demand. This result is expected as electron donating group (EDG) on the dienophile (two oxygen lone pairs) typically raise the energy of the HOMO, resulting in a better energy overlap with the diene LUMO.

===Thermochemistry (Endo and Exo Products)===

Thermochemistry data has been calculated at the B3LYP level (Table 6) to allow for the determination of the activation barriers and Gibbs Free energies associated with each reaction pathway. The activation barrier (activation energy) is the minumum amount of energy required for reactants to reach the TS before going to products via the minimum energy pathway. It can be seen from Table 6 that the activation barrier for the ENDO pathway to the ENDO TS is of lower energy and is thus more kinetically favourable. The ENDO product is the kinetic product due to an energetically favorable secondary orbital overlap between the oxygen lone pair p orbitals of the dioxole and the pi system of the cyclohexadiene. This overlap is only achieved through the ENDO TS and is shown in Figure 9.

The reaction energy (Gibbs Free energy) is the energy difference between reactants and products, a more negative reaction energy is indicative of a more stable product in relation to the reactant. In this reaction the ENDO product has a lower reaction energy and is thus more thermodynamically favourable, as highlighted in Table 6. This also indicates that the formation of the ENDO product is more exothermic compare to the EXO product, which is a result of the EXO product containing an unfavourable steric clash between the bridge head hydrogens and dioxole. As a consequence the ENDO product is lower in energy than the EXO product by ~ 3.59 KJ/mol<sup>-1</sup>

[[File:CP2215_ENDOTS_OXYGEN.png|x250px|thumb|left|'''Figure 9.''' Favourable secondary orbital overlap in ENDO TS (Cyclohexadiene and 1,3-Dioxole)]]

{| class="wikitable" border="1" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6. Thermochemical data (B3LYP level) for EXO and ENDO reaction pathways for cycloaddition of 1,3-dioxole and cyclohexadiene
! Product !! Energy Barrier (KJ/mol<sup>-1</sup>) !! Reaction Energy (KJ/mol<sup>-1</sup>)
|-
| EXO || 167.67 || -63.75
|-
| ENDO || 159.84 || -67.39
|}

From the data calculated (Table 4) we can thus say that the ENDO product is both the kinetic and thermodynamic product of the reaction, due to both electronic effects and steric effects.

=== LOG Files ===

[[Media:CP2215 B3LYP CYCLOHEXADIENE.LOG|Log file B3LYP Optimisation cyclohexadiene]]

[[Media:CP2215 B3LYP DIOXOLE.LOG|Log file B3LYP Optimisation 1,3-dioxole]]

[[Media:GUNNY EXO B3LYP.LOG|Log file B3LYP Optimisation EXO TS]]

[[Media:GUNNY ENDO B3LYP.LOG|Log file B3LYP Optimisation ENDO TS]]

[[Media:CP2215 EXO B3LYP PRODUCT.LOG|Log file B3LYP Optimisation EXO product]]

[[Media:CP2215 ENDO B3LYP PRODUCT.LOG|Log file B3LYP Optimisation ENDO product]]

[[Media:CP2215 EXOREACTANTS B3LYP ENERGY.LOG|Single point energy calculation reactants in EXO orientation (from IRC frame)]]

[[Media:CP2215 ENDOREACTANTS B3LYP ENERGY.LOG|Single point energy calculation reactants in ENDO orientation (from IRC frame)]]

== Reaction of O-Xylylene and SO<sub>2</sub> ==

===Reaction Scheme===

[[File:CP2215_SO2_rxn.png|x250px|thumb|center|'''Scheme 3.''' Reaction scheme for the Diels-Alder and Cheletropic reactions pathways (O-Xylylene and SO<sub>2</sup>)]]

===IRC Calculations===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:CP2215 ENDOIRC.gif|x100px|thumb|'''Figure 10.''' Endo Diels-Alder reaction pathway of O-xylylene and SO<sub>2</sub>|300x300px]]
|[[File:CP2215 EXOIRC.gif|x100px|thumb|'''Figure 11.''' Exo Diels-Alder reaction pathway of O-xylylene and SO<sub>2</sub>|400x400px]]
|[[File:CP2215 CHELETROPICIRC.gif|x100px|thumb|'''Figure 12.''' Cheletropic reaction pathway of O-xylylene and SO<sub>2</sub>|600x600px]]
|}

The possible reactions of the external diene of O-xylene and SO<sub>2</sub> are shown in scheme 3. These reactions were explored at the PM6 level. IRC's for each of these reactions are shown in figures 10 to 12. Figures 10 and 11 show that bond formation is asynchronous when the EXO or ENDO Diels Alder pathways are followed (i.e C-O and C-S bonds do not form simultaneously). In the EXO/ENDO pathways bond formation occurs between the carbon and the oxygen first before bond formation between the carbon and sulfur. Figure 12 indicates that the cheletropic pathway proceeds with synchronous bond formation between the carbon and sulfur atom, where C-S bonds form simultaneously. In this reaction the o-xylylene is particularly reactive due to gaining aromaticity in the product, which drives the forward reaction. Alternatively, due to the high instability of o-xylene it typically undergoes an electrocyclic reaction to gain aromaticity, hindering its reactivity towards dienophiles.

===Thermochemistry===

It can be seen from both Table 7 and figure 13, that the lowest energy barrier is associated with the ENDO reaction pathway and the most negative reaction energy is associated with the CHELETROPIC reaction pathway. These results indicate that the ENDO product is the kinetic product and the CHELETROPIC product is the thermodynamic product.

[[File:CP2215_SO2_energydiagram.png|x750px|thumb|right|'''Figure 13.'''Reaction energies and energy barriers for the Diels-Alder and Cheletropic reactions pathways (O-Xylylene and SO<sub>2</sup>)]]

{| class="wikitable" border="1"
|+ Table 7. Thermochemical data (PM6 level) for reaction pathways of o-xylene with SO<sub>2</sub>
! Product !! Energy Barrier (KJ/mol<sup>-1</sup>) !! Reaction Energy (KJ/mol<sup>-1</sup>)
|-
| EXO || 87.44 || -97.98
|-
| ENDO || 83.46 || -97.34
|-
| CHELETROPIC || 105.78 || -154.31
|}

Again, due to energetically favourable secondary orbital overlap the ENDO TS is favoured resulting the the ENDO pathway having the lowest energy barrier. In this reaction the secondary orbital overlap can only be achieved in the ENDO TS as the non-bonding oxygen of the SO<sub>2</sub> is in the correct orientation for its lone pair p orbital to interact with the pi system of the external diene of o-xylylene, as shown in figure 14.

[[File:CP2215_SO2_ENDOsecondary.png|x300px|thumb|left|'''Figure 14.'''Favourable secondary orbital overlap between SO<sub>2</sub> non-bonding oxygen and pi system of o-xylylene ( ENDO HOMO-1 TS MO O-Xylylene and SO<sub>2</sup>)]]

[[File:CP2215_SO2_sterics.png|x300px|thumb|left|'''Figure 15.'''Steric repulsion between the pseudo axial SO<sub>2</sub> S=O and nearby axial hydrogen in the newly formed ring ( ENDO O-Xylylene and SO<sub>2</sup> product)]]

The CHELETROPIC TS has the highest energy barrier owing to the sterically strained 5-membered ring formed during the TS (unlike the 6-membered rings formed in the ENDO or EXO TS which are less strained and lower energy), this can be visualized in in figure 12.

It can be clearly seen from figure 13 that the CHELETROPIC pathway is the most exothermic reaction leading to the most stable product, i.e. the thermodynamic product. This can be understood by analyzing the bond enthalpies of the bonds broken and bonds formed in the respective reactions. In the ENDO/EXO reactions one S=O bond must be broken whilst C-S, S-O and C-O bonds must form (in addition to the bond rearrangements leading to the aromaticity gain in the product). In the CHELETROPIC case two C-S bonds must form and the two S=O bonds are maintained (in addition to the bond rearrangements leading to the aromaticity gain in the product). In light of this, the bond energies involved in forming two C-S bonds and maintaining two S=O bonds (CHELETROPIC) exceeds the bond energies involved in breaking one S=O bond and forming the C-S,S-O and C-O bonds (ENDO/EXO).'''<ref name="nine"/>''' With regards to the ENDO and EXO products, the energy difference is marginal, however, the EXO product is slightly more stable. This can be explained by steric effects, as shown in figure 15, where an axial repulsion between the pseudo axial S=O and adjacent axial hydrogen in the formed ring system of the ENDO product is energetically unfavourable. This repulsion is not present in the ENDO product where the S=O sits pseudo equatorial.

===Alternative Diels Alder With Internal Diene===

There is an internal diene in o-xylene which does not undergo Diels-Alder reactions with SO<sub>2</sub>. The reason for this was evaluated at the PM6 level using Gaussian, thermochemical data is given below in Table 8.

{| class="wikitable" border="1"
|+ Table 6. Thermochemical data (PM6 level) for alternative EXO/ENDO pathways of o-xylene with SO<sub>2</sub>
! Product !! Energy Barrier (KJ/mol<sup>-1</sup>) !! Reaction Energy (KJ/mol<sup>-1</sup>)
|-
| EXO || 121.51 || 22.40
|-
| ENDO || 113.68 || 17.96

|}

From Table 8 it can be clearly seen that the energy barriers for these alternative ENDO/EXO pathways exceed those of the aforementioned external diene ENDO/EXO and CHELETROPIC pathways. It should be noted that reaching the ENDO TS with the internal diene requires lower energy, again explained by stabilization brought about secondary orbital overlap between the non-bonding SO<sub>2</sub> oxygen lone pair p orbital and the pi system of the internal diene of o-xylylene (akin to that in figure 14). In the alternative Diels-Alder reactions no aromaticity is gained (in addition to diene conjugation being lost) and so the products obtained are less stable than the products from the previously discussed pathways where aromatically is gained in all three cases. Thus, the reaction energies are positive indicating that both of these alternative ENDO/EXO pathways are endothermic reaction pathways. IRC's of each of the alternative ENDO/EXO Diels Alder pathways are given in figures 16-17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:CP2215 SO2 altendoirc.gif|x100px|thumb|'''Figure 16.''' Alternative Endo Diels-Alder reaction pathway of O-xylylene and SO<sub>2</sub>|300x300px]]
|[[File:CP2215 SO2 altexo IRC.gif|x100px|thumb|'''Figure 17.''' Alternativ Exo Diels-Alder reaction pathway of O-xylylene and SO<sub>2</sub>|400x400px]]
|}

=== LOG Files ===

[[Media:CP2215 SO2.LOG|Log file PM6 Optimisation SO2]]

[[Media:CP2215 XYLYLENE.LOG|Log file PM6 Optimisation O-Xylyene]]

[[Media:CP2215_SO2_EXO_OPTIMISEDTS.LOG|Log file PM6 Optimisation EXO TS]]

[[Media:CP2215_SO2_ENDO_OPTIMISEDTS.LOG|Log file PM6 Optimisation ENDO TS]]

[[Media:CP2215_SO2_CHELETROPIC_OPTIMISEDTS.LOG|Log file PM6 Optimisation CHELETROPIC TS]]

[[Media:CP2215_SO2_EXO_PRODUCT.LOG|Log file PM6 Optimisation EXO product]]

[[Media:CP2215_SO2_ENDO_PRODUCT.LOG|Log file PM6 Optimisation ENDO product]]

[[Media:CP2215_SO2_CHELETROPIC_PRODUCT.LOG|Log file PM6 Optimisation CHELETROPIC product]]

[[Media:CP2215_SO2_ALTEXO_OPTIMISEDTS.LOG|Log file PM6 Optimisation Alt. EXO TS]]

[[Media:CP2215_SO2_ALTENDO_OPTIMISEDTS_gfprint.LOG|Log file PM6 Optimisation Alt. ENDO TS]]

[[Media:CP2215_SO2_ALTEXO_OPTIMISEDPRODUCT.LOG|Log file PM6 Optimisation Alt. EXO product]]

[[Media:CP2215_SO2_ALTENDO_OPTIMISEDPRODUCT1.LOG|Log file PM6 Optimisation Alt. ENDO product]]

== [1,1']bicyclohexyl-1,1'-diene Photochemical 4π Electrocyclisation ==

===Reaction Scheme===

[[File:CP2215_extension_rxn.png|x250px|thumb|center|'''Scheme 4.''' Reaction scheme for the 4n electrocyclic reaction of [1,1']bicyclohexyl-1,1'-diene with corresponding optimised structures (PM6) note that the reactant does not have a plane of symmetry]]

===Möbius–Hückel Treatment===

Under photochemical conditions, a 4pi reaction is predicted to proceed via a Hückel aromatic transition state with suprafacial bond formation and a (presumed) plane of symmetry. The electrocyclic reaction of [1,1']bicyclohexyl-1,1'-diene was analysed computationally using Gaussian at the PM6 level (ground state).

The TS HOMO for a photochemical butadiene electrocylic closing is governed by a Hückel topology for 4n electrons and Möbius topology for 4n+2 electrons. In this reaction there are 4n pi electrons. The TS for the reaction is shown below in figure 18 and indicates that the reaction proceeds via a Möbius topology, as indicated by the slight twist in the termini orbitals where the new C-C bond forms, suggesting that the product is formed under thermal conditions.

(All these calculations are occurring on the ground state. Visualisation of the IRC or transition vector from a frequency calculation would confirm that 4pi electrocyclic reactions occur with disrotation [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:56, 4 April 2018 (BST))

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Figure 18. HOMO of TS (Möbius topology) for [1,1']bicyclohexyl-1,1'-diene electrocyclisation
!Figure 19. Negative vibration of the TS for the [1,1']bicyclohexyl-1,1'-diene electrocyclisation, bonds move in a controtatory fashion
|-
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The negative vibration for the TS, figure 19, suggests that the reaction proceeds in a conrotatory manner and is thus antarafacial. Interestingly, the stereochemical outcome has the two hydrogens with the same stereochemistry (both axial) which opposes what is expected with typical conrotatory motion, illustrated in figure 20. In other words suprafacial specificity is observed. This is most likely due to the orientations of the hydrogens, where they do not point towards eachother in the S-Cis conformer of [1,1']bicyclohexyl-1,1'-diene (see scheme 4). It would be energetically unfavorable for the hydrogens to point towards eachother in the S-Cis conformer, this is reinforced by the lack of symmetry in the starting reactant. The IRC for this reaction supports this further and can be visualised in figure 21. Note that in the TS the plane of symmetry is not conserved.

[[File:CP2215_conrot.png|x250px|thumb|'''Figure 20.''' Antarafacial overlap for a butadiene type ring closing]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:CP2215 photocyclic IRC.gif|thumb|'''Figure 21. 4n Electrocyclic reaction of [1,1']bicyclohexyl-1,1'-diene'''|300x300px]]
|}

=== LOG Files ===

[[Media:CP2215 PHOTOCYCLIC SM.LOG|Log file PM6 Optimisation [1,1']bicyclohexyl-1,1'-diene]]

[[Media:CP2215 PHOTOCYCLIC OPTIMISEDPRODUCT.LOG|Log file PM6 Optimisation electrocylisation product]]

[[Media:CP2215 PHOTOCYCLIC OPTIMISEDTS.LOG|Log file PM6 Optimisation TS]]

== Conclusion ==

In this work, four pericyclic reactions (cycloadditions and an electrocylisation) have been explored computationally at the PM6 and B3LYP/6-31G(d) level using GaussView to calculate geometries of the TS and products. Using the methods employed, reaction energetic's have also been probed to provide predictions for the outcome of each reaction and alternative reaction pathways. Calculations at the PM6 level have afforded sufficient structures within a short time frame owing to reduced computational cost associated with these calculations. PM6 has been successfully employed to determine how bond lengths (C-C and C=C) change in a butadiene-ethylene cycloaddition and the obtained results lie in parallel to literature. Optimisations at the B3LYP level allowed for the calculation of TSs with enhanced accuracy, specifically allowing for the quantitative determination of the electron demand of a cyclohexadiene and 1,3-dioxole cycloaddition reaction, in addition to the activation energy and reaction energy of the respective EXO and ENDO pathways. Methodology which involved drawing out products, guessing TSs and optimizing TSs (methdod 3) has worked particularly well on the cycloaddition of o-xylyene and SO2, affording reaction energies and energy barriers which match with theory regarding steric effects and electronic effects. In particular, the electronic effects of stabilizing secondary orbital interactions have been visualised through PM6 optimisations of the TS of the-oxylylene - SO2 cycloaddition on GaussView. An extension reaction involving the electrocylisation of [1,1']bicyclohexyl-1,1'-diene (4n pi system) has been explored at the PM6 level. Calculations have allowed for the exploration on the Möbius and Hückel topology of the TS, results indicate that the reaction can proceed via a Möbius TS (HOMO) in an antarafacial fashion.

This work demonstrates a simple approach in using time effective computations to predict outcomes of reactions prior to experiment, illustrating the sheer power of computational chemistry in organic chemistry.

== References ==

<references>

<ref name="one">
H.S Rzepa, J. Chem. Educ., 2007, 84 (9), p 1535
</ref>

<ref name="two">
D.J. Wales, Energy Landscapes: Applications to Clusters, Biomolecules and Glasses, CUP, Cambridge, 2003
</ref>

<ref name="three">
T. H. Dunning Jr, J. Chem. Phys., 1970, 53, 2823-2833.
</ref>

<ref name="four">
J.J.W. McDouall, Computational quantum chemistry : molecular structure and properties in silico, 2013
</ref>

<ref name="five">
B. Santra, Dissertation, Technische Universität Berlin, 2010
</ref>

<ref name="six">
J. Clayden,N. Greeves,S. Warren and P. Wothers, Organic Chemistry , 2001
</ref>

<ref name="seven">
A. Bondi., 1964. van der Waals volumes and radii. The Journal of physical chemistry, 68(3), pp.441-451
</ref>

<ref name="eight">
P.W Atkins & J. De Paula, Atkins' physical chemistry 9th ed., Oxford: Oxford University Press, 2009
</ref>

<ref name="nine">
Y.R Luo, Comprehensive handbook of chemical bond energies. CRC press, 2009
</ref>

Rep:Mod:jd2615TS

2018-04-07T11:27:01Z

Fv611: /* MO diagrams */

=Computational methods to determining transition states=
==Introduction==
The potential energy surface (PES) is useful representation of the many different energy states a particular species can exist in. It provides a mathematical relationship between's a molecules energy and it's structure. <ref name = lewars> E.G. Lewars, ''Computational Chemistry'', Springer, 2nd edn, 2011, ch 2, pg 9 </ref>. It can be extremely useful for computational chemists as it provides mathematical meaning for a molecules structure, while also providing a 'framework' for programmers to design a code which can accurately determine the energy of a species. <ref name =lewars />. With peaks being transition species and troughs being intermediates or products, the mathematical landscape of a three-dimensional PES provides a visual justification for the products formed in the synthesis lab and will hopefully shed light on the different species encountered in the experiment.

The Diels-Alder reaction has been a prominent synthetic tool for chemists for many years. The understanding of the nature of the diene and the dienophile has been the source of interest for both synthetic and computational chemists, providing more opportunity for electrocyclic chemistry and better correlation between synthetic results and molecular interactions. This experiment investigates the interaction between different dienes and dienophiles, focussing primarily on the orbital formations of the transition state by the use of computational techniques. Through the variety of reactants, this experiment hopes to shed light on the precise mechanistic dynamic by providing energies, bond distances and orbital conformations. Work by Domingo <ref name=domingo>Luis. R Domingo, ''The mechanism of ionic Diels–Alder reactions. A DFT study of the oxa-Povarov'', RSC Adv, 2014, 4 </ref> showed that the DFT methods at the B3LYP/6-31G level could be used to determine a reaction model for an ionic Diels-Alder reaction by the investigation of the oxa-Povarov reaction which is initialized by the ionic Diels-Alder of a cationic aryl oxonium and an alkene.<ref name=domingo/> They determined, through the analysis of the IRC, that the substituents on the alkene (i.e. the phenyl ring on phenyl ethylene) forced a two-step mechanism, as opposed to the usual concerted one step approach.<ref name=domingo/> Further work by Black <ref name=black> K. Black, ''Dynamics, transition states, and timing of bond formation in Diels–Alder reactions'', PNAS, 2012, 12860-12865 </ref> (computed by UB3LYP/6-31(G)) into the dynamics of bond formation of the Diels-Alder reaction observed that regardless of the symmetry of the reactants, the trajectories of bond formation are unequal in the transition state, but they concluded that at room temperature, due to shorter time gap of the formation of two new bonds compared to the C-C bond vibrational period, the Diels-Alder are concerted and stereospecific.<ref name=black />

==Computation Techniques==
In computational chemistry, there will be range of understanding of the structure a chemist is trying to identify. Different degrees of understanding require different techniques depending on whether an individual knows what their seeking. There are three methods for locating transition states with Gaussian:

Method 1: This method requires a good understanding of the transition state of a particular reaction. Here the chemist forms the starting materials in an arrangement which resembles the transition state of the reaction, the structure is optimized to a transition state that hopefully resembles natural state. The chemist must have a good understanding of bond angles and distances in order to accurately recreate the structure they are looking for.

Method 2: This method is more advanced than method one and still requires a knowledge of the transition state, but it is the fastest reliable method. Here the chemist draws the transition state from starting material according to their understanding of the structure. Then the bonds are frozen between the starting materials using Redundant Coordinate Editor. The structure is then optimised to a minimum with the frozen bonds so that the functional groups of the reacting molecules arrive at the most stable position. The minimised structure is then unfrozen and allowed to be minimised to a transition state that should resemble the natural state.

Method 3: This method requires more steps than method 1 or 2, but requires little knowledge of the transition state. Here the product is drawn and optimized to a minimum. The minimized product is then separated into the reacting fragments by breaking the bonds between them (i.e. separating the product into the two reactants). The reactant fragments are then separated slightly and frozen using redundant coordinates. The frozen structure is then optimized to a minimum, which is then optimized to a transition state.

The Hartree-Fock method is a set of equations which provide the best one-electron wave functions approximations to the problem of an electron in the motion of a field of atomic nuclei.<ref name=Slater> J. C. Slater, ''A simplification of the Hartree-Fock Method'', Physical Review, 1950, 81, 3, 385-386 </ref> The description of the relationship of an electron within the potential of the nuclei can provide an approximation for a structure of a molecular state. b3lyp calculations calculate electron distributions with the use of Density Functional Theory (DFT) which is when the electrons are described in accordance to their density and not individual wave functions, its a progression on from the Hartree-Fock method. The energy of a system can be separated into six components:

<math> E_{DFT} = E_{NN} + E_{T} + E_V + E_{coul} + E_{exch} + E_{corr} </math><ref name = Filatov> Michael Filatov, '' Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model'', J. Them. Theory Comput., 2013, 9, 3197-3932 </ref>

Where NN is nuclear-nuclear repulsion, v is attraction, coul is electron-electron Coulombic repulsion, T is kinetic energy of electrons, exch is the electron-electron exchange energy and corr describes the correlated movement of electrons of different spin. <ref name = Filatov />.

The The majority of these experiments will use the semi-empirical quantum chemistry method with are based on Hartree-Fock or DFT theory but also through application of approximate assumptions thus obtaining empirical data. <ref name = jan> Jan Řezáč, ''Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes'', J. Chem. Theory Comput., 2009, 5 , 1749–1760 </ref>. When molecules are very large, the use of semi-empirical over full Hartree-Fock as the whole calculation is less expensive. <ref name=jan />. One exercise in this experiment makes of b3lyp which

==Exercise 1==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Excellent work across the whole exercise. Great job!)

===Computational Method===
The starting materials were optimized to a minimum using semi-empirical PM6. The product was also optimized using this technique. Once the product was optimized, the bonds between the alkene and the diene were removed, moved slightly apart but still within the Van der Waals radius, and frozen using redundant coordinates. This structure was optimized to a miniumum using semi-empirical PM6 to minimise a transition state-like structure. The minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using semi-empirical PM6.

===Reaction Scheme===

This experiment saw the Diels-Alder simulation between butadiene and ethylene to give cyclohexene:

{|style="margin: 0 auto;"
| [[File:SchemeT1.jpg|400px|thumb|left| Reaction Scheme of the reaction of ethylene and butadiene]]
|}

The Diels-Alder reaction sees a [4+2] cycloaddition of a conjugated diene and an alkene dieneophile via the interaction of 4 pi electrons from the diene and 2 pi electrons from the alkene, where the driving force is provided by the more stable sigma bond formed between the reactants, when compared to the weaker pi bonds.

===MO diagram===

{|style="margin: 0 auto;"
| [[File:MO_diagram_T1_jd2615_1.jpg|400px|thumb|left| MO diagram for the reaction of ethylene and butadiene - All energy values are in Hartrees]]
|}

The transition state is given by the linear combination of the fragment HOMO-LUMO orbitals of both the butadiene and the ethylene. The orbitals are combined according to symmetry, where the symmetry is labelled with a small s (symmetric) or a (asymmetric) next to the energy level of the orbital being described. Only orbitals of the same symmetry can combine. The differing degrees of contribution are represented by the size of the orbitals within the formed MOs, where larger contributions due to the similar relative energy of the source fragment is shown as a larger orbital. For example, the HOMO -1 orbital has a larger orbital contribution from the HOMO of the butadiene (as this is closer in energy), thus is shown as larger orbitals. From the law of conservation of orbital number, 4 molecular orbitals are formed from 2 fragment orbitals from each reactant. The orbitals calculated using gaussview are represented by the jmol images below. The HOMO -1 (i.e. lowest energy) is formed from the two asymmetric fragments of the frontier orbitals. When comparing the calculated HOMO MOs, there is greater bonding character for the HOMO-1 relative to the HOMO, resulting in a more stable electronic distribution. The same reason applies to the LUMOs, where the LUMO +1 sees the greatest antibonding character thus being highest in energy.

===Jmol of orbitals===

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{|style="margin: 0 auto;"
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Analysis of direct linear combination of orbitals of different symmetry shows that the orbital overlap integral is zero:
{|style="margin: 0 auto;"
| [[File:Symmetry T1 jd2615.png|400px|thumb|left| Linear combination of symmetrical and asymmetrical frontier orbitals to form two MO's with an overlap integral of zero]]
|}
Both orbital MOs formed in the above diagram would have zero overlap integral as one p orbital from the alkene forms a bonding interaction whereas the other is anti-bonding. If this system saw a break of symmetry, then the integral will become non-zero and bonding interactions will occur.

===Bond Distances===
{|style="margin: 0 auto;"
| [[File:Bond_length_T1_jd2615.jpg|600px|thumb|left| Figure to show the bond length of each species involved in the Diels-Alder reaction between ethylene and butadiene]]
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<size>300</size>
<script>frame 73; vibration 1;rotate x -20; </script>
<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|}

The above figure shows the bond lengths of the various bonds of the reactants, transition state (TS) and products respectively. Firstly, the ethylene reactant sees a standard sp2 double bond length of 1.32755Å (C5-C6). Mechanistically, the pi electrons of the ethylene form one of the sigma bonds to the butadiene during the concerted electrocyclic process, thus forming an sp3 single bond in the product (C5-C6 = 1.54070Å) (the other sigma bond to the ethylene is formed from pi electrons on the butadiene). The bond lengths confirm this observation as the transitions state sees a single-double intermediate bond length of 1.38176Å. The same process occurs for the C3-C4 and C1-C2 which change from double to single bond with an intermediate bond length (C1-C2 (reactants) = 1.47079Å, C1-C2 (transition state) = 1.37977Å, C1-C2 (products) = 1.33761Å). The opposite process occurs for the C2-C3 where it is originally a single bond in butadiene (C2-C3 = 1.47079Å), which is slightly shorter than a normal sp3 single bond, which is a result of the conjugation between the alkenes resulting in a small degree of double bond character. The bond length shortens as it becomes a double to 1.41111Å in the transition state and 1.33761Å in the product. The C1-C6/C4-C5 bond length in the transition state is 2.11473Å. The Van der Waals radius of carbon is around 1.5Å, thus any carbon-carbon distance that is less than 3Å can constitute a bond, thus the bond length of the C1-C6 allows for the formation of the bond. This bond length shortens to 1.53996Å as a single bond forms.

The JSmol represents the vibration that forms the bond during the transition state. It is evident from the image that C2-C3 shortens as the ethylene and the butadiene approach. The symmetrical motion of this vibration and the equality of C4-C5/ C1-C6 bond lengths provides confidence to conclude that the formation of the two sigma bonds between the ethylene and the butadiene are synchronous.

===IRC analysis===
{|style="margin: 0 auto;"
| [[File:IRC_T1_jd2615.PNG|600px|thumb|left| IRC plot of the reaction between ethylene and butadiene - shows convergence and smooth gradients]]
| [[File:IRC_T1_movie_jd2615.gif|thumb|centre|700px|Animation IRC showing the formation of the bond between the butadiene and the ethylene]]
|}

The top IRC represents the conversion of the reactants to the products (right to left) via the high energy transition state. The bottom plot shows the first derivative of the top IRC plot, thus representing the change in gradient. The key features of the bottom plot include a starting gradient roughly equal to 0, then an increase in gradient as the energy barrier is overcome, then a drop to zero at the transition state. The IRC animation reiterates the synchronous nature of the formation of cyclohexene via a Diels-Alder reaction.

===Log Files===
[[Media: ETHENE OPT jd2615 1.LOG| ETHENE]]

[[Media: DIENE_OPT_jd2615.LOG| BUTADIENE]]

[[Media: TS T1 opt jd2615.LOG| CYCLOHEXENE TRANSITION STATE]]

[[Media: PRODUCT_OPT_1_ECLIPSED_jd2615.LOG| CYCLOHEXENE PRODUCT]]

==Exercise 2==
===Computational Methods===
For each reaction (ENDO or EXO), the starting materials were optimised to a minimum using DFT b3lyp/6-31G(d). The product was also optimized using this technique. Once the product was optimized, the bonds between the cyclohexadiene and the dixole were removed, moved slightly apart but still within the Van der Waals radius, and frozen using redundant coordinates. This structure was optimized to a minimum using DFT b3lyp/6-31G(d) to provide a minimised transition state-like structure. The bonds were unfrozen and the minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using DFT b3lyp/6-31G(d).

===Reaction Scheme===
This experiment saw the Diels-Alder reaction of cyclohexadiene and dioxole. The main variation in this reaction compared to butadiene and ethylene is that the approach of dienophile can result in two different products, endo and exo:

{|style="margin: 0 auto;"
| [[File:Reaction_scheme_T2_jd2615.jpg|400px|thumb|left| Reaction Scheme with bottom structure showing potential steric clash between protons and bridging group]]
|}

Here the two different products are a result of the different conformations of the transitions state. The ENDO-product has the dioxole pointing in the direction of the diene, whereas the EXO-product points away from the diene. The endo product is the kinetic product (i.e. higher energy product confirmation and lower energy transition state), whereas the EXO product is usually the thermodynamic product (i.e. lower energy product and higher energy transition state) but this is not the case for this reaction. From the analysis of the MO diagram, the stabilised transition state of the ENDO-product is a result of the p orbitals on the oxygen of the diaxole interacting with the p orbitals on carbon 2 and 3 of the cyclohexadiene, thus reducing the energy of the state. As the dioxole points away in the exo product, this particular orbital interaction does not occur, and the transition state is higher in energy. The ENDO-product is usually higher in energy as the protons, which ‘stick up’, are in steric clash with the carbon bridge (see figure 2).

===MO diagrams===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Again, lovely MO diagrams.)

{|style="margin: 0 auto;"
| [[File:EXO_mo_Diagram_T2_jd2615.jpg|400px|thumb|left| MO Digram of the formation of the EXO product from the reaction of 1,3-dioxole and cyclohexadiene - All energy values are in Hartrees]]
| [[File:ENDO_mo_Diagram_jd2615.jpg|440px|thumb|left| MO Digram of the formation of the ENDO product from the reaction of 1,3-dioxole and cyclohexadiene - All energy values are in Hartrees]]
|}

The difference in endo and exo states are rationalized again by the direction of the dienophile with respect to the diene. In the exo product, it is evident that the p orbitals on the oxygen of the dienophile are not involved by stabalisation of the state. The following image shows the secondary interaction which leads to the stabilization of the ENDO state:
{|style="margin: 0 auto;"
| [[File:Secondary_stabilisation_pic_jd2615.PNG|400px|thumb|left|Image to show secondary interaction which leads to stabilization of the ENDO state - direction of stabilization represented with yellow arrows]]
|}
It is possible to rationalise the orbitals calculated by comparing their structure to the orbital combinations in the MO diagram. The 4 MO’s in the diagram in ascending order are the LUMO -1, LUMO, HOMO and HOMO +1. An important feature to notice in the calculated MOs is the stabalising effects as a result of the interaction between the p orbital on the oxygens of dioxole and the p orbitals of the 2-3 carbon atoms on the diene (illustrated with the yellow arrow). The HOMO shows some stabilisation from the interaction of the p orbitals on the 2,3 carbons on the butadiene and the alkene p orbitals on the dioxole.

In order to determine the nature of the Diels-Alder, it is necessary to look at the electronics of the reactants. The normal electron demand Diels-Alder sees an electron rich diene and an electron poor dienophile. Cyclohexadiene is neither electron rich or poor in this example. However, the lone pair on the oxygen of diaxole readily feeds electron density onto the alkene, thus deeming it electron rich:
{|style="margin: 0 auto;"
| [[File:Resonance_of_diaxole_jd2615.jpg|400px|thumb|left|Canonical forms of the 1,3-dioxole to show conjugation of the lone pair on the oxygen resulting in an electron rich dienophile ]]
|}
This different electron destribution in the dienohphile means that the HOMO of the dienophile is higher in energy than the HOMO of the diene, which is characterisitic of an inverse demand Diels-Alder reaction.

===Energy Calculations===

{| class="wikitable"
|-
!
! Energy / Hartrees
|-
| Cyclohexadiene
| --233.324
|-
| Dioxole
| -267.068
|-
| Reactant total
| --500.393
|-
| ENDO-product
| -500.419
|-
| ENDO Transition State
| -500.351
|-
| EXO-product
| -500.417
|-
| EXO Transition State
| -500.329
|}

As expected, the total energy of the reactants is higher than the individual products. When comparing the energy of the transition states, the endo product is lower than the exo product, which contradicts previous hypothesis that the steric clash with the protons will increase the energy in the ENDO product. It is expected that potential steric clash between the dioxole group and the bridging group in the EXO product results in higher energy. The ENDO energy barrier calculated from the difference in energy from the reactants to the ENDO transition state is 0.0420 Hartrees. The EXO energy barrier calculated via the same technique was 0.033 Hartrees, showing that the EXO TS is higher in energy than the ENDO TS.

===Jmol images===
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Dioxole HOMO</title>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> DIOXOLE_T2_OPT_1_B3LYP_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Dioxole LUMO</title>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> DIOXOLE_T2_OPT_1_B3LYP_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene HOMO</title>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> DIENE_OPT_1_B3LYP_T2_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene LUMO</title>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> DIENE_OPT_1_B3LYP_T2_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS HOMO-1</title>
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<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS HOMO</title>
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<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS LUMO</title>
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<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS LUMO+1</title>
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<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Endo TS HOMO-1</title>
<size>200</size>
<script>frame 82; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> ENDO_4_TS_B3LYP_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Endo TS HOMO</title>
<size>200</size>
<script>frame 82; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> ENDO_4_TS_B3LYP_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Endo TS LUMO</title>
<size>200</size>
<script>frame 82; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> ENDO_4_TS_B3LYP_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Endo TS LUMO+1</title>
<size>200</size>
<script>frame 82; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> ENDO_4_TS_B3LYP_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Thermodynamics===

{|style="margin: 0 auto;"
| [[File:ENDO IRC T2 jd2615.png|400px|thumb|left| IRC for the formation of the ENDO-product]]
| [[File:ENDO_IRC_VID_T2_jd2615.gif|400px|thumb|left| IRC animation for the formation of the ENDO-product]]
|}
{|style="margin: 0 auto;"
| [[File:EXO IRC T2 jd2615.png|400px|thumb|left| IRC for the formation of the EXO-product]]
| [[File:EXO_IRC_VID_T2_jd2615.gif|400px|thumb|left| IRC animation for the formation of the EXO-product]]
|}

Both IRC pathways show a similar pattern. The top plot of both IRC’s is the actual energy along the reaction coordinate, where the peak corresponds to the energy of the transition state. The left side is the lower energy of the products, which is the result of the more stable sigma bond in comparison to the higher energy pi bonds of the reactants which are displayed on the right side. The lower plot IRC is the gradient along the reaction coordinate. The point where the gradient drops to zero corresponds to the transition (where the first derivative of the plot is zero.) The single peak of the IRC shows that the reaction occurs with one step, reflecting the concerted nature of the Diels-Alder, as two sigma bonds are formed simultaneously.

===Log Files===
[[Media: DIOXOLE_T2_OPT_1_B3LYP_jd2615.LOG| DIOXOLE]]

[[Media: DIENE_OPT_1_B3LYP_T2_jd2615.LOG| CYCLOHEXADIENE]]

[[Media: EXO_TS_B3LYP_TS1_jd2615.LOG| EXO TRANSITION STATE]]

[[Media: ENDO_4_TS_B3LYP_jd2615.LOG| ENDO TRANSITION STATE]]

[[Media: PRODUCT_MINIMISE_B3LYP_jd2615_ENDO_3.LOG| ENDO PRODUCT]]

[[Media: EXO_B3LYP_PRODUCT_jd2615_T2.LOG| EXO PRODUCT]]

==Exercise 3==
===Computational methods===
For each reaction in this exercise, the starting materials were optimized to a minimum using semi-empirical PM6. The products were also optimized using this technique. Once the product was optimized, the bonds between the Xylylene and the sulfer dioxide were removed, moved slightly apart but still within the Van der Waals radius, and frozen using redundant coordinates. This structure was optimized to a miniumum using semi-empirical PM6 to minimise a transition state-like structure. The minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using semi-empirical PM6.

===Reaction Scheme===

This experiment investigates the Diels-Alder reaction between o-Xylylene and Sulpher Dioxide. Unlike other Diels-Alder reaction, this reaction can go via a Chelotropic reaction which is a form of pericyclic reaction where, unlike the traditional Diels-Alder, both new bonds to the dienophile occur on a single atom (i.e. the Sulfer atom). This exercise seeks to rationalise which of the three potential products from this reaction could be the most stable.
{|style="margin: 0 auto;"
| [[File:Reaction_Scheme_T3_jd2615.jpg|400px|thumb|left| Reaction Scheme of o-Xylylene and Sulfer dioxide. Top Scheme shows the formation of the ENDO and EXO Diels-Alder product. Bottom Scheme shows the formation of the Cheletropic product - click to view]]
|}

The mechanism for the Cheletropic pericyclic reaction is a product of the sulfer being both electrophilic and nucleophilic, where the lone pair on the sulfer attacks the o-Xylylene.

{|style="margin: 0 auto;"
| [[File:Cheletropic_IRC_jd2615.PNG|400px|thumb|left| IRC plot of Cheletropic reaction of sulfer dioxide and o-Xylylene]]
| [[File:Cheletropic_IRC_animation_jd2615.gif|400px|thumb|left| IRC animation of Cheletropic reaction of sulfer dioxide and o-Xylylene]]
|}
{|style="margin: 0 auto;"
| [[File:ENDO_IRC_j2615_T3_1.PNG|400px|thumb|left| IRC plot of ENDO reaction of sulfer dioxide and o-Xylylene]]
|[[File:Endo_IRC_animation_jd2615.gif|400px|thumb|left| IRC animation of ENDO reaction of sulfer dioxide and o-Xylylene]]
|}

{|style="margin: 0 auto;"
| [[File:EXO_IRC_jd2615.PNG|400px|thumb|left| IRC plot of EXO reaction of sulfer dioxide and o-Xylylene]]
| [[File:EXO IRC animation jd2615.gif|400px|thumb|left| IRC animation of EXO reaction of sulfer dioxide and o-Xylylene]]
|}

The IRC for all these reactions shows that the energy barrier is very low. This can be rationalised by looking at the electronic structure of the six membered ring. The reaction results in formation of a stable aromatic benzene ring which is a lot more stable than the diene structure before, this results in a low activation and a much more stable product.

===Thermodynamics and kinetics of reaction===
{|style="margin: 0 auto;"
| [[File:rate_constants_T3_jd2615.jpg|400px|thumb|left| Figure showing the conversion of the starting materials to either the Cheletropic or ENDO/EXO Diels-Alder product. The length of the arrow represents how readily the product forms. k2 is greater than k1, thus showing that the Cheletropic reaction forms the thermodynamic product. <ref name=Sordo />]]
|}
From analysis of the thermochemistry extracted from the data produced by the calculation, it is evident that the thermodynamic product is the cheletropic product.

{|style="margin: 0 auto;"
| [[File:ENDO EXO energies jd2615.jpg|400px|thumb|left| Relative energies of the species formed during the ENDO/EXO Diels-Alder reaction]]
| [[File:cheletropic_energies_jd2615.jpg|400px|thumb|left| Energies of the species formed during the Cheletropic reaction]]
|}

The above plots show the relative energies of each species during the reaction of o-Xylylene and sulfer dioxide. From the calculated energies, the Cheletropic product is the thermodynamic product as a result of the more stable 5-membered ring, but it shows a large transition state energy, whereas both Diels-Alder products are the kinetic products. As with all Diels-Alder mechanisms, the kinetic stability of the endo transition state is a result of the interaction of the pi bond from the non-reacting S-O bond interacting with the p orbitals of the diene, as this S-O bond sits in the correct geometry. The non-reacting S-O bond points away from the diene, thus preventing any pi-p secondary interactions. There are no secondary orbital interactions for the cheletropic reaction, so that results in a higher energy transition state. When comparing the transition states for the Diels-Alder and Cheletropic, the six membered transition state shows less ring strain, thus causing stabilisation. The 5 membered transition state has greater ring strain, so is higher in energy.

Work by Jose Sordo <ref name=Sordo> Jose A. Sordo, ''Sulfer Dioxide Promotes Its hetero-Diels-Alder and Cheletropic Additions to 1,2-Dimethylidenecyclohexane'', J. Am. Chem. Soc, 1998, 120, 13276-13277 </ref> showed that during this mechanism, an external sulfer dioxide group is involved in the stability of the transition state and also provides an energy compensation for the free energy loss as a result of the decrease in entropy as two molecules form one.<ref name=Sordo />
{|style="margin: 0 auto;"
| [[File:Stabalising_effect_jd2615.PNG|400px|thumb|left|Structure described in the literature which is being investigated for stabilization effects on the transition state (represented with a dotted line).]]
|}
The image above shows the conformation of the accessory sulfer dioxide, where the dashed lines represent the stabalising interaction. A further calculation was set up to determine if the Sulpher dioxide had a stabilization effect on the transition state. In the literature it states that an MP2/6-31G calculation was set up, however a b3lyp/6-31G(d) calculation was used.<ref name=Sordo /> The amount of time it took for the calculation to complete meant that it was impractical to run to completion. The transition state with frozen bonds was successfully calculated. However; the optimization to transition state (Berny) took too long to optimize, but the following intermediate structures were formed, below:

{|style="margin: 0 auto;"
| [[File:TS vid E jd2615.gif|500px|thumb|left| Animation to show the non-convergence of the transition state. The sulfer dioxide remains in the area suggesting some degree of stability, but further work is still required]]
|}

From visual analysis, the calculation passes the previous transition state, bonding the Sulfer dioxide and diene together. The accessory sulfer dioxide remains in the same place, just changing it's orientation with respect to the conformation of the main molecule. However, if the position of the extra molecule was very unfavorable, it would rapidly change it's position, either towards or away from the Diels-Alder product. This observation suggests that the position of this molecule is relatively stable, however further experiment would be required with more time and computing power. The result of this experiment also suggests that the b3lyp may be inadequate for this type of calculation, so further experiments would require the reproduction of the literature method by using MP2/6-31G.<ref name=Sordo />

(Unfortunately MP2/6-31g(d) is also inadequate for this type of calculation. The gradient will be extremely small when looking at non-bonding interactions, making optimisations very difficult as you found above [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:27, 4 April 2018 (BST))

===Other potential Diels-Alder reactions===
The ENDO-site Diels-Alder reaction is as follows:
{|style="margin: 0 auto;"
| [[File:Reaction_Scheme_T3_EE_jd2615.jpg|400px|thumb|left| Reaction Scheme at for the ENDO-site Diels-Alder reactions]]
|}

Here the Sulfer dioxide reacts with the diene that is constituent of the six membrered ring. As with most Diels-Alder reactions, this reaction can either be ENDO or EXO with respect to the position of the non-reacting sulfer-oxygen bond.

{|style="margin: 0 auto;"
| [[FILE:IRC_EXO_T3_EE_pic.PNG|400px|thumb|left|IRC plot for EXO product at ENDO-site]]
| [[File:IRC_EXO_T3_EE_vid.PNG|400px|thumb|left|IRC animation for EXO product at ENDO-site]]
|}
{|style="margin: 0 auto;"
| [[File:IRC_TS_T3_EE_ENDO_PIC.gif|400px|thumb|left|IRC plot for ENDO product at ENDO-site]]
| [[File:IRC_vid_EE_jd2615_ENDO.gif|400px|thumb|left|IRC animation for ENDO product at ENDO-site]]
|}

The above IRCs represent the reaction coordinate of this reaction of Sulpher dioxide at this particular site of the diene. From analysis of this, the transition state and the product formed will be higher in energy because neither species are aromatic, unlike the reaction on the EXO-site (outside the 6 membered ring) of the molecule. The absence of aromaticity means the molecule is less stable compared to the EXO product.

{| class="wikitable"
|-
!
! Transition State / kJ/mol
! Product / kJ/mol
|-
| ENDO
| 267.98
| 172.25
|-
| EXO
| 275.82
| 176.68
|}

The lack of aromaticity of the transition state and the products is reflected in much higher energy values when compared to the EXO-site compounds. Again, the ENDO transition state is lower than the EXO because of the secondary p-pi orbital interaction between the oxygen on the alkene and the and pi orbitals of the diene (mentioned in previous sections).

===Log Files===
[[Media: SO2_MIN_jd2615.LOG| SULFER DIOXIDE]]

[[Media: XYLYLENE_jd2615.LOG| XYLYLENE]]

[[Media: EXO PM6 TS jd2615.LOG| EXO-SITE EXO TRANSITION STATE]]

[[Media: END PM6 TS1 jd2615.LOG| EXO-SITE ENDO TRANSITION STATE]]

[[Media: EXO_PM6_MIN_JD2615.LOG| EXO-SITE EXO PRODUCT]]

[[Media: END_PM6_MIN1_JD2615.LOG| EXO-SITE ENDO PRODUCT]]

[[Media: PRODUCT_EXO_TS_EE_JD2615.LOG| ENDO-SITE EXO TRANSITION STATE]]

[[Media: PRODUCT_TS_ENDO_EE_JD2615.LOG| ENDO-SITE ENDO TRANSITION STATE]]

[[Media:PRODUCT_EXO_MIN_JD2615_EE.LOG| ENDO-SITE EXO PRODUCT]]

[[Media: PRODUCT_OPT_EE_JD2615_ENDO.LOG| ENDO-SITE ENDO PRODUCT]]

Extension Log files: Failed to converge

[[Media: TS_BERRY_EXTRA_jd2615.LOG| Extension with accessory sulfer dioxide molecule]]

=Extension=
===Computational methods===
The product was optimized to a minimum using semi-empirical PM6. The length of the sigma bond formed during the reaction was increased and the bond was removed, where the new positions are frozen using redundant coordinates. This structure was optimized to a miniumum using semi-empirical PM6 to minimise a transition state-like structure. The minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using semi-empirical PM6.

===Hypothesized reaction===
Electrocyclic reactions can be distinguished according to whether they are conrotatory or disrotatory. Huckel theory describes the requirements for thermal and photochemical electrocyclic ring closures. The following reaction is being investigated to determine it's reaction coordinate and the orbital dynamics of the transition state:
{|style="margin: 0 auto;"
| [[File:Reaction_Scheme_jd2615.jpg|400px|thumb|left|Extension reaction scheme]]
|}

For a thermal reaction with 4 pi electrons, Huckel theory states that if the reaction is to proceed via a Huckel transition state, the sigma bond forms via disrotatory motion of the p orbitals at the end of the diene which are in an antarafacial arrangement:

(Not Hückel theory. Also, it would undergo conrotation [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:34, 4 April 2018 (BST))

{|style="margin: 0 auto;"
| [[File:Disrotatory_jd2615.jpg|400px|thumb|left|Suprafacial, disrotatory motions of p orbitals]]
|}

The transition state and IRC was optimised using PM6, semi empirical method. The following transition state was optimised which provided the transition state vibration represented with the negative frequency:

{|style="margin: 0 auto;"
|<jmol>
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<script>frame 23; vibration 1;rotate x -20; </script>
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|}

(This is conrotation [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:34, 4 April 2018 (BST))

==IRC Calculation==

{|style="margin: 0 auto;"
| [[File:IRC_path_E_jd2615.PNG|400px|thumb|left| IRC plot for electrocyclic ring closure]]
|[[File:Extension_IRC_jd2615_2.gif|400px|thumb|left| IRC animation for electrocyclic ring closure]]
|}

{|style="margin: 0 auto;"
| <jmol>
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<color>white</color>
<title>TS HOMO -1</title>
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<uploadedFileContents>E1_TS+PM6_2_jd2615.LOG</uploadedFileContents>
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</jmol>
| <jmol>
<jmolApplet>
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<title>TS HOMO</title>
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<uploadedFileContents>E1_TS+PM6_2_jd2615.LOG</uploadedFileContents>
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<jmolApplet>
<color>white</color>
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<uploadedFileContents>E1_TS+PM6_2_jd2615.LOG</uploadedFileContents>
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<uploadedFileContents>E1_TS+PM6_2_jd2615.LOG</uploadedFileContents>
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</jmol>
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The orbital of interest in the transition state is the LUMO. the twist in the molecular orbitals of the state result in a mobius aromaticity where molecular orbital follows the topology of a mobius strip, thus Huckel theory cannot be used to describe this species. In a mobius transition state, a thermal 4 electron system is antarafacial, conrotatory <ref name = rzepa> Henry S. Rzepa ''The Aromaticity of Pericyclic Reaction Transition States'', J. Chem. Educ., 2007, 84, 1535 </ref>:

{|style="margin: 0 auto;"
| [[File:Antarafacial jd2615.jpeg|400px|thumb|left| Antarafacial, conrotatory motion of p orbitals]]
|}

{|style="margin: 0 auto;"
| [[File:Mobius_strip_jd2615.PNG|400px|thumb|left| Mobius topology of p orbitals forming Mobius aromaticity]]
| [[File:Huckle strip jd2615.PNG|400px|thumb|left| Symmetrical arrangement of p orbitals forming Huckel aromaticity]]
|}

The above figure represents the mobius topology where each p orbital has a slight rotation when compared to it's adjacent partner, resulting in an aromatity that forms a loop with a half twist, unlike the huckle aromatic transitions state that shows no twist, just two symmetrical planes.<ref name = rzepa /> This diene complex undergoes the same principle where the pi-p orbitals involved in the butadiene undergo a disrotatory twist where the resulting transition state has mobius aromaticity, which is thermally allowed according to rules outlined in a publication by Henry S Rzepa which stated that a 4 pi pericyclic reaction can occur thermally as long as the p orbital arrangement forms a stable mobius aromatic species.<ref name = rzepa /> Further work in Henry S Rzepa's publication outlined interesting comparisons between the mobius and Huckel aromaticity, one being that the ideal mobius strip has only C2 symmetry, thus the absence of further symmetry means the mobius aromatic transition has a non-superimposible mirror image, unlike the Huckel which has a superimposible mirror image.<ref name = rzepa />

===Log Files===
[[Media:E1_MIN+PM6_4_jd2615.LOG| Extension product]]

[[Media:E1 TS+PM6 2 jd2615.LOG| Extension transition state]]

=Conclusion=
This experiment has attempted to rationalise the synthetic difference in yield by describing orbital interactions and their energies with the use of computational techniques. Exercise one saw the most basic Diels-Alder reaction of butadiene and ethylene. This experiment was useful in determining the standard MO diagram for this reaction, showing the primary interactions without any influence from functionality of the different reactants with no secondary interactions forming ENDO or EXO products. It showed the importance of symmetry of the interacting orbitals, where only orbitals of the same symmetry interact, and different symmetry orbital interactions lead to an overlap integral of zero.

The second experiment introduced functionality to the starting materials by reacting 1,3-dioxole and cyclohexadiene. This experiment showed how position of the dienophile with respect to the diene results in different products formed through secondary interactions. The ENDO product always has a lower energy transition state as the p orbitals of the oxygen on the dienophile interacts with the p orbitals on C2 and C3 of the diene (See 'bond distances' in 'Exercise 1'), causing a stabalising interaction. Further consequences of the oxygen in the dienophile is that it feeds electron density into the alkene which results in an inverse Diels-Alder reaction, where the HOMO of the dienophile is lower than HOMO of the diene.

The third experiment introduced a non-carbon based dienophile to undergo a hetero Diels-Alder reaction. Firstly the EXO site (non-carbon ring diene) of the molecule was explored. Other than both the ENDO and EXO product, this reaction saw the cheletropic reaction where the sulfer atom reacts as both the nucleophile and electrophile, where both new sigma bonds are formed on the same atom (i.e. the sulfer atom). This experiment showed that the cheletropic reaction formed the thermodynamic product as a result of the more stable 5 membered ring structure, while showing the highest transition state energy due to increased ring strain of the transitions species. Further experiments were undertaken to investigate the effects of an accessory sulfer dioxide molecule on the transition state energy (experiment inspired by literature). This experiment was inconclusive as the transition state failed to converge. Further work could could be done with more time and computing power conclude this experiment. The ENDO site (carbon ring diene) was then investigated. This showed that the transition state energy and the product energy were much higher than those of the ENDO-site products. This was a result of the lack of aromaticity of the TS and products, thus being less stable and higher energy.

The extension exercise explored the electrocyclic ring closure of a diene under thermal conditions. It was expected that the reaction coordinate would proceed via a disrotatory motion of the diene's p orbitals to form a sigma bond between the end of the diene, where the transition state was stabalised by the symmetrical huckel aromaticity. However, from analysis of the HOMO orbitals of the TS, the state was stabalised by a mobius loop aromaticity formed through the slight rotation of p orbitals with respect to it's adjacent partner, resulting in a conjugation with a mobius topology. For a mobius transition state with 4n pi electrons, the reaction must proceed via a conrotatory motion of the p orbitals to form a sigma bond between the end of the diene.

Computation techniques have proven effective at representing these structures. However in the light of the extension where an accessory sulfer dioxide molecule can have an influence on the stability of a transition state, it is felt that further experiments need to be done including many molecule systems before a fair comparison between computed energies and synthetic yield can be correlated.

=References=

Rep:Mod:jd2615TS

2018-04-07T11:25:50Z

Fv611: /* Exercise 1 */

=Computational methods to determining transition states=
==Introduction==
The potential energy surface (PES) is useful representation of the many different energy states a particular species can exist in. It provides a mathematical relationship between's a molecules energy and it's structure. <ref name = lewars> E.G. Lewars, ''Computational Chemistry'', Springer, 2nd edn, 2011, ch 2, pg 9 </ref>. It can be extremely useful for computational chemists as it provides mathematical meaning for a molecules structure, while also providing a 'framework' for programmers to design a code which can accurately determine the energy of a species. <ref name =lewars />. With peaks being transition species and troughs being intermediates or products, the mathematical landscape of a three-dimensional PES provides a visual justification for the products formed in the synthesis lab and will hopefully shed light on the different species encountered in the experiment.

The Diels-Alder reaction has been a prominent synthetic tool for chemists for many years. The understanding of the nature of the diene and the dienophile has been the source of interest for both synthetic and computational chemists, providing more opportunity for electrocyclic chemistry and better correlation between synthetic results and molecular interactions. This experiment investigates the interaction between different dienes and dienophiles, focussing primarily on the orbital formations of the transition state by the use of computational techniques. Through the variety of reactants, this experiment hopes to shed light on the precise mechanistic dynamic by providing energies, bond distances and orbital conformations. Work by Domingo <ref name=domingo>Luis. R Domingo, ''The mechanism of ionic Diels–Alder reactions. A DFT study of the oxa-Povarov'', RSC Adv, 2014, 4 </ref> showed that the DFT methods at the B3LYP/6-31G level could be used to determine a reaction model for an ionic Diels-Alder reaction by the investigation of the oxa-Povarov reaction which is initialized by the ionic Diels-Alder of a cationic aryl oxonium and an alkene.<ref name=domingo/> They determined, through the analysis of the IRC, that the substituents on the alkene (i.e. the phenyl ring on phenyl ethylene) forced a two-step mechanism, as opposed to the usual concerted one step approach.<ref name=domingo/> Further work by Black <ref name=black> K. Black, ''Dynamics, transition states, and timing of bond formation in Diels–Alder reactions'', PNAS, 2012, 12860-12865 </ref> (computed by UB3LYP/6-31(G)) into the dynamics of bond formation of the Diels-Alder reaction observed that regardless of the symmetry of the reactants, the trajectories of bond formation are unequal in the transition state, but they concluded that at room temperature, due to shorter time gap of the formation of two new bonds compared to the C-C bond vibrational period, the Diels-Alder are concerted and stereospecific.<ref name=black />

==Computation Techniques==
In computational chemistry, there will be range of understanding of the structure a chemist is trying to identify. Different degrees of understanding require different techniques depending on whether an individual knows what their seeking. There are three methods for locating transition states with Gaussian:

Method 1: This method requires a good understanding of the transition state of a particular reaction. Here the chemist forms the starting materials in an arrangement which resembles the transition state of the reaction, the structure is optimized to a transition state that hopefully resembles natural state. The chemist must have a good understanding of bond angles and distances in order to accurately recreate the structure they are looking for.

Method 2: This method is more advanced than method one and still requires a knowledge of the transition state, but it is the fastest reliable method. Here the chemist draws the transition state from starting material according to their understanding of the structure. Then the bonds are frozen between the starting materials using Redundant Coordinate Editor. The structure is then optimised to a minimum with the frozen bonds so that the functional groups of the reacting molecules arrive at the most stable position. The minimised structure is then unfrozen and allowed to be minimised to a transition state that should resemble the natural state.

Method 3: This method requires more steps than method 1 or 2, but requires little knowledge of the transition state. Here the product is drawn and optimized to a minimum. The minimized product is then separated into the reacting fragments by breaking the bonds between them (i.e. separating the product into the two reactants). The reactant fragments are then separated slightly and frozen using redundant coordinates. The frozen structure is then optimized to a minimum, which is then optimized to a transition state.

The Hartree-Fock method is a set of equations which provide the best one-electron wave functions approximations to the problem of an electron in the motion of a field of atomic nuclei.<ref name=Slater> J. C. Slater, ''A simplification of the Hartree-Fock Method'', Physical Review, 1950, 81, 3, 385-386 </ref> The description of the relationship of an electron within the potential of the nuclei can provide an approximation for a structure of a molecular state. b3lyp calculations calculate electron distributions with the use of Density Functional Theory (DFT) which is when the electrons are described in accordance to their density and not individual wave functions, its a progression on from the Hartree-Fock method. The energy of a system can be separated into six components:

<math> E_{DFT} = E_{NN} + E_{T} + E_V + E_{coul} + E_{exch} + E_{corr} </math><ref name = Filatov> Michael Filatov, '' Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model'', J. Them. Theory Comput., 2013, 9, 3197-3932 </ref>

Where NN is nuclear-nuclear repulsion, v is attraction, coul is electron-electron Coulombic repulsion, T is kinetic energy of electrons, exch is the electron-electron exchange energy and corr describes the correlated movement of electrons of different spin. <ref name = Filatov />.

The The majority of these experiments will use the semi-empirical quantum chemistry method with are based on Hartree-Fock or DFT theory but also through application of approximate assumptions thus obtaining empirical data. <ref name = jan> Jan Řezáč, ''Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes'', J. Chem. Theory Comput., 2009, 5 , 1749–1760 </ref>. When molecules are very large, the use of semi-empirical over full Hartree-Fock as the whole calculation is less expensive. <ref name=jan />. One exercise in this experiment makes of b3lyp which

==Exercise 1==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Excellent work across the whole exercise. Great job!)

===Computational Method===
The starting materials were optimized to a minimum using semi-empirical PM6. The product was also optimized using this technique. Once the product was optimized, the bonds between the alkene and the diene were removed, moved slightly apart but still within the Van der Waals radius, and frozen using redundant coordinates. This structure was optimized to a miniumum using semi-empirical PM6 to minimise a transition state-like structure. The minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using semi-empirical PM6.

===Reaction Scheme===

This experiment saw the Diels-Alder simulation between butadiene and ethylene to give cyclohexene:

{|style="margin: 0 auto;"
| [[File:SchemeT1.jpg|400px|thumb|left| Reaction Scheme of the reaction of ethylene and butadiene]]
|}

The Diels-Alder reaction sees a [4+2] cycloaddition of a conjugated diene and an alkene dieneophile via the interaction of 4 pi electrons from the diene and 2 pi electrons from the alkene, where the driving force is provided by the more stable sigma bond formed between the reactants, when compared to the weaker pi bonds.

===MO diagram===

{|style="margin: 0 auto;"
| [[File:MO_diagram_T1_jd2615_1.jpg|400px|thumb|left| MO diagram for the reaction of ethylene and butadiene - All energy values are in Hartrees]]
|}

The transition state is given by the linear combination of the fragment HOMO-LUMO orbitals of both the butadiene and the ethylene. The orbitals are combined according to symmetry, where the symmetry is labelled with a small s (symmetric) or a (asymmetric) next to the energy level of the orbital being described. Only orbitals of the same symmetry can combine. The differing degrees of contribution are represented by the size of the orbitals within the formed MOs, where larger contributions due to the similar relative energy of the source fragment is shown as a larger orbital. For example, the HOMO -1 orbital has a larger orbital contribution from the HOMO of the butadiene (as this is closer in energy), thus is shown as larger orbitals. From the law of conservation of orbital number, 4 molecular orbitals are formed from 2 fragment orbitals from each reactant. The orbitals calculated using gaussview are represented by the jmol images below. The HOMO -1 (i.e. lowest energy) is formed from the two asymmetric fragments of the frontier orbitals. When comparing the calculated HOMO MOs, there is greater bonding character for the HOMO-1 relative to the HOMO, resulting in a more stable electronic distribution. The same reason applies to the LUMOs, where the LUMO +1 sees the greatest antibonding character thus being highest in energy.

===Jmol of orbitals===

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>ETHENE HOMO</title>
<size>200</size>
<script>frame 10; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT jd2615 1.LOG</uploadedFileContents>
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<jmolApplet>
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<title>ETHENE LUMO</title>
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<uploadedFileContents>ETHENE OPT jd2615 1.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
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<title>Butadiene HOMO</title>
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<uploadedFileContents>DIENE_OPT_jd2615.LOG</uploadedFileContents>
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<jmolApplet>
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<title>Butadiene LUMO</title>
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<uploadedFileContents>DIENE_OPT_jd2615.LOG</uploadedFileContents>
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{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
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<title>TS HOMO - 1</title>
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<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
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<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
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<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
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<color>white</color>
<title>TS LUMO + 1</title>
<size>200</size>
<script>frame 28; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Analysis of direct linear combination of orbitals of different symmetry shows that the orbital overlap integral is zero:
{|style="margin: 0 auto;"
| [[File:Symmetry T1 jd2615.png|400px|thumb|left| Linear combination of symmetrical and asymmetrical frontier orbitals to form two MO's with an overlap integral of zero]]
|}
Both orbital MOs formed in the above diagram would have zero overlap integral as one p orbital from the alkene forms a bonding interaction whereas the other is anti-bonding. If this system saw a break of symmetry, then the integral will become non-zero and bonding interactions will occur.

===Bond Distances===
{|style="margin: 0 auto;"
| [[File:Bond_length_T1_jd2615.jpg|600px|thumb|left| Figure to show the bond length of each species involved in the Diels-Alder reaction between ethylene and butadiene]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 73; vibration 1;rotate x -20; </script>
<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|}

The above figure shows the bond lengths of the various bonds of the reactants, transition state (TS) and products respectively. Firstly, the ethylene reactant sees a standard sp2 double bond length of 1.32755Å (C5-C6). Mechanistically, the pi electrons of the ethylene form one of the sigma bonds to the butadiene during the concerted electrocyclic process, thus forming an sp3 single bond in the product (C5-C6 = 1.54070Å) (the other sigma bond to the ethylene is formed from pi electrons on the butadiene). The bond lengths confirm this observation as the transitions state sees a single-double intermediate bond length of 1.38176Å. The same process occurs for the C3-C4 and C1-C2 which change from double to single bond with an intermediate bond length (C1-C2 (reactants) = 1.47079Å, C1-C2 (transition state) = 1.37977Å, C1-C2 (products) = 1.33761Å). The opposite process occurs for the C2-C3 where it is originally a single bond in butadiene (C2-C3 = 1.47079Å), which is slightly shorter than a normal sp3 single bond, which is a result of the conjugation between the alkenes resulting in a small degree of double bond character. The bond length shortens as it becomes a double to 1.41111Å in the transition state and 1.33761Å in the product. The C1-C6/C4-C5 bond length in the transition state is 2.11473Å. The Van der Waals radius of carbon is around 1.5Å, thus any carbon-carbon distance that is less than 3Å can constitute a bond, thus the bond length of the C1-C6 allows for the formation of the bond. This bond length shortens to 1.53996Å as a single bond forms.

The JSmol represents the vibration that forms the bond during the transition state. It is evident from the image that C2-C3 shortens as the ethylene and the butadiene approach. The symmetrical motion of this vibration and the equality of C4-C5/ C1-C6 bond lengths provides confidence to conclude that the formation of the two sigma bonds between the ethylene and the butadiene are synchronous.

===IRC analysis===
{|style="margin: 0 auto;"
| [[File:IRC_T1_jd2615.PNG|600px|thumb|left| IRC plot of the reaction between ethylene and butadiene - shows convergence and smooth gradients]]
| [[File:IRC_T1_movie_jd2615.gif|thumb|centre|700px|Animation IRC showing the formation of the bond between the butadiene and the ethylene]]
|}

The top IRC represents the conversion of the reactants to the products (right to left) via the high energy transition state. The bottom plot shows the first derivative of the top IRC plot, thus representing the change in gradient. The key features of the bottom plot include a starting gradient roughly equal to 0, then an increase in gradient as the energy barrier is overcome, then a drop to zero at the transition state. The IRC animation reiterates the synchronous nature of the formation of cyclohexene via a Diels-Alder reaction.

===Log Files===
[[Media: ETHENE OPT jd2615 1.LOG| ETHENE]]

[[Media: DIENE_OPT_jd2615.LOG| BUTADIENE]]

[[Media: TS T1 opt jd2615.LOG| CYCLOHEXENE TRANSITION STATE]]

[[Media: PRODUCT_OPT_1_ECLIPSED_jd2615.LOG| CYCLOHEXENE PRODUCT]]

==Exercise 2==
===Computational Methods===
For each reaction (ENDO or EXO), the starting materials were optimised to a minimum using DFT b3lyp/6-31G(d). The product was also optimized using this technique. Once the product was optimized, the bonds between the cyclohexadiene and the dixole were removed, moved slightly apart but still within the Van der Waals radius, and frozen using redundant coordinates. This structure was optimized to a minimum using DFT b3lyp/6-31G(d) to provide a minimised transition state-like structure. The bonds were unfrozen and the minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using DFT b3lyp/6-31G(d).

===Reaction Scheme===
This experiment saw the Diels-Alder reaction of cyclohexadiene and dioxole. The main variation in this reaction compared to butadiene and ethylene is that the approach of dienophile can result in two different products, endo and exo:

{|style="margin: 0 auto;"
| [[File:Reaction_scheme_T2_jd2615.jpg|400px|thumb|left| Reaction Scheme with bottom structure showing potential steric clash between protons and bridging group]]
|}

Here the two different products are a result of the different conformations of the transitions state. The ENDO-product has the dioxole pointing in the direction of the diene, whereas the EXO-product points away from the diene. The endo product is the kinetic product (i.e. higher energy product confirmation and lower energy transition state), whereas the EXO product is usually the thermodynamic product (i.e. lower energy product and higher energy transition state) but this is not the case for this reaction. From the analysis of the MO diagram, the stabilised transition state of the ENDO-product is a result of the p orbitals on the oxygen of the diaxole interacting with the p orbitals on carbon 2 and 3 of the cyclohexadiene, thus reducing the energy of the state. As the dioxole points away in the exo product, this particular orbital interaction does not occur, and the transition state is higher in energy. The ENDO-product is usually higher in energy as the protons, which ‘stick up’, are in steric clash with the carbon bridge (see figure 2).

===MO diagrams===
{|style="margin: 0 auto;"
| [[File:EXO_mo_Diagram_T2_jd2615.jpg|400px|thumb|left| MO Digram of the formation of the EXO product from the reaction of 1,3-dioxole and cyclohexadiene - All energy values are in Hartrees]]
| [[File:ENDO_mo_Diagram_jd2615.jpg|440px|thumb|left| MO Digram of the formation of the ENDO product from the reaction of 1,3-dioxole and cyclohexadiene - All energy values are in Hartrees]]
|}

The difference in endo and exo states are rationalized again by the direction of the dienophile with respect to the diene. In the exo product, it is evident that the p orbitals on the oxygen of the dienophile are not involved by stabalisation of the state. The following image shows the secondary interaction which leads to the stabilization of the ENDO state:
{|style="margin: 0 auto;"
| [[File:Secondary_stabilisation_pic_jd2615.PNG|400px|thumb|left|Image to show secondary interaction which leads to stabilization of the ENDO state - direction of stabilization represented with yellow arrows]]
|}
It is possible to rationalise the orbitals calculated by comparing their structure to the orbital combinations in the MO diagram. The 4 MO’s in the diagram in ascending order are the LUMO -1, LUMO, HOMO and HOMO +1. An important feature to notice in the calculated MOs is the stabalising effects as a result of the interaction between the p orbital on the oxygens of dioxole and the p orbitals of the 2-3 carbon atoms on the diene (illustrated with the yellow arrow). The HOMO shows some stabilisation from the interaction of the p orbitals on the 2,3 carbons on the butadiene and the alkene p orbitals on the dioxole.

In order to determine the nature of the Diels-Alder, it is necessary to look at the electronics of the reactants. The normal electron demand Diels-Alder sees an electron rich diene and an electron poor dienophile. Cyclohexadiene is neither electron rich or poor in this example. However, the lone pair on the oxygen of diaxole readily feeds electron density onto the alkene, thus deeming it electron rich:
{|style="margin: 0 auto;"
| [[File:Resonance_of_diaxole_jd2615.jpg|400px|thumb|left|Canonical forms of the 1,3-dioxole to show conjugation of the lone pair on the oxygen resulting in an electron rich dienophile ]]
|}
This different electron destribution in the dienohphile means that the HOMO of the dienophile is higher in energy than the HOMO of the diene, which is characterisitic of an inverse demand Diels-Alder reaction.

===Energy Calculations===

{| class="wikitable"
|-
!
! Energy / Hartrees
|-
| Cyclohexadiene
| --233.324
|-
| Dioxole
| -267.068
|-
| Reactant total
| --500.393
|-
| ENDO-product
| -500.419
|-
| ENDO Transition State
| -500.351
|-
| EXO-product
| -500.417
|-
| EXO Transition State
| -500.329
|}

As expected, the total energy of the reactants is higher than the individual products. When comparing the energy of the transition states, the endo product is lower than the exo product, which contradicts previous hypothesis that the steric clash with the protons will increase the energy in the ENDO product. It is expected that potential steric clash between the dioxole group and the bridging group in the EXO product results in higher energy. The ENDO energy barrier calculated from the difference in energy from the reactants to the ENDO transition state is 0.0420 Hartrees. The EXO energy barrier calculated via the same technique was 0.033 Hartrees, showing that the EXO TS is higher in energy than the ENDO TS.

===Jmol images===
{|style="margin: 0 auto;"
| <jmol>
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<uploadedFileContents> DIENE_OPT_1_B3LYP_T2_jd2615.LOG</uploadedFileContents>
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{|style="margin: 0 auto;"
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===Thermodynamics===

{|style="margin: 0 auto;"
| [[File:ENDO IRC T2 jd2615.png|400px|thumb|left| IRC for the formation of the ENDO-product]]
| [[File:ENDO_IRC_VID_T2_jd2615.gif|400px|thumb|left| IRC animation for the formation of the ENDO-product]]
|}
{|style="margin: 0 auto;"
| [[File:EXO IRC T2 jd2615.png|400px|thumb|left| IRC for the formation of the EXO-product]]
| [[File:EXO_IRC_VID_T2_jd2615.gif|400px|thumb|left| IRC animation for the formation of the EXO-product]]
|}

Both IRC pathways show a similar pattern. The top plot of both IRC’s is the actual energy along the reaction coordinate, where the peak corresponds to the energy of the transition state. The left side is the lower energy of the products, which is the result of the more stable sigma bond in comparison to the higher energy pi bonds of the reactants which are displayed on the right side. The lower plot IRC is the gradient along the reaction coordinate. The point where the gradient drops to zero corresponds to the transition (where the first derivative of the plot is zero.) The single peak of the IRC shows that the reaction occurs with one step, reflecting the concerted nature of the Diels-Alder, as two sigma bonds are formed simultaneously.

===Log Files===
[[Media: DIOXOLE_T2_OPT_1_B3LYP_jd2615.LOG| DIOXOLE]]

[[Media: DIENE_OPT_1_B3LYP_T2_jd2615.LOG| CYCLOHEXADIENE]]

[[Media: EXO_TS_B3LYP_TS1_jd2615.LOG| EXO TRANSITION STATE]]

[[Media: ENDO_4_TS_B3LYP_jd2615.LOG| ENDO TRANSITION STATE]]

[[Media: PRODUCT_MINIMISE_B3LYP_jd2615_ENDO_3.LOG| ENDO PRODUCT]]

[[Media: EXO_B3LYP_PRODUCT_jd2615_T2.LOG| EXO PRODUCT]]

==Exercise 3==
===Computational methods===
For each reaction in this exercise, the starting materials were optimized to a minimum using semi-empirical PM6. The products were also optimized using this technique. Once the product was optimized, the bonds between the Xylylene and the sulfer dioxide were removed, moved slightly apart but still within the Van der Waals radius, and frozen using redundant coordinates. This structure was optimized to a miniumum using semi-empirical PM6 to minimise a transition state-like structure. The minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using semi-empirical PM6.

===Reaction Scheme===

This experiment investigates the Diels-Alder reaction between o-Xylylene and Sulpher Dioxide. Unlike other Diels-Alder reaction, this reaction can go via a Chelotropic reaction which is a form of pericyclic reaction where, unlike the traditional Diels-Alder, both new bonds to the dienophile occur on a single atom (i.e. the Sulfer atom). This exercise seeks to rationalise which of the three potential products from this reaction could be the most stable.
{|style="margin: 0 auto;"
| [[File:Reaction_Scheme_T3_jd2615.jpg|400px|thumb|left| Reaction Scheme of o-Xylylene and Sulfer dioxide. Top Scheme shows the formation of the ENDO and EXO Diels-Alder product. Bottom Scheme shows the formation of the Cheletropic product - click to view]]
|}

The mechanism for the Cheletropic pericyclic reaction is a product of the sulfer being both electrophilic and nucleophilic, where the lone pair on the sulfer attacks the o-Xylylene.

{|style="margin: 0 auto;"
| [[File:Cheletropic_IRC_jd2615.PNG|400px|thumb|left| IRC plot of Cheletropic reaction of sulfer dioxide and o-Xylylene]]
| [[File:Cheletropic_IRC_animation_jd2615.gif|400px|thumb|left| IRC animation of Cheletropic reaction of sulfer dioxide and o-Xylylene]]
|}
{|style="margin: 0 auto;"
| [[File:ENDO_IRC_j2615_T3_1.PNG|400px|thumb|left| IRC plot of ENDO reaction of sulfer dioxide and o-Xylylene]]
|[[File:Endo_IRC_animation_jd2615.gif|400px|thumb|left| IRC animation of ENDO reaction of sulfer dioxide and o-Xylylene]]
|}

{|style="margin: 0 auto;"
| [[File:EXO_IRC_jd2615.PNG|400px|thumb|left| IRC plot of EXO reaction of sulfer dioxide and o-Xylylene]]
| [[File:EXO IRC animation jd2615.gif|400px|thumb|left| IRC animation of EXO reaction of sulfer dioxide and o-Xylylene]]
|}

The IRC for all these reactions shows that the energy barrier is very low. This can be rationalised by looking at the electronic structure of the six membered ring. The reaction results in formation of a stable aromatic benzene ring which is a lot more stable than the diene structure before, this results in a low activation and a much more stable product.

===Thermodynamics and kinetics of reaction===
{|style="margin: 0 auto;"
| [[File:rate_constants_T3_jd2615.jpg|400px|thumb|left| Figure showing the conversion of the starting materials to either the Cheletropic or ENDO/EXO Diels-Alder product. The length of the arrow represents how readily the product forms. k2 is greater than k1, thus showing that the Cheletropic reaction forms the thermodynamic product. <ref name=Sordo />]]
|}
From analysis of the thermochemistry extracted from the data produced by the calculation, it is evident that the thermodynamic product is the cheletropic product.

{|style="margin: 0 auto;"
| [[File:ENDO EXO energies jd2615.jpg|400px|thumb|left| Relative energies of the species formed during the ENDO/EXO Diels-Alder reaction]]
| [[File:cheletropic_energies_jd2615.jpg|400px|thumb|left| Energies of the species formed during the Cheletropic reaction]]
|}

The above plots show the relative energies of each species during the reaction of o-Xylylene and sulfer dioxide. From the calculated energies, the Cheletropic product is the thermodynamic product as a result of the more stable 5-membered ring, but it shows a large transition state energy, whereas both Diels-Alder products are the kinetic products. As with all Diels-Alder mechanisms, the kinetic stability of the endo transition state is a result of the interaction of the pi bond from the non-reacting S-O bond interacting with the p orbitals of the diene, as this S-O bond sits in the correct geometry. The non-reacting S-O bond points away from the diene, thus preventing any pi-p secondary interactions. There are no secondary orbital interactions for the cheletropic reaction, so that results in a higher energy transition state. When comparing the transition states for the Diels-Alder and Cheletropic, the six membered transition state shows less ring strain, thus causing stabilisation. The 5 membered transition state has greater ring strain, so is higher in energy.

Work by Jose Sordo <ref name=Sordo> Jose A. Sordo, ''Sulfer Dioxide Promotes Its hetero-Diels-Alder and Cheletropic Additions to 1,2-Dimethylidenecyclohexane'', J. Am. Chem. Soc, 1998, 120, 13276-13277 </ref> showed that during this mechanism, an external sulfer dioxide group is involved in the stability of the transition state and also provides an energy compensation for the free energy loss as a result of the decrease in entropy as two molecules form one.<ref name=Sordo />
{|style="margin: 0 auto;"
| [[File:Stabalising_effect_jd2615.PNG|400px|thumb|left|Structure described in the literature which is being investigated for stabilization effects on the transition state (represented with a dotted line).]]
|}
The image above shows the conformation of the accessory sulfer dioxide, where the dashed lines represent the stabalising interaction. A further calculation was set up to determine if the Sulpher dioxide had a stabilization effect on the transition state. In the literature it states that an MP2/6-31G calculation was set up, however a b3lyp/6-31G(d) calculation was used.<ref name=Sordo /> The amount of time it took for the calculation to complete meant that it was impractical to run to completion. The transition state with frozen bonds was successfully calculated. However; the optimization to transition state (Berny) took too long to optimize, but the following intermediate structures were formed, below:

{|style="margin: 0 auto;"
| [[File:TS vid E jd2615.gif|500px|thumb|left| Animation to show the non-convergence of the transition state. The sulfer dioxide remains in the area suggesting some degree of stability, but further work is still required]]
|}

From visual analysis, the calculation passes the previous transition state, bonding the Sulfer dioxide and diene together. The accessory sulfer dioxide remains in the same place, just changing it's orientation with respect to the conformation of the main molecule. However, if the position of the extra molecule was very unfavorable, it would rapidly change it's position, either towards or away from the Diels-Alder product. This observation suggests that the position of this molecule is relatively stable, however further experiment would be required with more time and computing power. The result of this experiment also suggests that the b3lyp may be inadequate for this type of calculation, so further experiments would require the reproduction of the literature method by using MP2/6-31G.<ref name=Sordo />

(Unfortunately MP2/6-31g(d) is also inadequate for this type of calculation. The gradient will be extremely small when looking at non-bonding interactions, making optimisations very difficult as you found above [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:27, 4 April 2018 (BST))

===Other potential Diels-Alder reactions===
The ENDO-site Diels-Alder reaction is as follows:
{|style="margin: 0 auto;"
| [[File:Reaction_Scheme_T3_EE_jd2615.jpg|400px|thumb|left| Reaction Scheme at for the ENDO-site Diels-Alder reactions]]
|}

Here the Sulfer dioxide reacts with the diene that is constituent of the six membrered ring. As with most Diels-Alder reactions, this reaction can either be ENDO or EXO with respect to the position of the non-reacting sulfer-oxygen bond.

{|style="margin: 0 auto;"
| [[FILE:IRC_EXO_T3_EE_pic.PNG|400px|thumb|left|IRC plot for EXO product at ENDO-site]]
| [[File:IRC_EXO_T3_EE_vid.PNG|400px|thumb|left|IRC animation for EXO product at ENDO-site]]
|}
{|style="margin: 0 auto;"
| [[File:IRC_TS_T3_EE_ENDO_PIC.gif|400px|thumb|left|IRC plot for ENDO product at ENDO-site]]
| [[File:IRC_vid_EE_jd2615_ENDO.gif|400px|thumb|left|IRC animation for ENDO product at ENDO-site]]
|}

The above IRCs represent the reaction coordinate of this reaction of Sulpher dioxide at this particular site of the diene. From analysis of this, the transition state and the product formed will be higher in energy because neither species are aromatic, unlike the reaction on the EXO-site (outside the 6 membered ring) of the molecule. The absence of aromaticity means the molecule is less stable compared to the EXO product.

{| class="wikitable"
|-
!
! Transition State / kJ/mol
! Product / kJ/mol
|-
| ENDO
| 267.98
| 172.25
|-
| EXO
| 275.82
| 176.68
|}

The lack of aromaticity of the transition state and the products is reflected in much higher energy values when compared to the EXO-site compounds. Again, the ENDO transition state is lower than the EXO because of the secondary p-pi orbital interaction between the oxygen on the alkene and the and pi orbitals of the diene (mentioned in previous sections).

===Log Files===
[[Media: SO2_MIN_jd2615.LOG| SULFER DIOXIDE]]

[[Media: XYLYLENE_jd2615.LOG| XYLYLENE]]

[[Media: EXO PM6 TS jd2615.LOG| EXO-SITE EXO TRANSITION STATE]]

[[Media: END PM6 TS1 jd2615.LOG| EXO-SITE ENDO TRANSITION STATE]]

[[Media: EXO_PM6_MIN_JD2615.LOG| EXO-SITE EXO PRODUCT]]

[[Media: END_PM6_MIN1_JD2615.LOG| EXO-SITE ENDO PRODUCT]]

[[Media: PRODUCT_EXO_TS_EE_JD2615.LOG| ENDO-SITE EXO TRANSITION STATE]]

[[Media: PRODUCT_TS_ENDO_EE_JD2615.LOG| ENDO-SITE ENDO TRANSITION STATE]]

[[Media:PRODUCT_EXO_MIN_JD2615_EE.LOG| ENDO-SITE EXO PRODUCT]]

[[Media: PRODUCT_OPT_EE_JD2615_ENDO.LOG| ENDO-SITE ENDO PRODUCT]]

Extension Log files: Failed to converge

[[Media: TS_BERRY_EXTRA_jd2615.LOG| Extension with accessory sulfer dioxide molecule]]

=Extension=
===Computational methods===
The product was optimized to a minimum using semi-empirical PM6. The length of the sigma bond formed during the reaction was increased and the bond was removed, where the new positions are frozen using redundant coordinates. This structure was optimized to a miniumum using semi-empirical PM6 to minimise a transition state-like structure. The minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using semi-empirical PM6.

===Hypothesized reaction===
Electrocyclic reactions can be distinguished according to whether they are conrotatory or disrotatory. Huckel theory describes the requirements for thermal and photochemical electrocyclic ring closures. The following reaction is being investigated to determine it's reaction coordinate and the orbital dynamics of the transition state:
{|style="margin: 0 auto;"
| [[File:Reaction_Scheme_jd2615.jpg|400px|thumb|left|Extension reaction scheme]]
|}

For a thermal reaction with 4 pi electrons, Huckel theory states that if the reaction is to proceed via a Huckel transition state, the sigma bond forms via disrotatory motion of the p orbitals at the end of the diene which are in an antarafacial arrangement:

(Not Hückel theory. Also, it would undergo conrotation [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:34, 4 April 2018 (BST))

{|style="margin: 0 auto;"
| [[File:Disrotatory_jd2615.jpg|400px|thumb|left|Suprafacial, disrotatory motions of p orbitals]]
|}

The transition state and IRC was optimised using PM6, semi empirical method. The following transition state was optimised which provided the transition state vibration represented with the negative frequency:

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(This is conrotation [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:34, 4 April 2018 (BST))

==IRC Calculation==

{|style="margin: 0 auto;"
| [[File:IRC_path_E_jd2615.PNG|400px|thumb|left| IRC plot for electrocyclic ring closure]]
|[[File:Extension_IRC_jd2615_2.gif|400px|thumb|left| IRC animation for electrocyclic ring closure]]
|}

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The orbital of interest in the transition state is the LUMO. the twist in the molecular orbitals of the state result in a mobius aromaticity where molecular orbital follows the topology of a mobius strip, thus Huckel theory cannot be used to describe this species. In a mobius transition state, a thermal 4 electron system is antarafacial, conrotatory <ref name = rzepa> Henry S. Rzepa ''The Aromaticity of Pericyclic Reaction Transition States'', J. Chem. Educ., 2007, 84, 1535 </ref>:

{|style="margin: 0 auto;"
| [[File:Antarafacial jd2615.jpeg|400px|thumb|left| Antarafacial, conrotatory motion of p orbitals]]
|}

{|style="margin: 0 auto;"
| [[File:Mobius_strip_jd2615.PNG|400px|thumb|left| Mobius topology of p orbitals forming Mobius aromaticity]]
| [[File:Huckle strip jd2615.PNG|400px|thumb|left| Symmetrical arrangement of p orbitals forming Huckel aromaticity]]
|}

The above figure represents the mobius topology where each p orbital has a slight rotation when compared to it's adjacent partner, resulting in an aromatity that forms a loop with a half twist, unlike the huckle aromatic transitions state that shows no twist, just two symmetrical planes.<ref name = rzepa /> This diene complex undergoes the same principle where the pi-p orbitals involved in the butadiene undergo a disrotatory twist where the resulting transition state has mobius aromaticity, which is thermally allowed according to rules outlined in a publication by Henry S Rzepa which stated that a 4 pi pericyclic reaction can occur thermally as long as the p orbital arrangement forms a stable mobius aromatic species.<ref name = rzepa /> Further work in Henry S Rzepa's publication outlined interesting comparisons between the mobius and Huckel aromaticity, one being that the ideal mobius strip has only C2 symmetry, thus the absence of further symmetry means the mobius aromatic transition has a non-superimposible mirror image, unlike the Huckel which has a superimposible mirror image.<ref name = rzepa />

===Log Files===
[[Media:E1_MIN+PM6_4_jd2615.LOG| Extension product]]

[[Media:E1 TS+PM6 2 jd2615.LOG| Extension transition state]]

=Conclusion=
This experiment has attempted to rationalise the synthetic difference in yield by describing orbital interactions and their energies with the use of computational techniques. Exercise one saw the most basic Diels-Alder reaction of butadiene and ethylene. This experiment was useful in determining the standard MO diagram for this reaction, showing the primary interactions without any influence from functionality of the different reactants with no secondary interactions forming ENDO or EXO products. It showed the importance of symmetry of the interacting orbitals, where only orbitals of the same symmetry interact, and different symmetry orbital interactions lead to an overlap integral of zero.

The second experiment introduced functionality to the starting materials by reacting 1,3-dioxole and cyclohexadiene. This experiment showed how position of the dienophile with respect to the diene results in different products formed through secondary interactions. The ENDO product always has a lower energy transition state as the p orbitals of the oxygen on the dienophile interacts with the p orbitals on C2 and C3 of the diene (See 'bond distances' in 'Exercise 1'), causing a stabalising interaction. Further consequences of the oxygen in the dienophile is that it feeds electron density into the alkene which results in an inverse Diels-Alder reaction, where the HOMO of the dienophile is lower than HOMO of the diene.

The third experiment introduced a non-carbon based dienophile to undergo a hetero Diels-Alder reaction. Firstly the EXO site (non-carbon ring diene) of the molecule was explored. Other than both the ENDO and EXO product, this reaction saw the cheletropic reaction where the sulfer atom reacts as both the nucleophile and electrophile, where both new sigma bonds are formed on the same atom (i.e. the sulfer atom). This experiment showed that the cheletropic reaction formed the thermodynamic product as a result of the more stable 5 membered ring structure, while showing the highest transition state energy due to increased ring strain of the transitions species. Further experiments were undertaken to investigate the effects of an accessory sulfer dioxide molecule on the transition state energy (experiment inspired by literature). This experiment was inconclusive as the transition state failed to converge. Further work could could be done with more time and computing power conclude this experiment. The ENDO site (carbon ring diene) was then investigated. This showed that the transition state energy and the product energy were much higher than those of the ENDO-site products. This was a result of the lack of aromaticity of the TS and products, thus being less stable and higher energy.

The extension exercise explored the electrocyclic ring closure of a diene under thermal conditions. It was expected that the reaction coordinate would proceed via a disrotatory motion of the diene's p orbitals to form a sigma bond between the end of the diene, where the transition state was stabalised by the symmetrical huckel aromaticity. However, from analysis of the HOMO orbitals of the TS, the state was stabalised by a mobius loop aromaticity formed through the slight rotation of p orbitals with respect to it's adjacent partner, resulting in a conjugation with a mobius topology. For a mobius transition state with 4n pi electrons, the reaction must proceed via a conrotatory motion of the p orbitals to form a sigma bond between the end of the diene.

Computation techniques have proven effective at representing these structures. However in the light of the extension where an accessory sulfer dioxide molecule can have an influence on the stability of a transition state, it is felt that further experiments need to be done including many molecule systems before a fair comparison between computed energies and synthetic yield can be correlated.

=References=

Rep:Yg5515ts

2018-04-07T11:17:56Z

Fv611: /* MO analysis */

==3rd Year Computational Lab---Transition states and Reactivity==
In this Lab, the transition states (TS) of three Diels-Alder (DA) reactions were located and characterized by Gaussian.DA reactions play an important role in numerous new materials and natural products
Method 3 was adopted to locate the transition state. The procedure started from the optimized structure of either the reactant or the product, then the lengths of bonds which were involved in the reaction were adjusted and freezed to resemble that of the transition structure. The guessed transition state was optimized and checked with frequency calculations and intrinsic reaction coordinate(IRC).
===Introduction===
Computational quantum chemistry has provided an efficient way to compute experimental complex and expensive experiments. Computational method is able to offer useful information of molecular geometries and properties, and reaction kinetics and energetic, and orbitals as well.
In this lab, the reactivities of three DA reactions were explored by locating and characterizing the transition states from the PES. PES characterizes how the total potential energy varied as a function of the positions of nuclei geometry. Gaussian operates based on the Born-Oppenheimer approximation,which assumed that the nuclei are fixed in positions and electrons adjusts instantaneously to any movement of the nuclei. Gaussian investigates the electron distributions in accordance to the changes of nuclei geometries. For a molecule with N atoms, there are (3N-6) independent geometry variables which equal to the number of internal motions a molecule may have. <ref> Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207).</ref>

Minimum energy point is the stationary point on the PES and it is defined by the zero value of the first derivative. At the stationary point, the change of potential energy with respect to all 3N-6 coordinates is zero.

<math>\frac{\partial E_r}{\partial r}</math>= = -F(R) = 0

[[File:TS diagram.png|frame|center|400px|Figure 1 illustrates the reaction pathway from one energy minima to another via going through a transition state. The energy minima is a stationary point at which energy goes up in any directions on the PES, whereas transition state is a saddle point at which energy goes up in any directions apart from the coordinate aligned with the reaction pathway shown as the blue arrow in the figure ]]

The "opt" in job type served as molecular geometry optimization in Gaussian, which can be applied to search the local minimum on the PES by employing mathematical algorithms.

Although the optimization can help us to find stationary point, but it cannot provide further information to identify whether the stationary point is a energy minima or a stationary saddle point. A stationary saddle point lies at the maximum for only one coordinate which is the reaction coordinate and all the others lie at the minimum.To distinguish whether the stationary point is a energy minima or a transition state,the curvature of the PES around the stationary point need to be determined and therefore frequency calculations are required. It can be done by explore the second derivatives, which is the force constant.

<math>\frac{\partial^2 E_r}{\partial^2 r}</math>= = -F(R) = 0

The transition state is defined to satisfy the following relationship:

<math>\frac{\partial^2 E_r}{\partial r^2}</math> > 0 with one coordinate of <math>\frac{\partial^2 E_r}{\partial r^2}</math> < 0
This is manifested by the vibrational frequency analysis. There should be only one imaginary frequency for a transition state and zero for that of an energy minima.

The computational methods used in this lab were semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP. PM6 was fast and relatively inaccurate compared with B3LYP. To carry out B3LYP, chemical species were optimized on PM6 level first.

===Exercise 1 Reaction of Butadiene with Ethylene===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You are missing the discussion on the mechanism of bond formation, and are not showing the vibration corresponding to the bond forming mode. Additionally, your MO diagram is wrong: you are not at all taking into account the computed relative energies of your MOs.)
====reaction scheme====

[[File:ex1 mechanism.png|frame|center|400px|Figure.2 The reaction scheme of the [4+2] cycloaddition of butadiene with ethylene ]]

Current mechanism studies showed controversies in determining whether the reaction was proceeded via a one step concerted or a stepwise mechanism. In this exercise, the concerted TS was located by employing the method 3 with a frequency calculation. Reactants, the product and the transition state were all optimized by PM6.

====Optimization at PM6 level====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 1. Optimisation of Reactants, Product and transition state(PM6)'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethlyene
| style="text-align: center;" |transition state
| style="text-align: center;" |Cyclohexene
|-
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|<jmol>
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<uploadedFileContents>Yihan ethylene.LOG</uploadedFileContents>
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<uploadedFileContents>Yihan TS PM6.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
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====Frequency calculation and IRC====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 2. Frequency calculation and IRC for TS'''
|-
| style="text-align: center;" |Frequency calculation
| style="text-align: center;" |IRC(Total Energy)
| style="text-align: center;" |IRC(RMS Gradient Norm)
| style="text-align: center;" |reaction progress
|-
| [[File:Yihan ex1 TS freq.PNG]]
| [[File:Yihan ex1 IRC1.PNG]]
| [[File:yihan ex1 IRC2.PNG]]
| [[File:Yihan ex1 IRC movie.gif]]
|}
The frequency calculation showed that the PM6 optimized transition state has one imaginary frequency at -949.cm<sup>-1</sup>. An IRC analysis was done for confirmation. IRC followed a minimum energy pathway on the PES from the transition state to either the product or the reactant. In this experiment, an IRC path starting from the transition state to reactant was simulated. TS was successfully located and optimized because the energy gradients were at zero at the reactants , product and the TS.

====MO analysis====
[[File:Yihanex1MO.PNG|frame|center|100px|Figure 5, MO diagram of 1 reacting with 2. A represents asymmetric orbital label and S represents symmetric orbital label. HOMO is the highest occupied nolecular orbital and LUMO is the lowest occupied molecular orbital]]

{| class="wikitable"
| colspan="5" style="text-align: center; background: #f0ddf0" | '''Table 3. MO display of key orbitals (HOMO and LUMO) '''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethlyene
| style="text-align: center;" |TS occupied orbitals (in phase interaction)
| style="text-align: center;" |TS unoccupied orbitals (out of phase interaction)
|-
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 26; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yihan butadiene.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<title>S MO9(HOMO)</title>
<size>200</size>
<script>frame 38; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yihan ethylene.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<title>S MO6(HOMO)</title>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yihan TS PM6.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<title>S MO7(LUMO)</title>
<size>200</size>
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<uploadedFileContents>Yihan TS PM6.LOG</uploadedFileContents>
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|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>S MO3 (LUMO)</title>
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<uploadedFileContents>Yihan butadiene.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<title>A MO10 (LUMO)</title>
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|<jmol>
<jmolApplet>
<color>white</color>
<title>A MO5</title>
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<uploadedFileContents>Yihan TS PM6.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<title>A MO8</title>
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<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yihan TS PM6.LOG</uploadedFileContents>
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|}

Generally, molecular orbitals interact according to a set of rules.Firstly, only the MO which have the correct symmetry and close in energy tend to have large interactions. For example, the symmetric orbitals will interact with symmetric orbitals with non zero orbital overlap. This is also true for antisymmetric orbitals. However, orbital overlap is zero if symmetric orbital is combined with antisymmetric orbitals. In addition, HOMO and LUMO is a pair of occupied and unoccupied orbitals which closet in energy, therefore, the antisymmetric HOMO of butadiene (MO2) interacted strongly with the antisymmetric LUMO of enthylene, generating antisymmetric MO5 (bonding) and MO8 (antibonding). Also, the symmetric LUMO of butadiene (MO2) interacted strongly with the symmetric HOMO of enthylene, generating antisymmetric MO6 (bonding) and MO7 (antibonding). The occupied MO5 and MO6 of TS were resulted from in phase combination of the corresponding reactants' MO, whereas the occupied MO are generated by out of phase interactions.

{| class="wikitable"
| colspan="3" style="text-align: center; background: #f0ddf0" | '''Table 4. summary of orbital integrals'''
|-
|
| style="text-align: center;" |antisymmetric orbital
| style="text-align: center;" |symmetric orbital
|-
| style="text-align: center;" |antisymmetric orbital
| style="text-align: center;" |non zero
| style="text-align: center;" |zero
|-
| style="text-align: center;" |symmetric orbital
| style="text-align: center;" |zero
| style="text-align: center;" |non zero
|}
The reaction is a [4+2] cycloaddition. Woodward-Hoffmann rule is the commonly applied to analyze the orbital symmetry requirement for DA reactions.
In a thermal pericyclic reactions, the total number of (4q+2)s and (4r)a components need to be odd. s stands for suprafacial and a stands for antarafacial. As for suprafacial components, new bonds form on the same face at both ends, whereas an antarafacial component form new bonds at opposite faces.
[[File:Yihan woodward.PNG|frame|center|400px|Figure 3 butadiene is a suprafacial component with four π electrons and the ethylene is also a suprafacial component with two π electrons]]

There is totally one component fit the (4q+2)s and (4r)a , therefore the reaction is allowed.

====Carbon bond lengths====
Keeping track of the changes of carbon bond lengths as the reaction progressed can provide useful information of the structure of the transition states , at which bonds are partially broken and formed.
The hybridizations of the carbon atoms involved in the reaction have changed during the reaction. Therefore, the bond length also changed because it depended on the type of hybridization. The more s character the bond has, the stronger the electrons are hold to the nuclei thus the bond becomes shorter. sp2 hybridization has more s character than sp3 hybridization, so sp2-sp2 C-C is expected to be shorter than that of sp3-sp3 C-C. In addition, double bonds are shorter and stronger than single bonds, because the additional bonding attracted the nuclei stronger, pulling them closer.

{| class="wikitable"
| colspan="2" style="text-align: center; background: #f0ddf0" | '''Table 5. summary of carbon bond lengths'''
|-
| style="text-align: center;" |bond type
| style="text-align: center;" |bond length/Å
|-
| style="text-align: center;" |sp3-sp3 C-C
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |sp2-sp2 C-C
| style="text-align: center;" |1.47
|-
| style="text-align: center;" |sp2-sp3 C-C
| style="text-align: center;" |1.5
|-
| style="text-align: center;" |sp2-sp2 C=C
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |vand der wal
| style="text-align: center;" |1.7
|}
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 6. experimental bond length of reactants, product and transition state'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |transition state
| style="text-align: center;" |cyclohexene
|-
|[[File:Yihan diene labell.PNG|400px]]
|[[File:Yihan alkene label.PNG|350px]]
|[[File:YihanTS label.PNG]]
|[[File:Yihan Pdt label.PNG]]
|-
| style="text-align: center;" |C1-C2:1.47
C1-C4:1.34

C2-C3:1.34

| style="text-align: center;" |C1-C2:1.33
| style="text-align: center;" |C1-C2:1.38
C2-C3:1.41

C3-C4:1.38

C5-C6:1.38

C1-C6:2.11

C4-C5:2.11
| style="text-align: center;" |C1-C2:1.49
C1-C6:1.54

C6-C5:1.54

C4-C5:1.54
|}

{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" |'''Table 7. explanation of bond lengths of the transition state'''
|-
| style="text-align: center;" |bond number
| style="text-align: center;" |bond type changes
| style="text-align: center;" |explanation
|-
|C1-C2/C3-C4
|sp2-sp2 C=C to sp3-sp2 C-C
| 1.38 lies in the middle of the sp2-sp2 C=C (1.34) and sp3-sp2 C-C(1.5). The bond was lengthened to form a sp3-sp2 C-C bond
|-
|C2-C3
|sp2-sp2 C-C to sp2-sp2 C=C
|the bond was shortened to form a sp2-sp2 C=C
|-
|C1-C6
|non-bonding to sp3-sp3 C-C
|The sum of two carbon atoms' van der wal radii is 3.4Å, within which electrostatic attraction started to form, or in other words, a partial bond formed. The bond length is approximately the mean of the sum of two carbon atom's van der wal radii and the sp3-sp3 C-C.
|}

===Exercise 2 Reaction of Cyclohexadiene and 1,3-Dioxole===
====reaction scheme====

[[File:Exercise 2Reaction scheme.PNG|frame|center|400px|]]

As shown in the reaction scheme, this DA reaction can proceed via two pathways ,leading to either endo or exo products depending on the orientation of 1,3-Dioxole in the TS. In this exercise, the reactants, products and both the endo and exo TS were optimized on a B3LYP/6-31G(d) level. A MO and thermochemical analysis were also conducted.

The TS were located and characterized by employing Method 3 in the Tutorial. Firstly, the product was optimized. The bonds which were involved in the reaction were broken, altered and freezed to make the structure resemble the TS. Then the coordinates were unfreezed and the TS were optimized by B3LYP/6-31G(d). All the structures were firstly optimized on a fast and rough PM6 level then optimized by the slow and more accurate B3LYP/6-31G(d) method.

====Optimization of reactants and products====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 8. B3LYP/6-31G(d) Optimisation of reactant and products'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |1,3-Dioxole
| style="text-align: center;" |product(endo)
| style="text-align: center;" |product (exo)
|-
|<jmol>
<jmolApplet>
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<uploadedFileContents>Yihan reactant 1.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 44</script>
<uploadedFileContents>YihanREACANT 2 OPT.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 18</script>
<uploadedFileContents>YihanPRODUCT ENDO OPT.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6</script>
<uploadedFileContents>YihanPRODUCT EXO OPTIMIZED.LOG</uploadedFileContents>
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====TS optimization and characterization====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 9. B3LYP/6-31G(d)Optimisation of TS, frequency analysis and IRC'''
|-
|
| style="text-align: center;" |TS (endo)
| style="text-align: center;" |TS (exo)
|-
|optimized structure
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 30</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
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|-
|frequency analysis
|[[File:Yihan ex2Endo TS freq.PNG]]
|[[File:Yihan ex2Exo TS freq.PNG]]
|-
|IRC(total energy)
|[[File:YihanEndo IRC total E.PNG|400px]]
|[[File:YihanExo IRC total E.PNG|400px]]
|-
|IRC( RMS gradient norm)
|[[File:YihanEndo IRC g.PNG|400px]]
|[[File:YihanExo IRC g.PNG|400px]]
|-
|reaction progress
|[[File:Yihan ex2Endo movie.gif]]
|[[File:Yihan ex2Exo movie.gif]]
|}

Both endo and exo TS have only one imaginary frequencies. The convergences in the log file were checked. The geometries of the optimized TS were consistent with the structures of their corresponding products. IRC analysis showed that the TS were successfully located because the energy gradients were zero.

====MO analysis====

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) As before, your MO diagrams are wrong.)

|[[File:YihanMO 1endo.PNG]]
|[[File:YihanMO exo.PNG]]

{| class="wikitable"
|colspan="5" style="text-align: center; background: #f0ddf0" | '''Table 10. HOMO and LUMO of reactants, products and TS'''
|-
|
|Cyclohexadiene
|1,3-Dioxole
|TS(endo)
|TS(exo)
|-
|HOMO
|<jmol>
<jmolApplet>
<color>white</color>
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<title>A, MO1</title>
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<uploadedFileContents>Yihan reactant 1.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S, MO7</title>
<script>frame 44; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanREACANT 2 OPT.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S, MO4</title>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S,MO12</title>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
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|-
|LUMO
|<jmol>
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|<jmol>
<jmolApplet>
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<title>A,MO8</title>
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<uploadedFileContents>YihanREACANT 2 OPT.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S,MO5</title>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
<title>S,MO13</title>
<size>250</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
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|}
{| class="wikitable"
|colspan="5" style="text-align: center; background: #f0ddf0" | '''Table 11.other key orbitals of TS '''
|-
|
|TS(endo)
|TS(exo)
|-
| HOMO-1
| <jmol>
<jmolApplet>
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<title>A,MO3</title>
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<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
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|-
|LUMO+1
| <jmol>
<jmolApplet>
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<title>A, MO6</title>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
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<title>A, MO14</title>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
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|}
The MO interactions occurred in the region of HOMO and LUMO.

{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 12. energy comparison of endo and exo products and TS by B3LYP/6-31G(d))'''
|-
|style="text-align: center;" |chemical species
|style="text-align: center;" |Sum of electronic and thermal Free Energiesy,Hartree
|style="text-align: center;" |kJ mol<sup>-1<sup>
|-
|style="text-align: center;" |Cyclohexadiene
|style="text-align: center;" |-233.3243
|style="text-align: center;" |-612593.14656
|-
|style="text-align: center;" |1,3-Dioxole
|style="text-align: center;" |-267.0686
|style="text-align: center;" |-701188.7195
|-
|style="text-align: center;" |TS(endo)
|style="text-align: center;" |-500.3321
|style="text-align: center;" |-1313622.0545
|-
|style="text-align: center;" |TS (exo)
|style="text-align: center;" |-500.3291
|style="text-align: center;" |-1313614.2305
|-
|style="text-align: center;" |product(endo)
|style="text-align: center;" |-500.4186
|style="text-align: center;" |-1313849.2732
|-
|style="text-align: center;" |product(exo)
|style="text-align: center;" |-500.4173
|style="text-align: center;" |-1313845.6730
|}

The MO energies were checked with single point energies. It was observed that both the endo TS and endo product were more energetically stable than their exo counterpart. This is due to the extra stabilization resulted from the secondary orbital interactions.

{| class="wikitable"
| colspan="2" style="text-align: center; background: #f0ddf0" | '''Table 13. comparison of orbital interactions of the HOMO of endo and exo TS '''
|-
|style="text-align: center;" |TS endo
|style="text-align: center;" |TS exo
|-
|[[File:YihanEndo orbital.PNG|200px]]
|[[File:YihanExo orbital.PNG|200px]]
|}
The reaction barriers were calculated as the energy differences between the total energy of reactants and the TS. Reaction energies, i.e. ΔG, was the energy differences between the reactants and products.
{| class="wikitable"
| colspan="3" style="text-align: center; background: #f0ddf0" | '''Table 14. Activation energy and ΔG for endo and exo reaction pathways'''
|-
|
|style="text-align: center;" |Activation energy,kJ mol<sup>-1<sup>
|style="text-align: center;" |ΔG,kJ mol<sup>-1<sup>
|-
|style="text-align: center;" |endo pathway
|style="text-align: center;" |159
|style="text-align: center;" |-68
|-
|style="text-align: center;" |exo pathway
|style="text-align: center;" |167
|style="text-align: center;" |-64
|}

The four red p orbitals indicated in the diagram are involved in the secondary orbital interaction. There are significant interactions between the non bonding orbitals of the oxygen atoms and the p orbitals of the diene component.The four p orbitals combined in phase. As the endo transition state was stabilized, the energy barrier for endo pathway was expected to be smaller than that of the exo pathway. Therefore, the activation energy of endo pathway was lower and ΔG was more negative. Overall, in combination of the single energy analysis, the endo products are both the kinetically stable and thermaldynamically stable products.

====Normal or Inverse electron demand====
According to the energy differences between the LUMO and HOMO pairs of the reactants and products, DA reactions are classified as two types:
Normal electron demand: electron deficient dienophile with low energy LUMO and the electron rich diene with high energy HOMO
Inverse electron demand: electron rich dienophile with high energy LUMO and the electron difficient diene with low energy HOMO

{| class="wikitable"
| colspan="3" style="text-align: center; background: #f0ddf0" | '''Table 15 Energy difference of different LUMO and HOMO pairs'''
|-
|
|style="text-align: center;" |HOMO energy/a.u.
|style="text-align: center;" |LUMO energy/a.u
|-
|style="text-align: center;" |Cyclohexadiene
|style="text-align: center;" |-0.20554
|style="text-align: center;" |-0.01711
|-
|style="text-align: center;" |1,3-Dioxole
|style="text-align: center;" |-0.19594
|style="text-align: center;" |+0.03795
|}

ΔE of HOMO (Cyclohexadiene) and LUMO (1,3-Dioxole):0.243
ΔE of HOMO (1,3-Dioxole) and LUMO (Cyclohexadiene):0.179

The closer the energies of two molecular orbitals, the larger the interactions. The energy difference between the HOMO of cyclohexadiene and LUMO of 1,3-Dioxole, therefore, this DA reaction has an inverse electron demand. 1,3-Dioxole has high energy LUMO because the lone pairs of the two oxygen atoms have the ability to donate electrons into the π cloud, raising the orbital energies.

===Exercise 3 o-Xylylene-SO2 Cycloaddition===
====reaction scheme====
[[File:Ex3 Reaction scheme.png|700px]]

The reaction of o-Xylylene and SO2 can proceed via two pathways, DA and cheletropic. The DA reactions can go through both endo and exo transition state to the sultine product. The TS is a six membered heteroaromatic ring with 6 π electrons involved. The cheletropic reaction is a separate class of pericyclic reactions, they must also obey the Woodward Hoffmann rules. According to the selection rules for cheletropic reactions, o-Xylylene and SO2 reacted through a disrotatary fashion which the HOMO of the S atom pointed directly to the π system of the o-Xylylene, because the π system has 4n+2 π electrons. The TS is a five membered heteroaromatic ring with also 6 π electrons.<ref>Woodward, R.B.; Hoffman, R. Angew. Chem. Int. Ed. Engl. 1969, 8, 781–853.</ref>

====PM6 optimization====
The reactants, products and TS were optimized on PM6 level and the TS s were located by Method 3. Products were firstly optimized. Then, the bonds involved in the reaction were broken ,frozen and optimized to obtain a guessed TS stucture. The coordinated were unfrozed and optimized again to obtain the accurate TS structure.
{| class="wikitable"
| colspan="2" style="text-align: center; background: #f0ddf0" | '''Table 16 PM6 optimization of reactants'''
|-
|style="text-align: center;" |o-Xylylene
|style="text-align: center;" |SO2
|-
|<jmol>
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<uploadedFileContents>Yihan o-Xylylene.LOG</uploadedFileContents>
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<uploadedFileContents>Yihan REACTANT SO2.LOG</uploadedFileContents>
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{| class="wikitable"
|colspan="3" style="text-align: center; background: #f0ddf0" | '''Table 17 PM6 optimization of endo and exo products and TS'''
|-
|
|style="text-align: center;" |products
|style="text-align: center;" |TS
|-
|style="text-align: center;" |endo
|<jmol>
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<script>frame 76</script>
<uploadedFileContents>ex3ENDO PRODUCT.LOG ‎</uploadedFileContents>
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<script>frame 26</script>
<uploadedFileContents>Yihan ex3 ENDO TS UNFREEZ.LOG</uploadedFileContents>
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|-
|style="text-align: center;" |exo
|<jmol>
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<uploadedFileContents>YihanEXOPRODUCT PM6.LOG</uploadedFileContents>
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<uploadedFileContents>Yihan ex3EXO TS3.LOG</uploadedFileContents>
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|-
|style="text-align: center;" |Cheletropic
|<jmol>
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(Your cheletropic TS and product geometries are wrong. The oxygen atoms are too close together and have bonded. Your exo geometries are actually endo [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:11, 4 April 2018 (BST))

====TS characterization====
IRC and frequency analysis were carried out to confirm a TS has been successfully located. All the IRC showed that the energy gradients were zero at reactants, transition states and products. All the reactions were proceeded via a concerted fashion. It was observed that the energies involved in the reaction were quite small compared with the reactions in exercise 1 and exercise 2 which was due to the high energy o-Xylylene. For both the endo and exo DA pathways, two single bonds were formed, i.e. C-S and C-O, meanwhile, two C=C were reduced to one C=C as well as the S=O. In cheletropic pathway, two C-S were formed and two C=C were reduced to one.<ref>Woodward, R.B.; Hoffman, R. Angew. Chem. Int. Ed. Engl. 1969, 8, 781–853.</ref>

{| class="wikitable"
| colspan="6" style="text-align: center; background: #f0ddf0" | '''Table 18 TS characterization of endo and exo pathways at PM6 level'''
|-
|
|style="text-align: center;" |reaction progress
|style="text-align: center;" |IRC(total energy)
|style="text-align: center;" |IRC(energy norm gradient)
|-
|style="text-align: center;" |endo
|[[File:Yihan ex3 DA endo.gif]]
|[[File:Yihan ex3Endo total E.PNG]]
|[[File:YihanEndo E gradient.PNG]]
|-
|exo
|[[File:Yihan ex3 DA exo.gif ]]
|[[File:Yihan Exo total E.PNG]]
|[[File:Yihan Exo E gradient.PNG]]
|-
|style="text-align: center;" |Cheletropic
|[[File:Yihan Chele IRC.gif]]
|[[File:YihanChele total E.PNG ]]
|[[File:YihanChele E gradient.PNG]]
|}
For all the chemical species, convergences were checked. As for the reactants and products, there were no imaginary frequencies present and for TS, there was only one imaginary frequency.

====Thermochemical analysis====

The energies of reactants, products and TS were obtained from the log files. Activation barriers and ΔG were calculated.
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 19. energy comparison of endo and exo products and TS by B3LYP/6-31G(d))'''
|-
|style="text-align: center;" |chemical species
|style="text-align: center;" |Sum of Electronic and Thermal Free Energies/Hartree
|style="text-align: center;" |kJ mol<sup>-1<sup>
|-
! o-Xylylene
| style="text-align: center;" | +0.179059
| style="text-align: center;" | +470.119
|-
! SO<sub>2</sub>
| style="text-align: center;" | -0.119268
| style="text-align: center;" | -313.496
|-
! Diels-Alder Exo TS
| style="text-align: center;" | +0.090559
| style="text-align: center;" | +240.286
|-
! Diels-Alder Endo TS
| style="text-align: center;" | +0.090559
| style="text-align: center;" | +237.762
|-
! Cheletropic TS
| style="text-align: center;" | +0.099377
| style="text-align: center;" | +260.914
|-
! Diels-Alder Exo Product
| style="text-align: center;" | +0.021700
| style="text-align: center;" | +56.973
|-
! Diels-Alder Endo Product
| style="text-align: center;" | +0.021696
| style="text-align: center;" | +56.963
|-
! Cheletropic Product
| style="text-align: center;" | +0.000006
| style="text-align: center;" | +0.0158
|}

(Your cheletropic energy is inconsistent with the Jmol and log file you've produced [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:11, 4 April 2018 (BST))

{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 20. Activation energies and reaction energies'''
|-
|
|style="text-align: center;" |Activation energy,kJ mol<sup>-1<sup>
|style="text-align: center;" |ΔG,kJ mol<sup>-1<sup>
|-
! endo pathway
| style="text-align: center;" | 81.139
| style="text-align: center;" | 99.66
|-
! exo pathway
| style="text-align: center;" | 83.663
| style="text-align: center;" | 99.65
|-
! cheletropic reaction
| style="text-align: center;" | 104.291
| style="text-align: center;" | 156.60
|}
Activation barriers were calculated by the differences between the sum of energies of two reactants and the TS. ΔG was obtained by calculating the differences between the free energies of reactants and products.
====reaction profile====
[[File:Yihan reaction profile.png|600px]]

It was assumed that the reactants have zero energies with infinite separations. The reaction profile showed relative height of the TS and products of the three reaction pathways. Cheletropic products were the thermodynamic products because they were most energetically stable. There were extremely small energy differences between the exo and endo transition states as well as the products. However, the endo products and TS were slightly more stable than that of the exo. Therefore, the kinetic and thermodynamic products were generated from the endo pathway.Apart from the steric interactions, favorouble orbital interactions also play a role in energy stabilization. The non bonding p orbitals of S=O interacts with the π system.

Files:
Ex1:

butadiene : [[File:Yihan butadiene.LOG]]

transition state: [[File:Yihan TS PM6.LOG]]

cyclohexene: [[File:Yihan cyclohexene.LOG]]

Ex2

Cyclohexadiene: [[File:Yihan reactant 1.LOG]]

1,3-Dioxole : [[File:YihanREACANT 2 OPT.LOG]]

endo product:[[File:YihanPRODUCT ENDO OPT.LOG]]

exo product : [[File:YihanPRODUCT EXO OPTIMIZED.LOG]]

Ex3

o-Xylylene: [[File:Yihan o-Xylylene.LOG]]

SO2: [[File:Yihan REACTANT SO2.LOG]]

Endo TS: [[File:Yihan ex3 ENDO TS UNFREEZ.LOG]]

Exo TS: [[File:Yihan ex3EXO TS3.LOG]]

Cheletropic product: [[File:Yihan chele PRODUCT.LOG]]

Cheletropic TS: [[File:Yihan chele TS.LOG]]

Exo product: [[File:YihanEXOPRODUCT PM6.LOG]]

Endo product: [[File:ex3ENDO PRODUCT.LOG]]

References
<references/>

Rep:Yg5515ts

2018-04-07T11:10:59Z

Fv611: /* Exercise 1 Reaction of Butadiene with Ethylene */

==3rd Year Computational Lab---Transition states and Reactivity==
In this Lab, the transition states (TS) of three Diels-Alder (DA) reactions were located and characterized by Gaussian.DA reactions play an important role in numerous new materials and natural products
Method 3 was adopted to locate the transition state. The procedure started from the optimized structure of either the reactant or the product, then the lengths of bonds which were involved in the reaction were adjusted and freezed to resemble that of the transition structure. The guessed transition state was optimized and checked with frequency calculations and intrinsic reaction coordinate(IRC).
===Introduction===
Computational quantum chemistry has provided an efficient way to compute experimental complex and expensive experiments. Computational method is able to offer useful information of molecular geometries and properties, and reaction kinetics and energetic, and orbitals as well.
In this lab, the reactivities of three DA reactions were explored by locating and characterizing the transition states from the PES. PES characterizes how the total potential energy varied as a function of the positions of nuclei geometry. Gaussian operates based on the Born-Oppenheimer approximation,which assumed that the nuclei are fixed in positions and electrons adjusts instantaneously to any movement of the nuclei. Gaussian investigates the electron distributions in accordance to the changes of nuclei geometries. For a molecule with N atoms, there are (3N-6) independent geometry variables which equal to the number of internal motions a molecule may have. <ref> Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207).</ref>

Minimum energy point is the stationary point on the PES and it is defined by the zero value of the first derivative. At the stationary point, the change of potential energy with respect to all 3N-6 coordinates is zero.

<math>\frac{\partial E_r}{\partial r}</math>= = -F(R) = 0

[[File:TS diagram.png|frame|center|400px|Figure 1 illustrates the reaction pathway from one energy minima to another via going through a transition state. The energy minima is a stationary point at which energy goes up in any directions on the PES, whereas transition state is a saddle point at which energy goes up in any directions apart from the coordinate aligned with the reaction pathway shown as the blue arrow in the figure ]]

The "opt" in job type served as molecular geometry optimization in Gaussian, which can be applied to search the local minimum on the PES by employing mathematical algorithms.

Although the optimization can help us to find stationary point, but it cannot provide further information to identify whether the stationary point is a energy minima or a stationary saddle point. A stationary saddle point lies at the maximum for only one coordinate which is the reaction coordinate and all the others lie at the minimum.To distinguish whether the stationary point is a energy minima or a transition state,the curvature of the PES around the stationary point need to be determined and therefore frequency calculations are required. It can be done by explore the second derivatives, which is the force constant.

<math>\frac{\partial^2 E_r}{\partial^2 r}</math>= = -F(R) = 0

The transition state is defined to satisfy the following relationship:

<math>\frac{\partial^2 E_r}{\partial r^2}</math> > 0 with one coordinate of <math>\frac{\partial^2 E_r}{\partial r^2}</math> < 0
This is manifested by the vibrational frequency analysis. There should be only one imaginary frequency for a transition state and zero for that of an energy minima.

The computational methods used in this lab were semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP. PM6 was fast and relatively inaccurate compared with B3LYP. To carry out B3LYP, chemical species were optimized on PM6 level first.

===Exercise 1 Reaction of Butadiene with Ethylene===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You are missing the discussion on the mechanism of bond formation, and are not showing the vibration corresponding to the bond forming mode. Additionally, your MO diagram is wrong: you are not at all taking into account the computed relative energies of your MOs.)
====reaction scheme====

[[File:ex1 mechanism.png|frame|center|400px|Figure.2 The reaction scheme of the [4+2] cycloaddition of butadiene with ethylene ]]

Current mechanism studies showed controversies in determining whether the reaction was proceeded via a one step concerted or a stepwise mechanism. In this exercise, the concerted TS was located by employing the method 3 with a frequency calculation. Reactants, the product and the transition state were all optimized by PM6.

====Optimization at PM6 level====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 1. Optimisation of Reactants, Product and transition state(PM6)'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethlyene
| style="text-align: center;" |transition state
| style="text-align: center;" |Cyclohexene
|-
|<jmol>
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<uploadedFileContents>Yihan butadiene.LOG</uploadedFileContents>
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====Frequency calculation and IRC====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 2. Frequency calculation and IRC for TS'''
|-
| style="text-align: center;" |Frequency calculation
| style="text-align: center;" |IRC(Total Energy)
| style="text-align: center;" |IRC(RMS Gradient Norm)
| style="text-align: center;" |reaction progress
|-
| [[File:Yihan ex1 TS freq.PNG]]
| [[File:Yihan ex1 IRC1.PNG]]
| [[File:yihan ex1 IRC2.PNG]]
| [[File:Yihan ex1 IRC movie.gif]]
|}
The frequency calculation showed that the PM6 optimized transition state has one imaginary frequency at -949.cm<sup>-1</sup>. An IRC analysis was done for confirmation. IRC followed a minimum energy pathway on the PES from the transition state to either the product or the reactant. In this experiment, an IRC path starting from the transition state to reactant was simulated. TS was successfully located and optimized because the energy gradients were at zero at the reactants , product and the TS.

====MO analysis====
[[File:Yihanex1MO.PNG|frame|center|100px|Figure 5, MO diagram of 1 reacting with 2. A represents asymmetric orbital label and S represents symmetric orbital label. HOMO is the highest occupied nolecular orbital and LUMO is the lowest occupied molecular orbital]]

{| class="wikitable"
| colspan="5" style="text-align: center; background: #f0ddf0" | '''Table 3. MO display of key orbitals (HOMO and LUMO) '''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethlyene
| style="text-align: center;" |TS occupied orbitals (in phase interaction)
| style="text-align: center;" |TS unoccupied orbitals (out of phase interaction)
|-
|<jmol>
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<uploadedFileContents>Yihan butadiene.LOG</uploadedFileContents>
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|<jmol>
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|-
|<jmol>
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<uploadedFileContents>Yihan butadiene.LOG</uploadedFileContents>
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Generally, molecular orbitals interact according to a set of rules.Firstly, only the MO which have the correct symmetry and close in energy tend to have large interactions. For example, the symmetric orbitals will interact with symmetric orbitals with non zero orbital overlap. This is also true for antisymmetric orbitals. However, orbital overlap is zero if symmetric orbital is combined with antisymmetric orbitals. In addition, HOMO and LUMO is a pair of occupied and unoccupied orbitals which closet in energy, therefore, the antisymmetric HOMO of butadiene (MO2) interacted strongly with the antisymmetric LUMO of enthylene, generating antisymmetric MO5 (bonding) and MO8 (antibonding). Also, the symmetric LUMO of butadiene (MO2) interacted strongly with the symmetric HOMO of enthylene, generating antisymmetric MO6 (bonding) and MO7 (antibonding). The occupied MO5 and MO6 of TS were resulted from in phase combination of the corresponding reactants' MO, whereas the occupied MO are generated by out of phase interactions.

{| class="wikitable"
| colspan="3" style="text-align: center; background: #f0ddf0" | '''Table 4. summary of orbital integrals'''
|-
|
| style="text-align: center;" |antisymmetric orbital
| style="text-align: center;" |symmetric orbital
|-
| style="text-align: center;" |antisymmetric orbital
| style="text-align: center;" |non zero
| style="text-align: center;" |zero
|-
| style="text-align: center;" |symmetric orbital
| style="text-align: center;" |zero
| style="text-align: center;" |non zero
|}
The reaction is a [4+2] cycloaddition. Woodward-Hoffmann rule is the commonly applied to analyze the orbital symmetry requirement for DA reactions.
In a thermal pericyclic reactions, the total number of (4q+2)s and (4r)a components need to be odd. s stands for suprafacial and a stands for antarafacial. As for suprafacial components, new bonds form on the same face at both ends, whereas an antarafacial component form new bonds at opposite faces.
[[File:Yihan woodward.PNG|frame|center|400px|Figure 3 butadiene is a suprafacial component with four π electrons and the ethylene is also a suprafacial component with two π electrons]]

There is totally one component fit the (4q+2)s and (4r)a , therefore the reaction is allowed.

====Carbon bond lengths====
Keeping track of the changes of carbon bond lengths as the reaction progressed can provide useful information of the structure of the transition states , at which bonds are partially broken and formed.
The hybridizations of the carbon atoms involved in the reaction have changed during the reaction. Therefore, the bond length also changed because it depended on the type of hybridization. The more s character the bond has, the stronger the electrons are hold to the nuclei thus the bond becomes shorter. sp2 hybridization has more s character than sp3 hybridization, so sp2-sp2 C-C is expected to be shorter than that of sp3-sp3 C-C. In addition, double bonds are shorter and stronger than single bonds, because the additional bonding attracted the nuclei stronger, pulling them closer.

{| class="wikitable"
| colspan="2" style="text-align: center; background: #f0ddf0" | '''Table 5. summary of carbon bond lengths'''
|-
| style="text-align: center;" |bond type
| style="text-align: center;" |bond length/Å
|-
| style="text-align: center;" |sp3-sp3 C-C
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |sp2-sp2 C-C
| style="text-align: center;" |1.47
|-
| style="text-align: center;" |sp2-sp3 C-C
| style="text-align: center;" |1.5
|-
| style="text-align: center;" |sp2-sp2 C=C
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |vand der wal
| style="text-align: center;" |1.7
|}
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 6. experimental bond length of reactants, product and transition state'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |transition state
| style="text-align: center;" |cyclohexene
|-
|[[File:Yihan diene labell.PNG|400px]]
|[[File:Yihan alkene label.PNG|350px]]
|[[File:YihanTS label.PNG]]
|[[File:Yihan Pdt label.PNG]]
|-
| style="text-align: center;" |C1-C2:1.47
C1-C4:1.34

C2-C3:1.34

| style="text-align: center;" |C1-C2:1.33
| style="text-align: center;" |C1-C2:1.38
C2-C3:1.41

C3-C4:1.38

C5-C6:1.38

C1-C6:2.11

C4-C5:2.11
| style="text-align: center;" |C1-C2:1.49
C1-C6:1.54

C6-C5:1.54

C4-C5:1.54
|}

{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" |'''Table 7. explanation of bond lengths of the transition state'''
|-
| style="text-align: center;" |bond number
| style="text-align: center;" |bond type changes
| style="text-align: center;" |explanation
|-
|C1-C2/C3-C4
|sp2-sp2 C=C to sp3-sp2 C-C
| 1.38 lies in the middle of the sp2-sp2 C=C (1.34) and sp3-sp2 C-C(1.5). The bond was lengthened to form a sp3-sp2 C-C bond
|-
|C2-C3
|sp2-sp2 C-C to sp2-sp2 C=C
|the bond was shortened to form a sp2-sp2 C=C
|-
|C1-C6
|non-bonding to sp3-sp3 C-C
|The sum of two carbon atoms' van der wal radii is 3.4Å, within which electrostatic attraction started to form, or in other words, a partial bond formed. The bond length is approximately the mean of the sum of two carbon atom's van der wal radii and the sp3-sp3 C-C.
|}

===Exercise 2 Reaction of Cyclohexadiene and 1,3-Dioxole===
====reaction scheme====

[[File:Exercise 2Reaction scheme.PNG|frame|center|400px|]]

As shown in the reaction scheme, this DA reaction can proceed via two pathways ,leading to either endo or exo products depending on the orientation of 1,3-Dioxole in the TS. In this exercise, the reactants, products and both the endo and exo TS were optimized on a B3LYP/6-31G(d) level. A MO and thermochemical analysis were also conducted.

The TS were located and characterized by employing Method 3 in the Tutorial. Firstly, the product was optimized. The bonds which were involved in the reaction were broken, altered and freezed to make the structure resemble the TS. Then the coordinates were unfreezed and the TS were optimized by B3LYP/6-31G(d). All the structures were firstly optimized on a fast and rough PM6 level then optimized by the slow and more accurate B3LYP/6-31G(d) method.

====Optimization of reactants and products====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 8. B3LYP/6-31G(d) Optimisation of reactant and products'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |1,3-Dioxole
| style="text-align: center;" |product(endo)
| style="text-align: center;" |product (exo)
|-
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<size>250</size>
<script>frame 18</script>
<uploadedFileContents>YihanPRODUCT ENDO OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6</script>
<uploadedFileContents>YihanPRODUCT EXO OPTIMIZED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====TS optimization and characterization====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 9. B3LYP/6-31G(d)Optimisation of TS, frequency analysis and IRC'''
|-
|
| style="text-align: center;" |TS (endo)
| style="text-align: center;" |TS (exo)
|-
|optimized structure
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 30</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|frequency analysis
|[[File:Yihan ex2Endo TS freq.PNG]]
|[[File:Yihan ex2Exo TS freq.PNG]]
|-
|IRC(total energy)
|[[File:YihanEndo IRC total E.PNG|400px]]
|[[File:YihanExo IRC total E.PNG|400px]]
|-
|IRC( RMS gradient norm)
|[[File:YihanEndo IRC g.PNG|400px]]
|[[File:YihanExo IRC g.PNG|400px]]
|-
|reaction progress
|[[File:Yihan ex2Endo movie.gif]]
|[[File:Yihan ex2Exo movie.gif]]
|}

Both endo and exo TS have only one imaginary frequencies. The convergences in the log file were checked. The geometries of the optimized TS were consistent with the structures of their corresponding products. IRC analysis showed that the TS were successfully located because the energy gradients were zero.

====MO analysis====
|[[File:YihanMO 1endo.PNG]]
|[[File:YihanMO exo.PNG]]

{| class="wikitable"
|colspan="5" style="text-align: center; background: #f0ddf0" | '''Table 10. HOMO and LUMO of reactants, products and TS'''
|-
|
|Cyclohexadiene
|1,3-Dioxole
|TS(endo)
|TS(exo)
|-
|HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>A, MO1</title>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yihan reactant 1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S, MO7</title>
<script>frame 44; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanREACANT 2 OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S, MO4</title>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S,MO12</title>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S,MO2</title>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yihan reactant 1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>A,MO8</title>
<script>frame 44; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanREACANT 2 OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>S,MO5</title>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>S,MO13</title>
<size>250</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
{| class="wikitable"
|colspan="5" style="text-align: center; background: #f0ddf0" | '''Table 11.other key orbitals of TS '''
|-
|
|TS(endo)
|TS(exo)
|-
| HOMO-1
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>A,MO3</title>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>A,MO11</title>
<size>250</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|LUMO+1
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>A, MO6</title>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanENDO TS OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<title>A, MO14</title>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YihanTS EXO OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The MO interactions occurred in the region of HOMO and LUMO.

{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 12. energy comparison of endo and exo products and TS by B3LYP/6-31G(d))'''
|-
|style="text-align: center;" |chemical species
|style="text-align: center;" |Sum of electronic and thermal Free Energiesy,Hartree
|style="text-align: center;" |kJ mol<sup>-1<sup>
|-
|style="text-align: center;" |Cyclohexadiene
|style="text-align: center;" |-233.3243
|style="text-align: center;" |-612593.14656
|-
|style="text-align: center;" |1,3-Dioxole
|style="text-align: center;" |-267.0686
|style="text-align: center;" |-701188.7195
|-
|style="text-align: center;" |TS(endo)
|style="text-align: center;" |-500.3321
|style="text-align: center;" |-1313622.0545
|-
|style="text-align: center;" |TS (exo)
|style="text-align: center;" |-500.3291
|style="text-align: center;" |-1313614.2305
|-
|style="text-align: center;" |product(endo)
|style="text-align: center;" |-500.4186
|style="text-align: center;" |-1313849.2732
|-
|style="text-align: center;" |product(exo)
|style="text-align: center;" |-500.4173
|style="text-align: center;" |-1313845.6730
|}

The MO energies were checked with single point energies. It was observed that both the endo TS and endo product were more energetically stable than their exo counterpart. This is due to the extra stabilization resulted from the secondary orbital interactions.

{| class="wikitable"
| colspan="2" style="text-align: center; background: #f0ddf0" | '''Table 13. comparison of orbital interactions of the HOMO of endo and exo TS '''
|-
|style="text-align: center;" |TS endo
|style="text-align: center;" |TS exo
|-
|[[File:YihanEndo orbital.PNG|200px]]
|[[File:YihanExo orbital.PNG|200px]]
|}
The reaction barriers were calculated as the energy differences between the total energy of reactants and the TS. Reaction energies, i.e. ΔG, was the energy differences between the reactants and products.
{| class="wikitable"
| colspan="3" style="text-align: center; background: #f0ddf0" | '''Table 14. Activation energy and ΔG for endo and exo reaction pathways'''
|-
|
|style="text-align: center;" |Activation energy,kJ mol<sup>-1<sup>
|style="text-align: center;" |ΔG,kJ mol<sup>-1<sup>
|-
|style="text-align: center;" |endo pathway
|style="text-align: center;" |159
|style="text-align: center;" |-68
|-
|style="text-align: center;" |exo pathway
|style="text-align: center;" |167
|style="text-align: center;" |-64
|}

The four red p orbitals indicated in the diagram are involved in the secondary orbital interaction. There are significant interactions between the non bonding orbitals of the oxygen atoms and the p orbitals of the diene component.The four p orbitals combined in phase. As the endo transition state was stabilized, the energy barrier for endo pathway was expected to be smaller than that of the exo pathway. Therefore, the activation energy of endo pathway was lower and ΔG was more negative. Overall, in combination of the single energy analysis, the endo products are both the kinetically stable and thermaldynamically stable products.

====Normal or Inverse electron demand====
According to the energy differences between the LUMO and HOMO pairs of the reactants and products, DA reactions are classified as two types:
Normal electron demand: electron deficient dienophile with low energy LUMO and the electron rich diene with high energy HOMO
Inverse electron demand: electron rich dienophile with high energy LUMO and the electron difficient diene with low energy HOMO

{| class="wikitable"
| colspan="3" style="text-align: center; background: #f0ddf0" | '''Table 15 Energy difference of different LUMO and HOMO pairs'''
|-
|
|style="text-align: center;" |HOMO energy/a.u.
|style="text-align: center;" |LUMO energy/a.u
|-
|style="text-align: center;" |Cyclohexadiene
|style="text-align: center;" |-0.20554
|style="text-align: center;" |-0.01711
|-
|style="text-align: center;" |1,3-Dioxole
|style="text-align: center;" |-0.19594
|style="text-align: center;" |+0.03795
|}

ΔE of HOMO (Cyclohexadiene) and LUMO (1,3-Dioxole):0.243
ΔE of HOMO (1,3-Dioxole) and LUMO (Cyclohexadiene):0.179

The closer the energies of two molecular orbitals, the larger the interactions. The energy difference between the HOMO of cyclohexadiene and LUMO of 1,3-Dioxole, therefore, this DA reaction has an inverse electron demand. 1,3-Dioxole has high energy LUMO because the lone pairs of the two oxygen atoms have the ability to donate electrons into the π cloud, raising the orbital energies.

===Exercise 3 o-Xylylene-SO2 Cycloaddition===
====reaction scheme====
[[File:Ex3 Reaction scheme.png|700px]]

The reaction of o-Xylylene and SO2 can proceed via two pathways, DA and cheletropic. The DA reactions can go through both endo and exo transition state to the sultine product. The TS is a six membered heteroaromatic ring with 6 π electrons involved. The cheletropic reaction is a separate class of pericyclic reactions, they must also obey the Woodward Hoffmann rules. According to the selection rules for cheletropic reactions, o-Xylylene and SO2 reacted through a disrotatary fashion which the HOMO of the S atom pointed directly to the π system of the o-Xylylene, because the π system has 4n+2 π electrons. The TS is a five membered heteroaromatic ring with also 6 π electrons.<ref>Woodward, R.B.; Hoffman, R. Angew. Chem. Int. Ed. Engl. 1969, 8, 781–853.</ref>

====PM6 optimization====
The reactants, products and TS were optimized on PM6 level and the TS s were located by Method 3. Products were firstly optimized. Then, the bonds involved in the reaction were broken ,frozen and optimized to obtain a guessed TS stucture. The coordinated were unfrozed and optimized again to obtain the accurate TS structure.
{| class="wikitable"
| colspan="2" style="text-align: center; background: #f0ddf0" | '''Table 16 PM6 optimization of reactants'''
|-
|style="text-align: center;" |o-Xylylene
|style="text-align: center;" |SO2
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26</script>
<uploadedFileContents>Yihan o-Xylylene.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18</script>
<uploadedFileContents>Yihan REACTANT SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|colspan="3" style="text-align: center; background: #f0ddf0" | '''Table 17 PM6 optimization of endo and exo products and TS'''
|-
|
|style="text-align: center;" |products
|style="text-align: center;" |TS
|-
|style="text-align: center;" |endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 76</script>
<uploadedFileContents>ex3ENDO PRODUCT.LOG ‎</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26</script>
<uploadedFileContents>Yihan ex3 ENDO TS UNFREEZ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|style="text-align: center;" |exo
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 70</script>
<uploadedFileContents>YihanEXOPRODUCT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>Yihan ex3EXO TS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|style="text-align: center;" |Cheletropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 58</script>
<uploadedFileContents>Yihan chele PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 60</script>
<uploadedFileContents>Yihan chele TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(Your cheletropic TS and product geometries are wrong. The oxygen atoms are too close together and have bonded. Your exo geometries are actually endo [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:11, 4 April 2018 (BST))

====TS characterization====
IRC and frequency analysis were carried out to confirm a TS has been successfully located. All the IRC showed that the energy gradients were zero at reactants, transition states and products. All the reactions were proceeded via a concerted fashion. It was observed that the energies involved in the reaction were quite small compared with the reactions in exercise 1 and exercise 2 which was due to the high energy o-Xylylene. For both the endo and exo DA pathways, two single bonds were formed, i.e. C-S and C-O, meanwhile, two C=C were reduced to one C=C as well as the S=O. In cheletropic pathway, two C-S were formed and two C=C were reduced to one.<ref>Woodward, R.B.; Hoffman, R. Angew. Chem. Int. Ed. Engl. 1969, 8, 781–853.</ref>

{| class="wikitable"
| colspan="6" style="text-align: center; background: #f0ddf0" | '''Table 18 TS characterization of endo and exo pathways at PM6 level'''
|-
|
|style="text-align: center;" |reaction progress
|style="text-align: center;" |IRC(total energy)
|style="text-align: center;" |IRC(energy norm gradient)
|-
|style="text-align: center;" |endo
|[[File:Yihan ex3 DA endo.gif]]
|[[File:Yihan ex3Endo total E.PNG]]
|[[File:YihanEndo E gradient.PNG]]
|-
|exo
|[[File:Yihan ex3 DA exo.gif ]]
|[[File:Yihan Exo total E.PNG]]
|[[File:Yihan Exo E gradient.PNG]]
|-
|style="text-align: center;" |Cheletropic
|[[File:Yihan Chele IRC.gif]]
|[[File:YihanChele total E.PNG ]]
|[[File:YihanChele E gradient.PNG]]
|}
For all the chemical species, convergences were checked. As for the reactants and products, there were no imaginary frequencies present and for TS, there was only one imaginary frequency.

====Thermochemical analysis====

The energies of reactants, products and TS were obtained from the log files. Activation barriers and ΔG were calculated.
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 19. energy comparison of endo and exo products and TS by B3LYP/6-31G(d))'''
|-
|style="text-align: center;" |chemical species
|style="text-align: center;" |Sum of Electronic and Thermal Free Energies/Hartree
|style="text-align: center;" |kJ mol<sup>-1<sup>
|-
! o-Xylylene
| style="text-align: center;" | +0.179059
| style="text-align: center;" | +470.119
|-
! SO<sub>2</sub>
| style="text-align: center;" | -0.119268
| style="text-align: center;" | -313.496
|-
! Diels-Alder Exo TS
| style="text-align: center;" | +0.090559
| style="text-align: center;" | +240.286
|-
! Diels-Alder Endo TS
| style="text-align: center;" | +0.090559
| style="text-align: center;" | +237.762
|-
! Cheletropic TS
| style="text-align: center;" | +0.099377
| style="text-align: center;" | +260.914
|-
! Diels-Alder Exo Product
| style="text-align: center;" | +0.021700
| style="text-align: center;" | +56.973
|-
! Diels-Alder Endo Product
| style="text-align: center;" | +0.021696
| style="text-align: center;" | +56.963
|-
! Cheletropic Product
| style="text-align: center;" | +0.000006
| style="text-align: center;" | +0.0158
|}

(Your cheletropic energy is inconsistent with the Jmol and log file you've produced [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:11, 4 April 2018 (BST))

{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 20. Activation energies and reaction energies'''
|-
|
|style="text-align: center;" |Activation energy,kJ mol<sup>-1<sup>
|style="text-align: center;" |ΔG,kJ mol<sup>-1<sup>
|-
! endo pathway
| style="text-align: center;" | 81.139
| style="text-align: center;" | 99.66
|-
! exo pathway
| style="text-align: center;" | 83.663
| style="text-align: center;" | 99.65
|-
! cheletropic reaction
| style="text-align: center;" | 104.291
| style="text-align: center;" | 156.60
|}
Activation barriers were calculated by the differences between the sum of energies of two reactants and the TS. ΔG was obtained by calculating the differences between the free energies of reactants and products.
====reaction profile====
[[File:Yihan reaction profile.png|600px]]

It was assumed that the reactants have zero energies with infinite separations. The reaction profile showed relative height of the TS and products of the three reaction pathways. Cheletropic products were the thermodynamic products because they were most energetically stable. There were extremely small energy differences between the exo and endo transition states as well as the products. However, the endo products and TS were slightly more stable than that of the exo. Therefore, the kinetic and thermodynamic products were generated from the endo pathway.Apart from the steric interactions, favorouble orbital interactions also play a role in energy stabilization. The non bonding p orbitals of S=O interacts with the π system.

Files:
Ex1:

butadiene : [[File:Yihan butadiene.LOG]]

transition state: [[File:Yihan TS PM6.LOG]]

cyclohexene: [[File:Yihan cyclohexene.LOG]]

Ex2

Cyclohexadiene: [[File:Yihan reactant 1.LOG]]

1,3-Dioxole : [[File:YihanREACANT 2 OPT.LOG]]

endo product:[[File:YihanPRODUCT ENDO OPT.LOG]]

exo product : [[File:YihanPRODUCT EXO OPTIMIZED.LOG]]

Ex3

o-Xylylene: [[File:Yihan o-Xylylene.LOG]]

SO2: [[File:Yihan REACTANT SO2.LOG]]

Endo TS: [[File:Yihan ex3 ENDO TS UNFREEZ.LOG]]

Exo TS: [[File:Yihan ex3EXO TS3.LOG]]

Cheletropic product: [[File:Yihan chele PRODUCT.LOG]]

Cheletropic TS: [[File:Yihan chele TS.LOG]]

Exo product: [[File:YihanEXOPRODUCT PM6.LOG]]

Endo product: [[File:ex3ENDO PRODUCT.LOG]]

References
<references/>

Rep:Mod:HZ4315

2018-04-07T10:54:41Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Introduction ==

Chemical reactions are rarely as simple as they appear and often have various potential mechanisms leading to one or more products. Therefore, in order to determine the major product of a reaction and the path taken to reach it, one must consider the properties of the reactants and the nature of the interactions between molecular orbitals (MOs). In this lab, a variety of pericyclic reactions were explored to determine the key MO interactions involved and their associated energies. This was achieved by utilising computer based optimisation strategies and subsequently investigating MO and transition state (TS) energies. In certain cases, the reaction coordinate was also considered.

=== Quantum Background ===
<br>
[[File:HZ4315-Schrodinger.png|centre|thumb|300x300px|'''Figure 1: '''Time-Dependant Schrodinger equation. <sup>[1]</sup>]]
<br>

The Schrodinger equation is a fundamental equation which describes the quantum mechanical behaviour of a system. The time-dependant example (see '''Figure 1''') specifically describes the evolution of a physical system over a period of time. The wavefunction component of the equation describes the position of electrons with respect to the nuclei and predicts the probability of a certain event occurring. Consequently, it can be used to determine properties of molecules and the potential reactions that they can undergo. However, within any one system, the wavefunction varies depending on which point of the potential energy surface is being considered. Therefore, in order to make use of the wavefunction, we apply the Linear Combination of Atomic Orbitals (LCAO) theory.

LCAO theory involves the combination of atomic basis functions, which are known as basis sets, in order to depict MOs. This is achieved with reasonable accuracy and can then be used to solve the Hamiltonian operator. This provides an alternative to using a complete basis set which would be far too complicated to be utilised in calculations. The use of Gaussian functions further simplifies this complex set of calculations. Used as an alternative to Slater functions, which are notoriously difficult to integrate, singular Primitive Gaussian functions can be linearly combined to give 'Contracted Gaussian' functions (see '''Figure 2'''). Primitive functions give a poor description of a wavefunction and hence are generally contracted instead. Variation of the intrinsic exponents during a Hartree-Fock calculation (see '''Computational Techniques''' for further information) then allows a potential energy minimum to be achieved which helps build an approximated 'Slater-type' orbital. This can be further improved by increasing the number of atomic basis functions per atomic orbital.<sup>[2]</sup>

<br>
[[File:Contracted Gaussian Function.png|centre|thumb|300x300px|'''Figure 2: '''Contracted Gaussian function. <sup>[3]</sup>]]
<br>

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) describe the change in energy of a system as a function of one or more other variables. For a simple system with two degrees of freedom, a minimum point corresponds to a stationary point with a first derivative of zero and a positive (greater than zero) second derivative. However, for a complex system with additional degrees of freedom, the harmonic oscillator model cannot be applied and therefore results in a more complex set of minima. Whilst there is only one true minimum (global minimum), several local minima exist with similar energies, making the global minimum difficult to find. To put it into context, a system with N atoms has 3N-6 degrees of freedom and hence, the complexity increases very quickly. As mentioned above, the fact that this system cannot be modelled as a harmonic oscillator means that the associated force constant is difficult to calculate using the second derivative. Instead, a Hessian matrix is used. The matrix consists of second-order partial derivatives of the energy of the molecule in question and diagonalisation of this matrix gives rise to the force constants. The constants are eigenvectors and arrise from the linear combination of the degrees of freedom. Since all force constants are positive at a minimum, the corresponding frequencies must also be positive. Therefore, conducting frequency calculations and ensuring all the values are positive allows us to correctly determine the minimum.

In contrast, the transition state (TS) corresponds to a maximum on the minimum energy pathway. For a simple system with two degrees of freedom, derivatives are again used to determine the TS. Similarly to the minimum, the TS will have a first derivative of zero. However, unlike the minimum, the second derivative will be positive for all degrees of freedom except one. The particular one will therefore have a negative force constant and frequency. Whilst the systems explored in this lab were more complex (and therefore the second derivative alone is not conclusive), a similar trend is witnessed during the use of a Hessian Matrix and therefore, the position of the TS was confirmed when a negative frequency was seen.

=== Computational Techniques ===

====Hartree-Fock Method====
<br>
[[File:HZ4315-HF.png|centre|thumb|300x300px|'''Figure 3: '''The Hartree-Fock operator. <sup>[4]</sup>]]
<br>

The Hartree-Fock method is generally used to solve the time-independant Schrodinger equation for a many-electron system. This is achieved using LCAO to obtain a one-electron wavefunction which describes optimised MOs. Since the electron-electron repulsion term in the molecular Hamiltonian requires the coordinates of two separate electrons, all terms the Hamiltonian except the nuclear-nuclear repulsion term are re-expressed as a sum of one-electron operators in the Hartree-Fock operator (see '''Figure 3'''). Amongst other simplifications, it utilises the Born-Oppenheimer approximation and the mean-field approximation. The later implies that the electrons within the system experience an averaged field stemming from all the electrons within the system. Whilst this simplifies the calculation, it also means that that instantaneous interactions between electrons are disallowed and the repulsive field experienced by a particular electron is greater than it should be since the electron itself has not been neglected. Various methods which combine to form the 'post-Hartree-Fock' have been explored to improve this.

The semi-empirical PM6 optimisation method used during this lab is based on the Hartree-Fock method. The use of approximations and empirical data improves the efficiency of calculations and therefore allows more complex molecules to be investigated.

====B3LYP Optimisation====

B3LYP optimisation is a hybrid optimisation technique involving density functional theory (DFT) and the previously mentioned Hartree-Fock method. The former allows the properties of many-electron systems to be determined by using 'functionals'. Functionals are in essence, functions of functions (specifically the function of spatially dependant electron density). Used in conjunction with the Hartree-Fock method, a relatively inexpensive and efficient method of optimisation which incorporates both the exchange and electron correlation functionals is achieved.

== Exercise 1: Reaction of Butadiene with Ethylene ==
<br>
[[File:HZ4315(RS EX1).png|centre|thumb|800x800px|'''Scheme 1: '''The Diels-Alder reaction between Cis-Butadiene and Ethylene.]]
<br>

In this exercise, the Diels-Alder pericyclic reaction between cis-butadiene and ethylene (see '''Scheme 1''') was investigated. This involved the following:

1. Optimisation of cis-butadiene and ethylene to their minimum energy ground states.

2. Optimisation of the transition state (TS) to its minimum energy ground state followed by a TS (Berny) optimisation.

3. IRC analysis of the reaction.

4. Optimisation of the cyclohexene product.

All optimisations were conducted using a semi-empirical PM6 basis set and in accordance with Method 1 and 2. During the ground state optimisations, the distance between the terminal carbons on cis-butadiene and ethylene was set at 2.2Å (via the Redundant Coordinates tab).

===Key Molecular Orbitals===

====Reactants====

{| class="wikitable" style="margin: auto;"
!
! Ethylene
! Butadiene
|-
| '''HOMO'''
| <jmol>
<jmolApplet>
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</jmolApplet>
</jmol>
|<jmol>
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<uploadedFileContents>HZ4315 MIN BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| '''LUMO'''
| <jmol>
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</jmol>
| <jmol>
<jmolApplet>
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<script>frame 14; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 MIN BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ align="bottom" style="caption-side: bottom" | '''Table 1:''' Reactant HOMOs and LUMOs.
|}
<br>

====Transition State====

<br>
{| class="wikitable" style="margin: auto;"
!
! HOMO (-1)
! HOMO
! LUMO
! LUMO (+1)
|-
| '''Transition State'''
| <jmol>
<jmolApplet>
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<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 EX1 TS(2).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
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<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 EX1 TS(2).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
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<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 EX1 TS(2).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 EX1 TS(2).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ align="bottom" style="caption-side: bottom" | Table 2: HOMO (-1), HOMO, LUMO and LUMO (+1) of the Diels-Alder TS.
|}
<br>

===Molecular Orbital Diagram===
<br>
[[File:HZ4315(EX1 MO-3).png|centre|thumb|800x800px|'''Figure 4: '''MO diagram for the Diels-Alder reaction between Cis-Butadiene and Ethylene.]]

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You are missing the symmetry labels on this MO diagram.)
<br>

Once the TS was optimised, the relevant molecular orbitals and energies could be seen in Gaussview. These were used to produce the MO diagram for the reaction between cis-butadiene and ethylene (see '''Figure 4'''). It is useful in determining the bonding and non-bonding orbital interactions. Typically, for a reaction to 'allowed', the frontier molecular orbitals that are interacting must be similar in energy and share the same symmetry. This ensures that the overlap integral is zero since there is no net constructive or deconstructive interference experienced. Therefore, the allowed interactions are as follows:
<br>
{| class="wikitable" style="margin: auto;"
! !! Allowed !! Forbidden !! Orbital Overlap Integral
|-
| '''Symmetric-Symmetric''' || X || || Non-zero
|-
| '''Asymmetric-Asymmetric''' || X || || Non-zero
|-
| '''Symmetric-Asymmetric''' || || X || Zero
|}
<br>

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Be carful: your state in your discussion that the orbital overlap is zero for same symmetry orbitals, while you say the opposite in the table above.)

With this in mind, the relevant orbital interactions can be found in '''Table 3''' below:

<br>
{| class="wikitable" style="margin: auto;"
|+Table 3: The frontier MO interactions between the reactants and the resulting nature of the interactions in the TS.
|-
! Ethylene/Butadiene Pair
! Bonding Interaction
! Anti-bonding Interaction
|-
| HOMO ('''AS''')/LUMO ('''AS''')
| HOMO ('''-1''')
| LUMO ('''+1''')
|-
| LUMO ('''S''')/HOMO ('''S''')
| HOMO
| LUMO
|}
<br>

The first point of interest regarding the MO diagram in '''Figure 4''' is the relative displacement of the TS MOs in relation to the reactant MOs. Since TSs occur at a maximum on the PES, the energy of the MOs is expected to be higher than those of the reactants which is indeed the case. This difference in energy is defined as the activation energy. Furthermore, as indicated above, a Butadiene/Ethylene (HOMO/LUMO) interaction yields the TS Bonding (HOMO ('''-1''')) and Anti-bonding (LUMO ('''+1''')) interactions whilst a Butadiene/Ethylene (LUMO/HOMO) interaction yields the TS Bonding (HOMO) and Anti-bonding (LUMO) interactions. The splitting observed for the former is greater than the latter which stems from the frontier orbitals being more similar in energy and therefore interacting more strongly. The resulting HOMO ('''-1''') and LUMO ('''+1''') energies indicate that the reaction proceeds via a normal electron demand Diels-Alder mechanism. The fact that the HOMO ('''-1''') interaction has a higher energy w/r to the butadiene HOMO and the LUMO ('''+1''') has a lower energy w/r to the ethylene LUMO shows that the diene is electron rich compared to the dienophile.

===Bond Lengths===
<br>
[[File:HZ4315(EX1 BL-3).png|centre|thumb|500x500px|'''Figure 5: '''Reactants, TS and product with numbered carbon atoms.]]
<br>

The relevant bond lengths (in Å) for the molecules shown in '''Figure 5''' can be found in '''Table 4''' below:
<br>
{| class="wikitable" style="margin: auto;"
|+ Table 4 - The relevant bond lengths (Å) in the reactants, transition states and product.
! !! Ethylene !! Butadiene !! TS !! Cyclohexene
|-
| C<sub>1</sub>-C<sub>2</sub> || - || 1.33358 || 1.37983 || 1.50033
|-
| C<sub>2</sub>-C<sub>3</sub> || - || 1.47083 || 1.41116 || 1.33758
|-
| C<sub>3</sub>-C<sub>4</sub> || - || 1.33357 || 1.37971 || 1.50033
|-
| C<sub>4</sub>-C<sub>5</sub> || - || - || 2.11553 || 1.54002
|-
| C<sub>5</sub>-C<sub>6</sub> || 1.32731 || - || 1.38178 || 1.54063
|-
| C<sub>6</sub>-C<sub>1</sub> || - || - || 2.11393 || 1.54002
|}
<br>

Before discussing the changes in bond lengths witnessed in the reaction, it is worth noting some typical bond lengths and radii for varying carbon hybridisations:

- Bond length (sp<sup>3</sup>-sp<sup>3</sup>) = 1.54Å

- Bond length (sp<sup>3</sup>-sp<sup>2</sup>) = 1.50Å

- Bond length (sp<sup>2</sup>-sp<sup>2</sup>) = 1.34Å

- Carbon VdW radius = 1.7Å

Analysis of the relative bond lengths raise some key points. Firstly, the ethylene double bond (corresponding to C<sub>5</sub>-C<sub>6</sub> in ethylene and the TS) is seen to become longer during the progression towards the product. This is expected as the bond undergoes conversion from a π bond to a sigma bond whereby it ultimately converges at the expected value of 1.54Å. Likewise, the butadiene double bonds (C<sub>1</sub>-C<sub>2</sub> and C<sub>3</sub>-C<sub>4</sub>) also elongate for the same reason. They do however converge at a slightly shorter length (1.50Å) which is due to the double bond forming between them (C<sub>2</sub>-C<sub>3</sub>). This results in a sp<sup>3</sup>-sp<sup>2</sup> type bond. The shortening of the C<sub>2</sub>-C<sub>3</sub> bond confirms the conversion from a sigma bond to a π bond with the bond ultimately converging close to the expected value of 1.34Å.

The changes witnessed in the bond lengths do coincide with transition state theory as the TS structure lies between the structures of the reactants and product. This can be confirmed by considering the lengths of C<sub>4</sub>-C<sub>5</sub> and C<sub>6</sub>-C<sub>1</sub>. The observed length of 2.1Å is shorter than the typical distance maintained between atoms (i.e. 2 x vdW radius = 1.7 x 2 = 3.4Å) which indicates an interaction between orbitals. However, analysis of the IRC (see '''Figure 6''') shows the TS to be closer in energy to the reactants than products.

<br>
[[File:IRC Path.png|centre|thumb|500x500px|'''Figure 6: '''IRC for the reaction in question.]]
<br>

With the TS being closer in energy to the reactants, an early TS is witnessed with the structure resembling that of the reactants. This can be confirmed by considering the bond length values in the TS. C<sub>1</sub>-C<sub>2</sub> and C<sub>3</sub>-C<sub>4</sub> have lengths of ~1.38Å which is closer to the value of ~1.33Å in butadiene than ~1.50Å in cyclohexene. Overall, the reaction proceeds like so:

<br>
[[File:HZ4315 EX1 IRC MOV.gif|frame|center|'''Figure 7:''' IRC movie for the Diels-Alder reaction.]]
<br>

===Transition State Vibrations===
<br>
[[File:HZ4315 EX1 TS VIB.gif|frame|center|'''Figure 8:''' TS vibration.]]
<br>

In order to identify the correct TS, TS (berny) optimisations were conducted until a structure exhibiting a single negative vibrational frequency was witnessed. The animation shown in '''Figure 8''' corresponds to a negative frequency of -948.37 cm<sup>-1</sup>. Since the terminal carbons on both molecules approach each other in a concerted fashion, the reaction must be synchronous.

== Exercise 2: Reaction of Cyclohexadiene with 1,3-Dioxole ==
<br>
[[File:HZ4315(EX2-RS-2).png|centre|thumb|400x400px|'''Scheme 2:''' The reaction between 1,3-Dioxole and Cyclohexadiene.]]
<br>

In this exercise, the pericyclic reaction between 1,3-dioxole and cyclohexadiene was investigated. Both the endo and exo products of the reaction were considered. The investigation involved:

1. Optimisation of the reactants to their minimum energy ground states (PM6 and B3LYP).

2. Optimisation of the TS to its minimum energy ground state followed by a TS (Berny) optimisation (PM6 and B3LYP).

3. IRC analysis of the reaction (PM6 only).

4. A single point energy (SPE) calculation on the IRC product.

5. Optimisation of the product (PM6 and B3LYP).

Method 2 was primarily used throughout. During ground state optimisations, the distance between the terminal carbons was again set at 2.2Å.

===Key Molecular Orbitals===

====Reactants====

{| class="wikitable" style="margin: auto;"
!
! Cyclohexadiene
! 1,3-Dioxole
|-
| '''HOMO'''
| <jmol>
<jmolApplet>
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|<jmol>
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<uploadedFileContents>HZ4315 EX2 Diox.LOG</uploadedFileContents>
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</jmol>
|-
| '''LUMO'''
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| <jmol>
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<script>frame 28; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 EX2 Diox.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ align="bottom" style="caption-side: bottom" | '''Table 4:''' Reactant HOMOs and LUMOs.
|}
<br>

====Transition State====

=====Endo=====

<br>
{| class="wikitable" style="margin: auto;"
!
! HOMO (-1)
! HOMO
! LUMO
! LUMO (+1)
|-
| '''TS (Endo)'''
| <jmol>
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<uploadedFileContents>HZ4315 EX2 ENDO TS.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>HZ4315 EX2 ENDO TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ align="bottom" style="caption-side: bottom" | Table 5: HOMO (-1), HOMO, LUMO and LUMO (+1) of the Endo TS.
|}
<br>

=====Exo=====

<br>
{| class="wikitable" style="margin: auto;"
!
! HOMO (-1)
! HOMO
! LUMO
! LUMO (+1)
|-
| '''TS (Exo)'''
| <jmol>
<jmolApplet>
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| <jmol>
<jmolApplet>
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<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 EX2 EXO TS.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
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<uploadedFileContents>HZ4315 EX2 EXO TS.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>HZ4315 EX2 EXO TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ align="bottom" style="caption-side: bottom" | Table 6: HOMO (-1), HOMO, LUMO and LUMO (+1) of the Exo TS.
|}
<br>

=====Comparison=====
<br>
{| class="wikitable" style="margin: auto;"
! !! Energy (Endo) !! Energy (Exo) !! Energy Difference (Endo - Exo)
|-
| '''LUMO(+1)''' || 0.01543 || 0.01019 || 0.00524
|-
| '''LUMO''' || -0.00462 || -0.00699 || 0.00237
|-
| '''HOMO''' || -0.19051 || -0.18560 || -0.00491
|-
| '''HOMO(-1)''' || -0.19648 || -0.19801 || 0.00153
|+ align="bottom" style="caption-side: bottom" | Table 7: Comparison of the HOMO (-1), HOMO, LUMO and LUMO (+1) energies in the Endo and Exo TSs (in Hartrees).
|}
<br>

From '''Table 7''' we can see a difference of -0.00491 Hartrees between the endo and exo HOMO energy levels. This indicates that the endo TS is more stable (since it has a lower energy HOMO level). This stems from secondary orbital interactions experienced between the oxygen lone pair within the dioxole ring and the pi bonds within the cyclohexadiene. These are not possible in the exo TS.

===Molecular Orbital Diagrams===
Once the relevant MOs and their associated energies were obtained in Gaussview, the MO diagrams below ('''Figure 9''' and '''Figure 10''') were constructed.

<br>
[[File:HZ4315(EX2 ENDO MO-2).png|centre|thumb|800x800px|'''Figure 9: '''MO diagram for the Endo TS in the reaction between 1,3-dioxole and cyclohexadiene.]]
<br>

<br>
[[File:HZ4315(EX2 EXO MO).png|centre|thumb|900x900px|'''Figure 10: '''MO diagram for the Exo TS in the reaction between 1,3-dioxole and cyclohexadiene.]]
<br>

The MO diagrams above shed light on the possible mechanism of this Diels-Alder reaction (i.e. normal vs inverse electron demand). In terms of the splitting witnessed, the interaction between the HOMO of cyclohexadiene (diene) and the LUMO of 1,3-dioxole (dienophile) appears to be the strongest. This is characteristic of 'inverse electron demand'. However, in order to confirm this, quantitative analysis is required. Since the MOs seen in '''Table 5''' and '''Table 6''' arise from different potential energy surfaces, their associated Hamiltonian potentials and relative energies will also vary. Therefore, in order to carry out the necessary analysis, a single point energy (SPE) calculation is required.

===Single Point Energy (SPE) Calculation===

=====Endo=====

<br>
{| class="wikitable" style="margin: auto;"
!
! HOMO (-1)
! HOMO
! LUMO
! LUMO (+1)
|-
| '''TS (Endo)'''
| <jmol>
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</jmol>
| <jmol>
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|<jmol>
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<uploadedFileContents>HZ4315 EX2 ENDO SPE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ align="bottom" style="caption-side: bottom" | Table 8: HOMO (-1), HOMO, LUMO and LUMO (+1) of the Endo TS (energies obtained using an SPE calculation).
|}
<br>

=====Exo=====

<br>
{| class="wikitable" style="margin: auto;"
!
! HOMO (-1)
! HOMO
! LUMO
! LUMO (+1)
|-
| '''TS (Exo)'''
| <jmol>
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</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
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<script>frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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| <jmol>
<jmolApplet>
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</jmol>
|<jmol>
<jmolApplet>
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<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 EX2 EXO SPE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ align="bottom" style="caption-side: bottom" | Table 9: HOMO (-1), HOMO, LUMO and LUMO (+1) of the Exo TS (energies obtained using an SPE calculation).
|}
<br>

=====Discussion=====
<br>
{| class="wikitable" style="margin: auto;"
! !! Energy (Endo) !! Energy (Exo)
|-
| '''LUMO(+1)''' || 0.03219 || 0.02979
|-
| '''LUMO''' || 0.02288 || 0.02110
|-
| '''HOMO''' || -0.31696 || -0.32207
|-
| '''HOMO(-1)''' || -0.32135 || -0.32215
|+ align="bottom" style="caption-side: bottom" | Table 10: Comparison of the HOMO (-1), HOMO, LUMO and LUMO (+1) energies in the Endo and Exo TSs (after a SPE calculation).
|}
<br>

The SPE calculation was performed on the last frame of the associated IRC for each transition state. The resulting MOs share a common potential energy surface and can therefore be compared quantitatively. Analysis of the MO energies confirms the 'inverse electron demand' nature of this reaction with the 1,3-dioxole (dienophile) having a higher energy HOMO in both TSs. This stems from the electron rich nature of 1,3-dioxole which acts as an electron donating group. Typically, electron donating dienophiles experience an increase in energy for both their HOMO and LUMO MOs. This is indeed the case here with the dienophile's oxygen atom donating electrons into the diene's π* and consequently raising its own HOMO and LUMO (π and π* respectively).

===Energy Analysis/Reaction Coordinate===

In order to determine the reaction coordinate, the following energies were determined:

1. Reactants - This was achieved by individually optimising cyclohexadiene and 1,3-dioxole (B3LYP level) then adding the energies together.

2. Transition states - Obtained using a TS (Berny) calculation (B3LYP level).

3. Products - Obtained by optimising the product frame from the IRC (B3LYP level)

The results of these calculations are shown in '''Table 11''' below:

<br>
{| class="wikitable" style="margin: auto;"
! !! Endo Energy (KJ/mol) !! Exo Energy (KJ/mol)
|-
| '''Reactants''' || -1313781.98 || -1313781.98
|-
| '''Transition State''' || -1313622.16 || -1313614.31
|-
| '''Product''' || -1313849.37 || -1313845.78
|-
| '''E<sub>a</sub>''' || 159.82 || 165.46
|-
| '''ΔH<sub>r</sub><sup>⊖</sup>''' || -67.39 || -63.80
|+ align="bottom" style="caption-side: bottom" | Table 11: Reactant, TS and Product energies for the reaction between Cyclohexadiene and 1,3-Dioxole.
|}
<br>

These energies give rise to the following reaction coordinate:

<br>
[[File:HZ4315(EX2 RC-2).png|centre|thumb|600x600px|'''Figure 11: '''A reaction coordinate for the reaction between 1,3-Dioxole and Cyclohexadiene (Blue = Endo pathway, Red = Exo pathway).]]
<br>

From this reaction coordinate we can infer that the endo reaction/product will dominate over its exo counterpart. The activation energy (E<sub>a</sub>) for the exo reaction is 5.64 KJ/mol higher than the endo reaction and the exo product is also 3.59 KJ/mol higher in energy. Consequently, the endo reaction is both thermodynamically and kinetically favoured. In terms of the thermodynamics, the exo product experiences steric clash between the protons contained within the dioxole and the carbon based bridge. This is avoided by the endo conformer. Kinetically, the endo reaction has a lower E<sub>a</sub> which stems from the secondary orbital interactions discussed previously.

Product Energy Log Files:

Endo: [[File:HZ4315 EX2 ENDOPROD(6-31G).LOG]]

Exo: [[File:HZ4315 EX2 EXOPROD(6-31G).LOG]]

== Exercise 3: Diels-Alder vs Cheletropic ==
<br>
[[File:HZ4315 EX3(RS).png|600px|thumb|center|'''Scheme 3:''' The Diels-Alder and Cheletropic reactions between o-Xylylene and Sulfur Dioxide.]]
<br>

In this exercise, the endocyclic and exocyclic Diels-Alder reactions between o-xylylene and sulfur dioxide were investigated alongside the cheletropic alternative reaction. in contrast to the previous exercises, Method 3 was used. The investigation of each pathway involved:

1. Optimisation of the products to their minimum ground state energy.

2. Breaking of the C-S and C-O bonds to obtain a guess TS.

3. Optimisation of the TS to its minimum ground state energy followed by a TS (Berny) optimisation.

4. IRC analysis.

5. Establishment of the reaction coordinates using reaction energies.

All optimisations were carried at the PM6 level. For ground state optimisations, the C-S and C-O bond lengths were frozen at 2.4Å and 2.0Å respectively.

===IRC Analysis===

====Diels-Alder: Endo====
<br>
[[File:HZ4315 EX3 DA ENDO IRCpath.png|centre|thumb|500x500px|'''Figure 12: '''IRC for the Endo Diels-Alder exocyclic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

<br>
[[File:HZ4315-MAIN-ENDO-IRCMOV.gif|frame|center|'''Figure 13:''' IRC movie for the Endo Diels-Alder exocyclic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

====Diels-Alder: Exo====
<br>
[[File:HZ4315 EX3 DA EXO IRCpath.png|centre|thumb|500x500px|'''Figure 14: '''IRC for the Exo Diels-Alder exocyclic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

<br>
[[File:HZ4315-MAIN-EXO-IRCmov.gif|frame|center|'''Figure 15:''' IRC movie for the Exo Diels-Alder exocyclic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

====Cheletropic====
<br>
[[File:HZ4315 EX3 CH path.png|centre|thumb|500x500px|'''Figure 16: '''IRC for the Cheletropic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

<br>
[[File:HZ4315-CHEL-IRCmov.gif|frame|center|'''Figure 17:''' IRC movie for the Cheletropic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

(These diagrams can be grouped in a table for clarity [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:12, 4 April 2018 (BST))

===Energy Analysis/Reaction Coordinate===

Similarly to Exercise 2, in order to determine the reaction coordinate, a series of optimisations (PM6 level) were conducted and the resulting energies can be found in '''Table 12''' below:

<br>
{| class="wikitable" style="margin: auto;"
! !! Endo Energy (KJ/mol) !! Exo Energy (KJ/mol) !! Cheletropic Energy (KJ/mol)
|-
| '''Reactants''' || 158.25 || 158.25 || 158.25
|-
| '''Transition State''' || 237.76 || 241.75 || 260.08
|-
| '''Product''' || 56.98 || 56.32 || 0.0026
|-
| '''E<sub>a</sub>''' || 79.51 || 83.5 || 101.83
|-
| '''ΔH<sub>r</sub><sup>⊖</sup>''' || -101.27 || -101.98 || -158.25
|+ align="bottom" style="caption-side: bottom" | Table 12: Reactant, TS and Product energies for the reaction between o-Xylylene and SO<sub>2</sub>.
|}
<br>

There energies gave rise to the following coordinate:

<br>
[[File:HZ4315 EX3(RP1).png|centre|thumb|600x600px|'''Figure 17: '''A reaction coordinate for the reaction between o-Xylylene and SO<sub>2</sub> (Blue = Endo pathway, Red = Exo pathway, Green = Cheletropic pathway).]]
<br>

Consideration of the energies and reaction coordinates of the three pathways gives rise to some important points. In terms of the activation energies and the relative TS energies, the endo pathways has the smallest (E<sub>a</sub> = 79.51 KJ/mol), making it kinetically favourable. As mentioned in Exercise 2, secondary orbital interactions involving the donation of electrons from heteroatoms within a dienophile to the diene can help stabilise a TS. Therefore, it is possible that the oxygen atom within the SO<sub>2</sub> molecule is donating its lone pair into the π* orbital of o-xylylene. However, in this case, the most stable product is actually reached via the cheletropic pathway. A product energy of 0.0026 KJ/mol is 56.955 KJ/mol and 56.317 KJ/mol lower than the endo and exo products respectively. Since aromaticity is restored in all three products, the reason for the stability of the cheletropic product lies with the nature of the bonds and rings. Firstly, by forming a five membered ring with only the sulfur atom contained within it, an additional strong S=O bond is preserved. The formation of an addition C-O bond does not compensate for breaking this bond in the Diels-Alder reactions. Furthermore, the five membered ring also relieves the strain experienced in the six membered ring which stems from the larger size of sulfur atoms compared to carbon atoms.

===Alternative Reaction===
<br>
[[File:HZ4315(EX3-AltRS).png|600px|thumb|center|'''Scheme 4:''' An alternative reaction between o-Xylylene and Sulfur Dioxide.]]
<br>

As shown in '''Scheme 4''', an alternative, endocyclic reaction between o-Xylylene and Sulfur Dioxide is possible. Therefore, to check its thermodynamic viability, optimisations were conducted on the products, TS and reactants (PM6 level) using Method 3 and IRC and energy analysis was subsequently carried out.

====IRC Analysis====

=====Endo=====

<br>
[[File:HZ4315(EX3-ALT-ENDO-IRCpath.png|centre|thumb|500x500px|'''Figure 18: '''IRC for the endo product formation during the endocyclic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

<br>
[[File:HZ4315-ALT-ENDO-IRCmov.gif|frame|center|'''Figure 19:''' IRC movie for endo product formation during the endocyclic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

=====Exo=====

<br>
[[File:HZ4315(EX3-ALT-EXO-IRCpath.png|centre|thumb|500x500px|'''Figure 20: '''IRC for the exo product formation during the endocyclic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

<br>
[[File:HZ4315-ALT-EXO-IRCmov.gif|frame|center|'''Figure 21:''' IRC movie for the exo product formation during the endocyclic reaction between o-Xylylene and SO<sub>2</sub>.]]
<br>

====Energy Analysis====

<br>
{| class="wikitable" style="margin: auto;"
! !! Endo Energy (KJ/mol) !! Exo Energy (KJ/mol)
|-
| '''Reactants''' || 158.25 || 158.25
|-
| '''Transition State''' || 267.98 || 275.82
|-
| '''Product''' || 172.25 || 177.49
|-
| '''E<sub>a</sub>''' || 109.73 || 117.57
|-
| '''ΔH<sub>r</sub><sup>⊖</sup>''' || 14.00 || 19.24
|+ align="bottom" style="caption-side: bottom" | Table 13: Reactant, TS and Product energies for the alternative endocyclic reaction between o-Xylylene and SO<sub>2</sub>.
|}
<br>

The first point to note from these energies is the increase in energy of both the endo and exo TSs compared to those witnessed in the typical exocyclic Diels-Alder and cheletropic reactions. This may be due to the disruption to aromaticity experienced when the product forms. In the exocyclic examples. the products are re-aromatised however, this is not the case here. Consequently, we would expect the TSs to be comparitively destablised. Furthermore,
the enthalpy of reaction is positive which indicates that the reaction is endothermic. Consequently, the reaction would not be thermodynamically favourable.

===Log Files===

Reactants:

SO<sub>2</sub>: [[File:HZ4315 SO2.LOG]]
o-Xylylene: [[File:HZ4315-XYLYLENE.LOG]]

Exocyclic Reaction (Endo):

TS: [[File:HZ4315-MAIN-ENDO(TS).LOG]]
Product: [[File:HZ4315-MAIN-EXO-PROD.LOG]]

Exocyclic Reaction (Exo):

TS: [[File:HZ4315-MAIN-EXO(TS).LOG]]
Product: [[File:HZ4315-MAIN-EXO-PROD2.LOG]]

Exocyclic Reaction (Cheletropic):

TS: [[File:HZ4315-MAIN-CHEL-TS.LOG]]
Product: [[File:HZ4315-MAIN-CHEL-PROD.LOG]]

Endocyclic Reaction (Endo):

TS: [[File:HZ4315-ALT-ENDO-TS.LOG]]
Product: [[File:HZ4315-ALT-ENDO-PROD.LOG]]

Endocyclic Reaction (Exo):

TS: [[File:HZ4315-ALT-EXO-TS.LOG]]
Product: [[File:HZ4315-ALT-EXO-PROD.LOG]]

== Further Work: Electrocyclic Ring Closure of [1,1']bicyclohexyl-1,1'-diene ==
<br>
[[File:HZ4315(FW RS).png|600px|thumb|center|'''Scheme 5:''' The electrocyclic ring closure for Diene X.]]
<br>

As an extension, the mode of the electrocyclic ring closure of [1,1']bicyclohexyl-1,1'-diene ('''Diene X''') (see '''Scheme 5''') was explored. Typically, under photochemical conditions, the closure occurs via a disrotatory mechanism whereby the new C-C bond forms as a result of suprafacial approach (see '''Figure 21'''). This stems from the photochemical excitation of an electron from the original HOMO of one of the diene's double bonds into the LUMO. This essentially makes this the new HOMO and since it is now similar in energy to the corresponding LUMO on the other double bond, orbital interactions can occur, leading to the formation of a new bond. However, in this computational lab, reactions were modelled using PM6 optimised reactants, TSs and products. Since PM6 optimisations are under thermal conditions, the mode of ring closure for systems with 4n π-electrons is expected to be conrotatory. To confirm this, optimisations of the reactants, TS and product were carried out after which IRC and energy analysis was conducted.

<br>
[[File:HZ4315-FW-Disrotation-2.png|600px|thumb|center|'''Figure 22:''' Electrocyclic ring closure via disrotation.]]
<br>

(Why are you showing disrotation when this mechanism is conrotation on ground state?)

===Transition State Vibration===

As was the case throughout the lab, the TS was confirmed by the presence of a single, negative frequency. In this case, it occurred at -494.99 cm<sup>-1</sup> and can be seen in '''Figure 23''' below.

<br>
[[File:HZ4315-FW-TSMOV.gif|frame|center|'''Figure 23:''' TS vibration in Diene X.]]
<br>

===IRC Analysis===
<br>
[[File:HZ4315-FW-IRCMOV.gif|frame|center|'''Figure 24:''' IRC movie for the electrocyclic ring closure of Diene X.]]
<br>

From the IRC movie shown above it is clear that both hydrogen atoms situated at each double bond within Diene X rotate in a clockwise fashion, making the ring closure conrotatory. This is expected for systems with 4n π-electrons under thermal conditions. Since Diene X has 4 π-electrons, a value of zero for 'n' satisfies the equation and hence, the computational analysis matches the theory. The schematic representation for this can be seen in '''Figure 25''' below.

<br>
[[File:HZ4315-FW-Conrotation.png|600px|thumb|center|'''Figure 25:''' Electrocyclic ring closure via conrotation.]]
<br>

===Energy Analysis===
<br>
{| class="wikitable" style="margin: auto;"
|+ Table 14. The energies of the reactant, TS and product of the electrocyclic ring closure of Diene X.
! Reactant (kJ/mol)
! Transition State (kJ/mol)
! Product (kJ/mol)
! E<sub>a</sub> (kJ/mol)
! ΔH<sub>r</sub><sup>⊖</sup> (kJ/mol)
|-
| 740.07
| 802.09
| 603.42
| 62.02
| -136.65
|}
<br>

The negative ΔH<sub>r</sub><sup>⊖</sup> value witnessed indicates that the reaction is exothermic, making it thermodynamically viable.

== Conclusion ==

Using both the PM6 (semi-empirical) and B3LYP, a variety of pericylic reactions were modelled and explored to determine the necessary properties for the reaction to occur and the likely path it progresses through. In Exercise 1, the Diels-Alder reaction between cis-butadiene and ethylene was investigated. Considering that the overlap integral for two orbitals was required to be zero, it was found that both interacting orbitals must share the same symmetry. Subsequent analysis of the relevant MOs and their energies showed the diene's MO energy to increase in the TS whilst the dienophile's MO energies fell, indicating that the reaction proceeds via normal electron demand. Analysis of the IRC and bond lengths also suggested that the TS more closely resembled the reactants, making it an early TS.

In contrast, the Diels-Alder reaction between 1,3-dioxole and cyclohexadiene explored in Exercise 2 proceeded via an inverse electron demand mechanism. This was again inferred by comparing the energies of the MOs in the reactants and in the TS. It was found that the dienophile's frontier MOs were raised in energy, making the interaction between its HOMO and the diene's LUMO stronger. To confirm this, a single point energy calculation was performed. In terms of the thermodynamic and kinetic products, the endo product satisfied both. Thermodynamically, the endo product had the lowest energy, whilst kinetically, the endo route had the lowest activation energy.

Exercise 3 explored the reaction between o-xylylene and sulfur dioxide. The possible reaction pathways were Diels-Alder and cheletropic reactions. Within the Diels-Alder reaction, depending on the approach of SO<sub>2</sub>, both exocyclic and endocyclic reactions were possible. Comparison of the three reactions showed the endo product from the exocyclic pathway to have the lowest activation energy, making the product kinetically favourable. This may have stemmed from secondary orbital interactions between the oxygen lone pair and the alkene π*. Thermodynamically, the cheletropic product was favoured as it had the lowest energy. This was attributed to the retention of an additional strong S=O bond as well as reduced strain within the five-membered heterocyclic ring compared to its six-membered counterpart.

As an extension, the electrocyclic ring closure of Diene X (see '''Further Work''' for its chemical name) was explored. The reaction was expected to be conrotatory under thermal conditions since the diene has 4π electrons (and thus satisfies the 4n equation where n =0). Analysis of the IRC confirmed this with the hydrogen atoms on the diene moving in a clockwise manner. Analysis of the reaction energies also showed the reaction to be exothermic.

== References ==

1. Https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

2. http://www.helsinki.fi/kemia/fysikaalinen/opetus/jlk/luennot/Lecture1.pdf

3. https://en.wikipedia.org/wiki/Gaussian_orbital

4. https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method

Rep:Lo915 Transition States and Reactivity

2018-04-07T10:23:52Z

Fv611: /* MO Diagrams */

=Introduction=

The aim of this experiement was to find and optimise the transition state structures of a number of different Diels-Alder reactions. The transition state is the structure with the highest energy point along a reaction coordinate, as can be seen in Figure 1, with the molecule needing enough energy to reach this point for the reaction to proceed. However the reaction is not just controlled by one reaction coordinate as is shown here, but will have many degrees of freedom. By using multiple reaction coordinates a multi-dimensional potential energy surface can be created.
[[File:lo915_energy_profile.jpg|thumb|Figure 1. Potential Energy Profile diagram along one reaction coordinate|center|500px]]

A stationary point on the PES is the point at which all of the forces vanish, and every component of the gradient is zero. This is shown be equation 1. The values of q are the reaction coordinate, and 3N-6 is the number of normal modes of the system, with N being the number of atoms.<ref>Lewars E, ''Computational Chemistryː The Concept of the Potential Energy Surface'',2016,Springer International Publishing,Cham, pp 9-49</ref>

<math>\frac{\partial E(q)}{\partial q_\alpha} = 0 \quad where \quad \alpha = 1,2...(3N-6)</math>

The stationary point includes both the minima and the maxima of the potential energy surface. There are many local minima on a multi-dimensional surface which are at the lowest energy point in that region of the PES, with the global minima being the one with the lowest energy overall, where there is the greatest stability. The transition state is at the maxima, so in order to distinguish this, the second order derivatives must be found. These give the eigenvalues for a 3N-6 x 3N-6 matrix, known as the Hessian. A transition state is the stationary point with a single negative Hessian eigenvalue, which can be found after diagonalising the Hessian matrix. This allows the transtion state to be distinguished from the reactant and product wells, for which all diagonal components of the Hessian are positive.
The lowest energy path bewtween two minima is the intrinsic reaction coordinate, and the transition state is the maxima along this path. While most of the molecules will follow the IRC, those with enough energy may have alternate pathways. Knowing the structure and energy of the transition state enables the kinetics and thermodynamics of the system to be investigated, as well as an orbital analysis.<ref>Yepes, D et al.''Phys. Chem. Chem. Phys.'', '''2012''',14, 11125-11134 </ref>

Gaussian was used in order to calculate the position and energy of the transition state. Two types of calculation were used - the semi-emperical method PM6, to generate faster but more approximate results, and the Density Functional Theory (DFT) method B3LYP,with the 6-31g(d) basis set, to generate more accurate results, but needing a greater amount of time. The semi-empirical method is a simplified version of the Hartree-Fock method, where assumptions allow the use of experimental data for thermochemistry and molecular geometries, with DFT results being used where this is lacking. The PM6 methods uses a greater variety of types of references data than previous versions, which create 'rules' that are used for the optimisation of parameters.<ref>Stewart, J ''J Mol Model'', '''2007''', ''13''(12), 1173-1213</ref> The B3LYP is a hybrid functional, which combines both DFT and the Hartree-Fock theory, from which the exact exchange energy can be used.<ref>Devlin, F. J. et al.''J. Phys. Chem.'', '''1995''', ''99'' (46), 16883–16902</ref>

There were three methods that were used to find the transition state. The first method simply involved guessing the structure of the transition state and optimising, however while this method is fast, it is also unreliable and requires previous knowledge of the transition state, in order for the structure to be close enough for the optimisation to be successful.The second methods involves guessing the structure of the transition state, then freezing the bonds at an appropriate distance before optimising as in method 1. This method is fast and more reliable than method 1, however it does still require knowledge of the transition state. Method 3 is the most reliable, and does not require as much knowledge on the transition state as the previous methods as it involves starting from the reactant or product, altering the bond length, then using method 2 to find the transition state. However this method is longer and more involved, and is also difficult if the products or reactants do not resemble the transition state. Method 2 was used for exercises 1 and 2, while excercise 3 and the electrocyclic reaction used method 3.

=Exercise 1=

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very good job in this whole section!)

This exercise involved a Diels-Alder Reaction between ethene and butadiene. The transition state was optimised using a PM6 calculation, with the reactants and product also optimised at this level. An MO diagram was constructed and compared to the MOs visualised for both the transition state and reactants. The bond distances of the carbon atoms were compared along the reaction coordinate from the reactants to the products, and the reaction path vibration was visualised.

[[File:lo915_1_reaction_scheme.jpg|thumb|Figure 2. Reaction scheme for the Diels-Alder reaction between ethene and butadiene|center|500px]]

===MO diagram===
[[File:lo915_1_MO_diagram2.jpg|thumb|Figure 3. Reaction scheme for the Diels-Alder reaction between ethene and butadiene|center|500px]]
The MO diagram for the formation of the transition state between ethene and butadiene can be seen in Figure 3. The energies of the reactant orbitals were obtained from a single point energy calculation of the reactants from the IRC, to ensure they were in same reference framework and could be compared. This shows that the LUMO and HOMO of ethene have the highest and lowest energies respectively, with the LUMO of the dienophile having a higher energy than that of the diene. The ethene LUMO is asymmetric while the butadiene LUMO is symmetric. Therefore while these two orbitals are closest in energy they are symmetry forbidden, as the integral that results from the interaction of two orbitals is only non-zero if they are of the same symmetry (symmetric with symmetric and asymmetric with asymmetric), resulting in the LUMO of ethene overlapping with the asymmetric HOMO of butadiene, producing asymmetric orbitals of the transition state. This gives an out of phase interaction of the orbitals giving the LUMO + 1, and an in phase interaction giving the HOMO-1
The LUMO+1 formed from this interaction is lower in energy that the LUMO of ethene, while the HOMO-1 is higher in energy than the HOMO of butadiene, decreasing the energy gap between them from that expected of cyclohexadiene. This is due to the fact that MO diagram is for a transition state, rather than for the product of the reaction, therefore the bonds have not fully formed. As the transition state is at the highest energy of the reaction coordinate, the orbitals are also at the highest energy, and are destabilised. The HOMO of ethene and LUMO of butadiene interact to form the HOMO (an in phase interaction) and LUMO (an out of phase interaction) of the transition state. As both are symmetric this is a symmetry allowed interaction, forming symmetric orbitals. As before, these orbitals are destabilised compared to those of the product. This reaction is a normal Diels-Alder reaction, as the HOMO of the dienophile is lower in energy than that of the diene, by a value of 0.038 Ha.
These orbitals can be visualised from the PM6 calculations, and can be seen in Figure 4.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="font-weight:normal" |Figure 4. Molecular orbitals of the reactants and transition state
!colspan="4"|Reactant MOs
|-
| <jmol>
<jmolApplet>
<title>Ethene HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 106; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_1_IRC_REACTANTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethene LUMO</title>
<color>white</color>
<size>200</size>
<script>frame 106; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_1_IRC_REACTANTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 106; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_1_IRC_REACTANTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>200</size>
<script>frame 106; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_1_IRC_REACTANTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!colspan="4"|Transition state MOs
|-
| <jmol>
<jmolApplet>
<title>HOMO - 1</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_1_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_1_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_1_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO + 1</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_1_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

From Figure 4, the symmetry of the orbitals can be seen clearly, with the HOMO and LUMO of the transition state being symmetrical, and the HOMO-1 and LUMO+1 being asymmetrical.

===Bond Distances===
[[File:Numbered_Reaction_scheme.cdx|thumb|center|400| Figure 5. Reaction Scheme with carbons numbered ‎]]
Table 1 shows the bond lengths of the carbon-carbon bonds in the reactants, transition state and product. The numbers of the carbons correspond to those seen on the reaction scheme in Figure 5.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ '''Table 1. Bond lengths in the reactants, transition state and product'''
! colspan="1" style="border: none; background: none;"|
! colspan="4"| Bond Length (Å)
|-
!Bond Position
!Ethene
!Butadiene
!Transition State
!Cyclohexadiene
|-

! C1-C2
| — || 1.335 || 1.380 || 1.501
|-
! C2-C3
| — || 1.468 || 1.411 || 1.337
|-
! C3-C4
| — || 1.335 || 1.380 || 1.501
|-
! C4-C5
| — || — || 2.115 || 1.537
|-
! C5-C6
| 1.327 || — || 1.382 || 1.535
|-
! C6-C1
| — || — || 2.115 || 1.537
|}

As can be seen in table 1, the C5-C6 bond is shortest in ethene and longest in cyclohexadiene, increasing from 1.327 Å, to 1.535 Å. The same occurs with the C1-C2 and C3-C4 bonds, increasing from 1.335 Å in butadiene to 1.501 Å, with the transition state bond being in between the two. This is due to the change from a π bond to a σ bond. This can be seen by a comparison with the average length of C=C bond (1.34 Å), which is similar to those in the reactants, and the average length of a C-C bond (1.54 Å). The C1-C2 and C3-C4 bonds are slightly shorter than this value, which is due to the fact that they are adjacent to the double bond in the product. The opposite occurs with the C2-C3 bond, which decreases from 1.468 Å in butadiene to 1.337 Å in cyclohexadiene, as this is changing from a σ bond to a π bond. While the bond in the product is similar to that of an average double bond, in butadiene it is noticeably shorter than the average single bond. This is because both the carbons are sp<sup>2</sup>, as it is adjacent to two π bonds. In the transition state, these bonds are closer in length to the bonds in the reactants than the bonds in the product, suggesting that the transition state is more similar to the reactants than the product, and is therefore an early transition state.
The van der Waals radius of the carbon atom is 1.70 Å<ref>Mantina, M et al.''J. Phys. Chem. A'','''2009''', ''113'', 19, 5806-5812</ref>, meaning that two carbon atoms within a distance of 3.4 Å will have van der Waals interactions between them. The σ bonds formed in this reaction (C4-C5 and C6-C1) have a bond length of 2.115 Å, showing that there are van der Waals interactions between them, however the bonds have not yet formed, as they are outside twice the covalent radius of the carbon atoms, which is 0.76 Å<ref>Mikhailov, B. M.,''Bull. Acad. Sci. USSR, Div. Chem. Sci.'','''1960''', ''9'',8,1284–1290</ref>. In the product, the length has decreased to 1.537 Å, as is expected for a C-C σ bond.

[[File:Lo915_1_bond_distances2.PNG|thumb|center|500px|Figure 6. Graph showing the change in bond lengths as the reaction between ethene and butadiene progresses]]

Figure 6 shows the change in bond distances throughout the reaction, obtained from the IRC. This shows the change from the product to the reactants, therefore the forwards reaction runs from left to right. Viewing the graph this way, it can be seen that the two bonds formed start at a high 'bond length' as there is no interaction between them, then as the reaction progresses the distance between them decreases, until the bond is formed. The C5-C6 bond has the same bond length as the C3-C4 bond, however increases by a greater amount and having the same bond length as the C6-C1 and C4-5 bonds. From the graph it can also been that there a point along the reaction coordinate at which all of the bonds apart from those being formed have the same bond length, which is in between that of a single and double bond.

===Reaction path Vibration===
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Figure 7. Reaction path vibration

The vibration that corresponds to the reaction path at the transition state can be seen in Figure 7. This vibration is an the imaginary frequecy of 948i cm<sup>-1</sup>. This vibration shows that the Diels-Alder reaction between ethene and butadiene is a concerted process, with synchronous formation of the two bonds. Further evidence can be of this can be seen in table 1, as the bonds formed are equal in length.

=Exercise 2=
This exercise involved a Diels Alder Reaction between cyclohexadiene and 1,3-dioxole. The transition state was first optimised using a PM6 calculation, and then further optimised at the B3LYP/631-G(d). The reactants and products were also optimised at this level. This reaction has both an endo and an exo product, as can be seen in Figure 9. The MO diagram for each of these reactions was constructed and the two compared. The reaction barriers and energies were also looked at for each of the reactions.

[[File:Lo915_2_Reaction_Scheme.jpg|thumb|Figure 8. Reaction scheme for the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, showing both the exo and endo products|center|500px]]

===MO Diagrams===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Nice MO diagrams. Well done!)

{| style="margin-left: auto; margin-right: auto; border: none; background: none;"
|-
|[[File:lo915_2_endo_MO2.jpg|thumb|Figure. 9 MO diagram for the endo reaction between cyclohexadiene and 1,3-dioxole|center|500px]]
|[[File:lo915_2_exo_MO2.jpg|thumb|Figure. 10 MO diagram for the exo reaction between cyclohexadiene and 1,3-dioxole|center|500px]]
|- style="text-align: center;"
|}
Figure 9 and 10 shows that in both the endo and the exo reaction, the LUMO of the dienophile (1,3-dioxole) has a higher energy than that of the diene (cyclobutadiene) as in the previous reaction. However in this reaction, the HOMO of the dieneophile is at a higher energy than that of the diene, unlike the reaction in exercise 1, showing that this reaction is an inverse electron demand Diels-Alder reaction. This is due to the electron-donating oxygens present in 1,3-dioxole, resulting in the species being electron rich, rather than having the electron-poor dienophile as there would be in a normal electron demand Diels-Alder reaction. For both the endo and the exo reaction the same orbitals overlap, (and the ordering of the orbitals is the same) with the asymmetric orbitals of the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole overlapping to form the LUMO + 1 and the HOMO -1 of the transition state, and the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene overlapping to form the HOMO and LUMO of the transition state. This also shows an inverse demand Diels-Alder, as in a normal Diels-Alder reaction, it is the LUMO of the dienophile and the HOMO of the diene which form the HOMO and LUMO orbitals of the product. The energies of the orbitals in each of the transition states is different, with the HOMO-1, LUMO+1 and LUMO of the endo transition state being higher in energy, and therefore destabilised relative to those of the exo , and the HOMO being lower in energy, as it is stabilised. The HOMO of the exo transition state is 0.005 Ha (or 13.13 kJmol<sup>-1</sup>) higher in energy. This creates a larger energy gap between the HOMO and LUMO in the endo transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 2. Single point energies for the endo and exo HOMO and LUMO
! colspan="2" rowspan="2" style="border: none; background: none;"|
! colspan="2"| MO Energy (Ha)
|-
! Endo !! Exo
|-
! rowspan="2"| HOMO
! 1,3-dioxole
| -0.317 || -0.322
|-
! Cyclohexadiene
| -0.321 || -0.322
|-
! rowspan="2"| LUMO
! 1,3-dioxole
| 0.032 || 0.030
|-
! Cyclohexadiene
| 0.023 || 0.021
|}

In order for the energies of the reactant orbitals to be quantitively assessed, a single point energy calculation was run for the endo and the exo reaction, with the results shown in Table 2. From this it can be seen that while there is no difference in the energy of the HOMO of each of the reactants in the exo reactions (to 3 d.p), the endo reaction shows that the HOMO of the dienophile is lower in energy by 0.004 Ha (10.5 kJmol<sup>-1</sup>)

Figure 11. shows the visualisation of the endo and exo transition state orbitals. From these the orientation of the 1,3-dioxole in the endo relative to the exo can be clearly seen, as well as the symmetry of each of the orbitals.
{| style="margin-left: auto; margin-right: auto; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 11. Transition state MOs for the endo and exo reaction
|-
!colspan="4"|Endo Transition State MOs
|-
| <jmol>
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|-
!colspan="4"|Exo Transition state MOs
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===Secondary Orbital Interactions===

The reason for the lower energy of the HOMO of the endo transition state relative to the exo can be seen in the secondary orbital interactions between the p orbitals of the cyclohexadiene and the p orbitals on the oxygens of the 1,3-dioxole. The endo transition state places these in the correct position for overlap between them, therefore stabilising the transition state and lowering its energy, however as the exo transition state has the oxygens on the opposite side, there is no opporunity for interaction between these orbitals, and therefore no stabilisation. Another reason for the lower energy of the endo transition state is due to steric hindrance that occurs in the exo product, as the 1,3-dioxole is positioned up towards the carbon bridge, while in the endo product, it points down away from the carbon bridge, and therefore avoids this destabilising steric interaction.
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 12. Secondary orbital interactions of the transition state HOMO orbital
|-
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===Energies===
The energies of the reactants, transistion states and products were obtained from the B3LYP optimised structures, and converted from Hartrees to kJmol<sup>-1</sup>.These vaules can be seen in table 3. From this, the activation energies and reaction energies were calculated and an energy profile diagram was created to clearly illustrate these values (Figure 12).
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 3. Energies of the reactants, transition states and product, with the activation and reaction energies calculated
! colspan="1" style="border: none; background: none;"|
! colspan="7"| Energy (kJmol<sup>-1</sup>)
|-
! Reaction type !! 1,3-dioxole !! Cyclohexadiene !! Reactant total !! Transition State !! Activation Energy !! Product !! Reaction Energy
|-
!Endo
| rowspan="2" | -701187.38
| rowspan="2" |-612593.15
| rowspan="2" |-1313780.53
| -1313622.06
| 158.47
| -1313849.27
| -68.75
|-
!Exo
| -1313614.22
| 168.27
| -1313845.68
| -65.15
|-
|}

From the reaction energies it can be seen that both the exo and the endo reactions are exothermic, and are therfore thermodynamically favoured, however the reaction energy is greater for the endo product, showing that this is the preferred thermodynamic product as it is more stable than the exo product. The activation energy of the endo reaction is smaller than that of the exo, showing that less energy is needed to reach the endo transition state, therefore it will be formed faster than the exo transition state, meaning that the endo reaction is also kinetically preferred. This is due to the stabilisation of the endo transition state compared to that of the exo, as was seen previously.

[[File:Lo915_2_energies.jpg|thumb|Figure 12. Energy profile diagram for the endo and exo Diels-Alder reactions between cyclohexadiene and 1,3-dioxole|center|500px]]

=Exercise 3=
In this exercise, the reactions between xylylene and SO<sub>2</sub> was investigated. As before there is a Diels-Alder reaction, which can proceed in an endo or an exo reaction, however there is also a cheletropic reaction which can occure, and this can be seen in the reaction scheme in Figure 13. There is also an alternate Diels-Alder reaction which can occur with the diene inside the 6-membered ring. The reaction coordinate for these reactions were investigated, and the activation energies and reaction energies were compared.
[[File:Lo915_3_Reaction_Scheme.jpg|thumb|Figure 13. Reaction scheme for the reaction between xylylene and SO<sub>2</sub>|center|500px]]
===Visualisation of the reaction coordinate===
The reaction coordinate of each reaction type was visualised using the IRC at the PM6 level, and these are shown in Figure 14. The IRC of the exo Diels-Alder reaction shows the oxygen not involved in the formation of the ring orientated away from xylylene, while in the endo reaction is is orientated towards it. In both of the Diels-Alder reactions it can be seen that the C-O bond forms before the C-S bond, therefore there is asynchronous bond formation, however in the cheletropic reaction, both of the C-S bonds form simultaneously, showing synchronous bond formation. In all of the reactions the 6-membered ring forms an aromatic system with 6π electrons as SO<sub>2</sub> starts to bond to xylylene. This is what drives the reaction forward, giving stability to the products and causes xylylene to be highly unstable.

(GaussView uses a distance cutoff to decide when to draw a visual bond, but you can't use this to decide when a bond is formed [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 4 April 2018 (BST))

{|style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 14. Animations of the IRCs for the endo and exo Diels-Alder reactions and the cheletropic reaction
!Endo Diels-Alder
!Exo Diels-Alder
!Cheletropic
|-
|[[File:Lo915_3_endo3.gif]]
|[[File:Lo915_3_exo2.gif]]
|[[File:Lo915_3_cheletropic2.gif]]
|}

===Energies===
The energies of the reactants, transition state and product was obtained from the PM6 calculation for the endo, exo and cheletropic reaction. The activation energies and reaction energies were calculated, and these are shown in table 5. As in exercise 2, an energy profile digram was created to visualise these results easily (figure 15).
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 4. Energies of the reactants, transition states and products for the reactions between xylylene and SO<sub>2</sub>
! colspan="1" style="border: none; background: none;"|
! colspan="7"| Energy (kJmol<sup>-1</sup>)
|-
! Reaction type !! SO<sub>2</sub> !! Xylylene!! Reactant total !! Transition State !! Activation Energy !! Product !! Reaction Energy
|-
!Exo
| rowspan="3" | -311.38
| rowspan="3" | 466.43
| rowspan="3" | 154.94
| 241.75
| 86.81
| 56.32
| -98.61
|-
!Endo
| 237.77
| 82.83
| 56.98
| -97.97
|-
!Cheletropic
| 260.09
| 105.15
| 0.00
| -154.94
|}

[[File:lo915_3_energies1.jpg|thumb|Figure 15. Energy profile diagram for the endo and exo Diels-Alder reactions and cheletropic reaction between xylylene and SO<sub>2</sub>|center|500px]]

From the activation energies it can be seen that the cheletropic reaction has the largest energy barrier to the reaction, so is the least kinetically preferred. This is due to the formation of the strained 5-membered ring in comparison to the 6-membered ring formed in the Diels-Alder transition state, which has a lower degree of strain. The activation of the endo and exo reaction are more similar in energy, however the endo reaction has the lowest activation energy and is therefore the kinetically preferred product, and will be formed fastest, needing the least energy for the reaction to occur. This is due to the secondary orbital interactions between the p orbitals of the oxygen being able to overlap with those in xylylene in the endo orientation, however as the oxygen points away from xylyene in the exo orientation, this stabilisation is not possible. The reaction energies show that all of these reactions are thermodynamically favourable, however the cheletropic reaction has the greatest reaction energy and so is the thermodynamically preferred product.This is due to there being a loss of three π bonds in the Diels-Alder reactions with one π bond and two σ bonds formed, compared to the loss of only two π bonds in the cheletropic reaction, with again one π bond and two σ bonds formed. The endo and exo products are very similar in energy, and are both higher in energy than the cheletropic product, however the endo product has a slightly higher energy than the exo, therefore has a slightly greater reaction energy.

===Alternative Diels-Alder Reactions===

Another option for a Diels-Alder reaction comes from the diene within the 6-membered ring of xylylene, and this could be a endo or an exo reaction, as for the previous Diels-Alder reaction. The reaction coordinate for these were also visualised with the IRC at the PM6 level, and can be seen in figure 15. As before the bond formation is asynchronous, however unlike before, due to the fact that bond formation is occuring at the 6-membered ring, there is no opportunity for an aromatic system to form.

{|style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 16. Animations of the IRCs for the internal endo and exo Diels-Alder reactions
|-
!Internal Endo Diels-Alder
!Internal Exo Diels-Alder
|-
|[[File:Lo915_3_int_endo2.gif]]
|[[File:Lo915_3_int_exo2.gif]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 4. Energies of the reactants, transition states and products for the internal Diels-Alder reactions
! colspan="1" style="border: none; background: none;"|
! colspan="7"| Energy (kJmol<sup>-1</sup>)
|-
! Reaction type !! SO<sub>2</sub> !! Xylylene!! Reactant total !! Transition State !! Activation Energy !! Product !! Reaction Energy
|-
!Exo
| rowspan="2" | -311.38
| rowspan="2" | 466.43
| rowspan="2" | 154.94
| 275.82
| 120.88
| 176.70
| 21.77
|-
!Endo
| 267.98
| 113.05
| 172.26
| 17.32
|-
|}

From the reaction energies shown in table 4 it can be seen that these reactions are endothermic and therefore not thermodynamically favourable, which is due to the lack of aromaticity to stabilise the products. The activation energy for both reactions is also very high compared to the previous Diels-Alder reactions, showing that the reactions are also kinetically unfavourable. The endo reaction is kinetically and preferred over the exo reaction, which is due to the stabilisation that comes from the orbital interaction of the p orbital of the oxygen with that of the diene, as before.

=Electrocyclic reaction=
The electrocyclic reaction of a diene was investigated at the PM6 level. Figure 16 shows the reaction scheme for this reaction. This is a thermal reaction rather than a photochemical reaction as at the PM6 level, the molecules are in the ground state, and for a photochemical reaction to occur, they would need to be able to reach an excited state. This means that as there are 4n electrons, therefore the groups on the diene will both rotate in the same direction (conrotation). This results in both hydrogens facing upwards as can be seen in the reaction path vibration (figure 17)
[[File:lo915_4_reaction_scheme.jpg|thumb|Figure 16. Reaction scheme for the thermal electrocyclic reaction|center|500px]]

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Figure 17. Vibration of reaction path
[[File:lo915_4_conrotation2.jpg|thumb|Figure 18. Controtation in electrocyclic reaction|center|500px]]

(Very close but you're using Ψ4 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:36, 4 April 2018 (BST))

Figure 18 shows the formation of the HOMO of the product, with the C<sub>2</sub> axis of symmetry labelled. This axis of symmetry is used to label the orbitals as either symmetric or asymmetric. Figure 19 shows the correlation diagram for the reaction, where it can be seen that the order of the occupied orbitals is reversed, with symmetric HOMO of the reactant forming the symmetric σ orbital formed in the product, while the HOMO orbital of the product (the π orbital) has the same symmetry as the HOMO-1 of the reactant. The same occurs with the unoccupied orbitals, with the asymmetric LUMO of the reactant forming the asymmetric LUMO+1 of the product (the σ<sup>*</sup> orbital), and the LUMO+1 orbitals of the reactant forming the LUMO of the product (the π<sup>*</sup> orbital)
[[File:lo915_4_MOs2.jpg|thumb|Figure 19. Correlation diagram|center|500px]]
The reaction goes through a mobius transition state, with a node in the phases of the orbitals. As it is a 4n electron reaction, the transition state is termed 'aromatic'.<ref>Dolbier, W. R''Acc. Chem. Res.'', '''1996''', ''29'', 471-477</ref> This can be seen in the visualisation of the transition state orbitals in figure 16.

{| style="margin-left: auto; margin-right: auto; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 20. Reactant, product and transition state MOs
|-
!colspan="4"|Reactant MOs
|-
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|-
!colspan="4"|Product MOs
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<uploadedFileContents>Lo915_4_IRC_FINAL.LOG</uploadedFileContents>
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</jmol>
|-
!colspan="4"|Transition State MOs
|-
| <jmol>
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| <jmol>
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<uploadedFileContents>Lo915_4_TS.LOG</uploadedFileContents>
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<uploadedFileContents>Lo915_4_TS.LOG</uploadedFileContents>
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|}

=Conclusion=
For all of the reactions, the transition state was found and optimised successfully. It was found that the first Diels-Alder reaction was normal demand, while the second Diels-Alder was inverse electron demand, due to the electron rich nature of the dienophile. For both exercises 2 and 3, it was found that the endo Diels-Alder reaction was thermodynamically preferred to the exo reaction, due to the stabilising secondary orbital overlap. For exercise 3, the cheletropic product was the thermodynamically preferred product, while the alternate Diels-Alder reactions were thermodynamically unfavourable as there is no aromatic ring formation as for the original Diels-Alder reactions and the cheletropic reaction. In the electrocyclic reaction it was found to proceed in a conrotatory fashion, as expected for a thermal 4n eletron elecrocyclic reaction. This could be extended by investigated the photochemical reaction, which would preocceed in a disrotatory fashion, however the PM6 level could not be used for these calculations due to the need for excited states.

=Files=
===Exercise 1===
[[Media:Lo915_1_ETHENE.LOG|Log file of ethene (PM6)]]

[[Media:Lo915_1_BUTADIENE.LOG|Log file of butadiene]]

[[Media:LO915_REACTANTS_ENERGY.LOG||Log file of Single point energy of reactants]]

[[Media:Lo915_1_TS.LOG|Log file of transition state]]

[[Media:Lo915_1_TSIRC.LOG|Log file of IRC]]

[[Media:Lo915_1_IRC_PRODUCTS.LOG|Log file of product]]

===Exercise 2===
[[Media:Lo915_2_DIOXOLE_B3LYP.LOG|Log file of 1,3-dioxole ]]

[[Media:Lo915_2_CYCLOHEXADIENE_B3LYP.LOG|Log file of cyclohexadiene]]

[[Media:Lo915_2_TS_ENDO_B3LYP.LOG|Log file of endo transition state]]

[[Media:Lo915_2_TS_EXO_B3LYP.LOG|Log file of exo transition state]]

[[Media:Lo915_2_ENDO_IRC.LOG|Log file of endo IRC]]

[[Media:Lo915_2_EXO_IRC_PM6.LOG|Log file of exo IRC]]

[[Media:Lo915_2_ENDO_PRODUCTS_B3LYP.LOG|Log file of endo product]]

[[Media:Lo915_2_EXO_PRODUCTS_B3LYP.LOG|Log file of exo product]]

===Exercise 3===
[[Media:lo915_3_SO2.LOG|Log file of SO<sub>2</sub>]]

[[Media:lo915_3_XYLENE2.LOG|Log file of xylylene]]

[[Media:lo915_3_TS_ENDO.LOG|Log file of endo transition state]]

[[Media:lo915_3_TS_ENDO_IRC.LOG|Log file of endo IRC]]

[[Media:lo915_3_ENDO_PROD.LOG|Log file of endo product]]

[[Media:lo915_3_TS_EXO.LOG|Log file of exo transition state]]

[[Media:lo915_3_EXO_IRC.LOG|Log file of exo IRC]]

[[Media:lo915_3_EXO_PROD.LOG|Log file of exo product]]

[[Media:lo915_3_CHELETROPIC_TS.LOG|Log file of cheletropic transition state]]

[[Media:lo915_3_CHELETROPIC_IRC.LOG|Log file of cheletropic IRC]]

[[Media:lo915_3_CHELETROPIC_PROD.LOG|Log file of cheletropic product]]

[[Media:lo915_3_INT_ENDO_TS.LOG|Log file of internal endo transition state]]

[[Media:lo915_3_INT_ENDO_IRC.LOG|Log file of internal endo IRC]]

[[Media:lo915_3_INT_ENDO_PROD.LOG|Log file of internal endo product]]

[[Media:lo915_3_INT_EXO_TS.LOG|Log file of internal exo transition state]]

[[Media:lo915_3_INT_EXO_IRC.LOG|Log file of internal exo IRC]]

[[Media:lo915_3_INT_EXO_PROD.LOG|Log file of internal exo product]]

===Electrocyclic Reaction===
[[Media:lo915_4_TS.LOG|Log file of transition state]]

[[Media:lo915_4_IRC.LOG|Log file of IRC]]

[[Media:lo915_4_IRC_INITIAL.LOG|Log file of reactant]]

[[Media:lo915_4_IRC_FINAL.LOG|Log file of product]]

=References=

Rep:Lo915 Transition States and Reactivity

2018-04-07T10:22:50Z

Fv611: /* Exercise 1 */

=Introduction=

The aim of this experiement was to find and optimise the transition state structures of a number of different Diels-Alder reactions. The transition state is the structure with the highest energy point along a reaction coordinate, as can be seen in Figure 1, with the molecule needing enough energy to reach this point for the reaction to proceed. However the reaction is not just controlled by one reaction coordinate as is shown here, but will have many degrees of freedom. By using multiple reaction coordinates a multi-dimensional potential energy surface can be created.
[[File:lo915_energy_profile.jpg|thumb|Figure 1. Potential Energy Profile diagram along one reaction coordinate|center|500px]]

A stationary point on the PES is the point at which all of the forces vanish, and every component of the gradient is zero. This is shown be equation 1. The values of q are the reaction coordinate, and 3N-6 is the number of normal modes of the system, with N being the number of atoms.<ref>Lewars E, ''Computational Chemistryː The Concept of the Potential Energy Surface'',2016,Springer International Publishing,Cham, pp 9-49</ref>

<math>\frac{\partial E(q)}{\partial q_\alpha} = 0 \quad where \quad \alpha = 1,2...(3N-6)</math>

The stationary point includes both the minima and the maxima of the potential energy surface. There are many local minima on a multi-dimensional surface which are at the lowest energy point in that region of the PES, with the global minima being the one with the lowest energy overall, where there is the greatest stability. The transition state is at the maxima, so in order to distinguish this, the second order derivatives must be found. These give the eigenvalues for a 3N-6 x 3N-6 matrix, known as the Hessian. A transition state is the stationary point with a single negative Hessian eigenvalue, which can be found after diagonalising the Hessian matrix. This allows the transtion state to be distinguished from the reactant and product wells, for which all diagonal components of the Hessian are positive.
The lowest energy path bewtween two minima is the intrinsic reaction coordinate, and the transition state is the maxima along this path. While most of the molecules will follow the IRC, those with enough energy may have alternate pathways. Knowing the structure and energy of the transition state enables the kinetics and thermodynamics of the system to be investigated, as well as an orbital analysis.<ref>Yepes, D et al.''Phys. Chem. Chem. Phys.'', '''2012''',14, 11125-11134 </ref>

Gaussian was used in order to calculate the position and energy of the transition state. Two types of calculation were used - the semi-emperical method PM6, to generate faster but more approximate results, and the Density Functional Theory (DFT) method B3LYP,with the 6-31g(d) basis set, to generate more accurate results, but needing a greater amount of time. The semi-empirical method is a simplified version of the Hartree-Fock method, where assumptions allow the use of experimental data for thermochemistry and molecular geometries, with DFT results being used where this is lacking. The PM6 methods uses a greater variety of types of references data than previous versions, which create 'rules' that are used for the optimisation of parameters.<ref>Stewart, J ''J Mol Model'', '''2007''', ''13''(12), 1173-1213</ref> The B3LYP is a hybrid functional, which combines both DFT and the Hartree-Fock theory, from which the exact exchange energy can be used.<ref>Devlin, F. J. et al.''J. Phys. Chem.'', '''1995''', ''99'' (46), 16883–16902</ref>

There were three methods that were used to find the transition state. The first method simply involved guessing the structure of the transition state and optimising, however while this method is fast, it is also unreliable and requires previous knowledge of the transition state, in order for the structure to be close enough for the optimisation to be successful.The second methods involves guessing the structure of the transition state, then freezing the bonds at an appropriate distance before optimising as in method 1. This method is fast and more reliable than method 1, however it does still require knowledge of the transition state. Method 3 is the most reliable, and does not require as much knowledge on the transition state as the previous methods as it involves starting from the reactant or product, altering the bond length, then using method 2 to find the transition state. However this method is longer and more involved, and is also difficult if the products or reactants do not resemble the transition state. Method 2 was used for exercises 1 and 2, while excercise 3 and the electrocyclic reaction used method 3.

=Exercise 1=

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very good job in this whole section!)

This exercise involved a Diels-Alder Reaction between ethene and butadiene. The transition state was optimised using a PM6 calculation, with the reactants and product also optimised at this level. An MO diagram was constructed and compared to the MOs visualised for both the transition state and reactants. The bond distances of the carbon atoms were compared along the reaction coordinate from the reactants to the products, and the reaction path vibration was visualised.

[[File:lo915_1_reaction_scheme.jpg|thumb|Figure 2. Reaction scheme for the Diels-Alder reaction between ethene and butadiene|center|500px]]

===MO diagram===
[[File:lo915_1_MO_diagram2.jpg|thumb|Figure 3. Reaction scheme for the Diels-Alder reaction between ethene and butadiene|center|500px]]
The MO diagram for the formation of the transition state between ethene and butadiene can be seen in Figure 3. The energies of the reactant orbitals were obtained from a single point energy calculation of the reactants from the IRC, to ensure they were in same reference framework and could be compared. This shows that the LUMO and HOMO of ethene have the highest and lowest energies respectively, with the LUMO of the dienophile having a higher energy than that of the diene. The ethene LUMO is asymmetric while the butadiene LUMO is symmetric. Therefore while these two orbitals are closest in energy they are symmetry forbidden, as the integral that results from the interaction of two orbitals is only non-zero if they are of the same symmetry (symmetric with symmetric and asymmetric with asymmetric), resulting in the LUMO of ethene overlapping with the asymmetric HOMO of butadiene, producing asymmetric orbitals of the transition state. This gives an out of phase interaction of the orbitals giving the LUMO + 1, and an in phase interaction giving the HOMO-1
The LUMO+1 formed from this interaction is lower in energy that the LUMO of ethene, while the HOMO-1 is higher in energy than the HOMO of butadiene, decreasing the energy gap between them from that expected of cyclohexadiene. This is due to the fact that MO diagram is for a transition state, rather than for the product of the reaction, therefore the bonds have not fully formed. As the transition state is at the highest energy of the reaction coordinate, the orbitals are also at the highest energy, and are destabilised. The HOMO of ethene and LUMO of butadiene interact to form the HOMO (an in phase interaction) and LUMO (an out of phase interaction) of the transition state. As both are symmetric this is a symmetry allowed interaction, forming symmetric orbitals. As before, these orbitals are destabilised compared to those of the product. This reaction is a normal Diels-Alder reaction, as the HOMO of the dienophile is lower in energy than that of the diene, by a value of 0.038 Ha.
These orbitals can be visualised from the PM6 calculations, and can be seen in Figure 4.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="font-weight:normal" |Figure 4. Molecular orbitals of the reactants and transition state
!colspan="4"|Reactant MOs
|-
| <jmol>
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|-
!colspan="4"|Transition state MOs
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| <jmol>
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| <jmol>
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From Figure 4, the symmetry of the orbitals can be seen clearly, with the HOMO and LUMO of the transition state being symmetrical, and the HOMO-1 and LUMO+1 being asymmetrical.

===Bond Distances===
[[File:Numbered_Reaction_scheme.cdx|thumb|center|400| Figure 5. Reaction Scheme with carbons numbered ‎]]
Table 1 shows the bond lengths of the carbon-carbon bonds in the reactants, transition state and product. The numbers of the carbons correspond to those seen on the reaction scheme in Figure 5.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ '''Table 1. Bond lengths in the reactants, transition state and product'''
! colspan="1" style="border: none; background: none;"|
! colspan="4"| Bond Length (Å)
|-
!Bond Position
!Ethene
!Butadiene
!Transition State
!Cyclohexadiene
|-

! C1-C2
| — || 1.335 || 1.380 || 1.501
|-
! C2-C3
| — || 1.468 || 1.411 || 1.337
|-
! C3-C4
| — || 1.335 || 1.380 || 1.501
|-
! C4-C5
| — || — || 2.115 || 1.537
|-
! C5-C6
| 1.327 || — || 1.382 || 1.535
|-
! C6-C1
| — || — || 2.115 || 1.537
|}

As can be seen in table 1, the C5-C6 bond is shortest in ethene and longest in cyclohexadiene, increasing from 1.327 Å, to 1.535 Å. The same occurs with the C1-C2 and C3-C4 bonds, increasing from 1.335 Å in butadiene to 1.501 Å, with the transition state bond being in between the two. This is due to the change from a π bond to a σ bond. This can be seen by a comparison with the average length of C=C bond (1.34 Å), which is similar to those in the reactants, and the average length of a C-C bond (1.54 Å). The C1-C2 and C3-C4 bonds are slightly shorter than this value, which is due to the fact that they are adjacent to the double bond in the product. The opposite occurs with the C2-C3 bond, which decreases from 1.468 Å in butadiene to 1.337 Å in cyclohexadiene, as this is changing from a σ bond to a π bond. While the bond in the product is similar to that of an average double bond, in butadiene it is noticeably shorter than the average single bond. This is because both the carbons are sp<sup>2</sup>, as it is adjacent to two π bonds. In the transition state, these bonds are closer in length to the bonds in the reactants than the bonds in the product, suggesting that the transition state is more similar to the reactants than the product, and is therefore an early transition state.
The van der Waals radius of the carbon atom is 1.70 Å<ref>Mantina, M et al.''J. Phys. Chem. A'','''2009''', ''113'', 19, 5806-5812</ref>, meaning that two carbon atoms within a distance of 3.4 Å will have van der Waals interactions between them. The σ bonds formed in this reaction (C4-C5 and C6-C1) have a bond length of 2.115 Å, showing that there are van der Waals interactions between them, however the bonds have not yet formed, as they are outside twice the covalent radius of the carbon atoms, which is 0.76 Å<ref>Mikhailov, B. M.,''Bull. Acad. Sci. USSR, Div. Chem. Sci.'','''1960''', ''9'',8,1284–1290</ref>. In the product, the length has decreased to 1.537 Å, as is expected for a C-C σ bond.

[[File:Lo915_1_bond_distances2.PNG|thumb|center|500px|Figure 6. Graph showing the change in bond lengths as the reaction between ethene and butadiene progresses]]

Figure 6 shows the change in bond distances throughout the reaction, obtained from the IRC. This shows the change from the product to the reactants, therefore the forwards reaction runs from left to right. Viewing the graph this way, it can be seen that the two bonds formed start at a high 'bond length' as there is no interaction between them, then as the reaction progresses the distance between them decreases, until the bond is formed. The C5-C6 bond has the same bond length as the C3-C4 bond, however increases by a greater amount and having the same bond length as the C6-C1 and C4-5 bonds. From the graph it can also been that there a point along the reaction coordinate at which all of the bonds apart from those being formed have the same bond length, which is in between that of a single and double bond.

===Reaction path Vibration===
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Figure 7. Reaction path vibration

The vibration that corresponds to the reaction path at the transition state can be seen in Figure 7. This vibration is an the imaginary frequecy of 948i cm<sup>-1</sup>. This vibration shows that the Diels-Alder reaction between ethene and butadiene is a concerted process, with synchronous formation of the two bonds. Further evidence can be of this can be seen in table 1, as the bonds formed are equal in length.

=Exercise 2=
This exercise involved a Diels Alder Reaction between cyclohexadiene and 1,3-dioxole. The transition state was first optimised using a PM6 calculation, and then further optimised at the B3LYP/631-G(d). The reactants and products were also optimised at this level. This reaction has both an endo and an exo product, as can be seen in Figure 9. The MO diagram for each of these reactions was constructed and the two compared. The reaction barriers and energies were also looked at for each of the reactions.

[[File:Lo915_2_Reaction_Scheme.jpg|thumb|Figure 8. Reaction scheme for the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, showing both the exo and endo products|center|500px]]

===MO Diagrams===
{| style="margin-left: auto; margin-right: auto; border: none; background: none;"
|-
|[[File:lo915_2_endo_MO2.jpg|thumb|Figure. 9 MO diagram for the endo reaction between cyclohexadiene and 1,3-dioxole|center|500px]]
|[[File:lo915_2_exo_MO2.jpg|thumb|Figure. 10 MO diagram for the exo reaction between cyclohexadiene and 1,3-dioxole|center|500px]]
|- style="text-align: center;"
|}
Figure 9 and 10 shows that in both the endo and the exo reaction, the LUMO of the dienophile (1,3-dioxole) has a higher energy than that of the diene (cyclobutadiene) as in the previous reaction. However in this reaction, the HOMO of the dieneophile is at a higher energy than that of the diene, unlike the reaction in exercise 1, showing that this reaction is an inverse electron demand Diels-Alder reaction. This is due to the electron-donating oxygens present in 1,3-dioxole, resulting in the species being electron rich, rather than having the electron-poor dienophile as there would be in a normal electron demand Diels-Alder reaction. For both the endo and the exo reaction the same orbitals overlap, (and the ordering of the orbitals is the same) with the asymmetric orbitals of the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole overlapping to form the LUMO + 1 and the HOMO -1 of the transition state, and the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene overlapping to form the HOMO and LUMO of the transition state. This also shows an inverse demand Diels-Alder, as in a normal Diels-Alder reaction, it is the LUMO of the dienophile and the HOMO of the diene which form the HOMO and LUMO orbitals of the product. The energies of the orbitals in each of the transition states is different, with the HOMO-1, LUMO+1 and LUMO of the endo transition state being higher in energy, and therefore destabilised relative to those of the exo , and the HOMO being lower in energy, as it is stabilised. The HOMO of the exo transition state is 0.005 Ha (or 13.13 kJmol<sup>-1</sup>) higher in energy. This creates a larger energy gap between the HOMO and LUMO in the endo transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 2. Single point energies for the endo and exo HOMO and LUMO
! colspan="2" rowspan="2" style="border: none; background: none;"|
! colspan="2"| MO Energy (Ha)
|-
! Endo !! Exo
|-
! rowspan="2"| HOMO
! 1,3-dioxole
| -0.317 || -0.322
|-
! Cyclohexadiene
| -0.321 || -0.322
|-
! rowspan="2"| LUMO
! 1,3-dioxole
| 0.032 || 0.030
|-
! Cyclohexadiene
| 0.023 || 0.021
|}

In order for the energies of the reactant orbitals to be quantitively assessed, a single point energy calculation was run for the endo and the exo reaction, with the results shown in Table 2. From this it can be seen that while there is no difference in the energy of the HOMO of each of the reactants in the exo reactions (to 3 d.p), the endo reaction shows that the HOMO of the dienophile is lower in energy by 0.004 Ha (10.5 kJmol<sup>-1</sup>)

Figure 11. shows the visualisation of the endo and exo transition state orbitals. From these the orientation of the 1,3-dioxole in the endo relative to the exo can be clearly seen, as well as the symmetry of each of the orbitals.
{| style="margin-left: auto; margin-right: auto; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 11. Transition state MOs for the endo and exo reaction
|-
!colspan="4"|Endo Transition State MOs
|-
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|-
!colspan="4"|Exo Transition state MOs
|-
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| <jmol>
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| <jmol>
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===Secondary Orbital Interactions===

The reason for the lower energy of the HOMO of the endo transition state relative to the exo can be seen in the secondary orbital interactions between the p orbitals of the cyclohexadiene and the p orbitals on the oxygens of the 1,3-dioxole. The endo transition state places these in the correct position for overlap between them, therefore stabilising the transition state and lowering its energy, however as the exo transition state has the oxygens on the opposite side, there is no opporunity for interaction between these orbitals, and therefore no stabilisation. Another reason for the lower energy of the endo transition state is due to steric hindrance that occurs in the exo product, as the 1,3-dioxole is positioned up towards the carbon bridge, while in the endo product, it points down away from the carbon bridge, and therefore avoids this destabilising steric interaction.
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 12. Secondary orbital interactions of the transition state HOMO orbital
|-
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===Energies===
The energies of the reactants, transistion states and products were obtained from the B3LYP optimised structures, and converted from Hartrees to kJmol<sup>-1</sup>.These vaules can be seen in table 3. From this, the activation energies and reaction energies were calculated and an energy profile diagram was created to clearly illustrate these values (Figure 12).
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 3. Energies of the reactants, transition states and product, with the activation and reaction energies calculated
! colspan="1" style="border: none; background: none;"|
! colspan="7"| Energy (kJmol<sup>-1</sup>)
|-
! Reaction type !! 1,3-dioxole !! Cyclohexadiene !! Reactant total !! Transition State !! Activation Energy !! Product !! Reaction Energy
|-
!Endo
| rowspan="2" | -701187.38
| rowspan="2" |-612593.15
| rowspan="2" |-1313780.53
| -1313622.06
| 158.47
| -1313849.27
| -68.75
|-
!Exo
| -1313614.22
| 168.27
| -1313845.68
| -65.15
|-
|}

From the reaction energies it can be seen that both the exo and the endo reactions are exothermic, and are therfore thermodynamically favoured, however the reaction energy is greater for the endo product, showing that this is the preferred thermodynamic product as it is more stable than the exo product. The activation energy of the endo reaction is smaller than that of the exo, showing that less energy is needed to reach the endo transition state, therefore it will be formed faster than the exo transition state, meaning that the endo reaction is also kinetically preferred. This is due to the stabilisation of the endo transition state compared to that of the exo, as was seen previously.

[[File:Lo915_2_energies.jpg|thumb|Figure 12. Energy profile diagram for the endo and exo Diels-Alder reactions between cyclohexadiene and 1,3-dioxole|center|500px]]

=Exercise 3=
In this exercise, the reactions between xylylene and SO<sub>2</sub> was investigated. As before there is a Diels-Alder reaction, which can proceed in an endo or an exo reaction, however there is also a cheletropic reaction which can occure, and this can be seen in the reaction scheme in Figure 13. There is also an alternate Diels-Alder reaction which can occur with the diene inside the 6-membered ring. The reaction coordinate for these reactions were investigated, and the activation energies and reaction energies were compared.
[[File:Lo915_3_Reaction_Scheme.jpg|thumb|Figure 13. Reaction scheme for the reaction between xylylene and SO<sub>2</sub>|center|500px]]
===Visualisation of the reaction coordinate===
The reaction coordinate of each reaction type was visualised using the IRC at the PM6 level, and these are shown in Figure 14. The IRC of the exo Diels-Alder reaction shows the oxygen not involved in the formation of the ring orientated away from xylylene, while in the endo reaction is is orientated towards it. In both of the Diels-Alder reactions it can be seen that the C-O bond forms before the C-S bond, therefore there is asynchronous bond formation, however in the cheletropic reaction, both of the C-S bonds form simultaneously, showing synchronous bond formation. In all of the reactions the 6-membered ring forms an aromatic system with 6π electrons as SO<sub>2</sub> starts to bond to xylylene. This is what drives the reaction forward, giving stability to the products and causes xylylene to be highly unstable.

(GaussView uses a distance cutoff to decide when to draw a visual bond, but you can't use this to decide when a bond is formed [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 4 April 2018 (BST))

{|style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 14. Animations of the IRCs for the endo and exo Diels-Alder reactions and the cheletropic reaction
!Endo Diels-Alder
!Exo Diels-Alder
!Cheletropic
|-
|[[File:Lo915_3_endo3.gif]]
|[[File:Lo915_3_exo2.gif]]
|[[File:Lo915_3_cheletropic2.gif]]
|}

===Energies===
The energies of the reactants, transition state and product was obtained from the PM6 calculation for the endo, exo and cheletropic reaction. The activation energies and reaction energies were calculated, and these are shown in table 5. As in exercise 2, an energy profile digram was created to visualise these results easily (figure 15).
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 4. Energies of the reactants, transition states and products for the reactions between xylylene and SO<sub>2</sub>
! colspan="1" style="border: none; background: none;"|
! colspan="7"| Energy (kJmol<sup>-1</sup>)
|-
! Reaction type !! SO<sub>2</sub> !! Xylylene!! Reactant total !! Transition State !! Activation Energy !! Product !! Reaction Energy
|-
!Exo
| rowspan="3" | -311.38
| rowspan="3" | 466.43
| rowspan="3" | 154.94
| 241.75
| 86.81
| 56.32
| -98.61
|-
!Endo
| 237.77
| 82.83
| 56.98
| -97.97
|-
!Cheletropic
| 260.09
| 105.15
| 0.00
| -154.94
|}

[[File:lo915_3_energies1.jpg|thumb|Figure 15. Energy profile diagram for the endo and exo Diels-Alder reactions and cheletropic reaction between xylylene and SO<sub>2</sub>|center|500px]]

From the activation energies it can be seen that the cheletropic reaction has the largest energy barrier to the reaction, so is the least kinetically preferred. This is due to the formation of the strained 5-membered ring in comparison to the 6-membered ring formed in the Diels-Alder transition state, which has a lower degree of strain. The activation of the endo and exo reaction are more similar in energy, however the endo reaction has the lowest activation energy and is therefore the kinetically preferred product, and will be formed fastest, needing the least energy for the reaction to occur. This is due to the secondary orbital interactions between the p orbitals of the oxygen being able to overlap with those in xylylene in the endo orientation, however as the oxygen points away from xylyene in the exo orientation, this stabilisation is not possible. The reaction energies show that all of these reactions are thermodynamically favourable, however the cheletropic reaction has the greatest reaction energy and so is the thermodynamically preferred product.This is due to there being a loss of three π bonds in the Diels-Alder reactions with one π bond and two σ bonds formed, compared to the loss of only two π bonds in the cheletropic reaction, with again one π bond and two σ bonds formed. The endo and exo products are very similar in energy, and are both higher in energy than the cheletropic product, however the endo product has a slightly higher energy than the exo, therefore has a slightly greater reaction energy.

===Alternative Diels-Alder Reactions===

Another option for a Diels-Alder reaction comes from the diene within the 6-membered ring of xylylene, and this could be a endo or an exo reaction, as for the previous Diels-Alder reaction. The reaction coordinate for these were also visualised with the IRC at the PM6 level, and can be seen in figure 15. As before the bond formation is asynchronous, however unlike before, due to the fact that bond formation is occuring at the 6-membered ring, there is no opportunity for an aromatic system to form.

{|style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 16. Animations of the IRCs for the internal endo and exo Diels-Alder reactions
|-
!Internal Endo Diels-Alder
!Internal Exo Diels-Alder
|-
|[[File:Lo915_3_int_endo2.gif]]
|[[File:Lo915_3_int_exo2.gif]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 4. Energies of the reactants, transition states and products for the internal Diels-Alder reactions
! colspan="1" style="border: none; background: none;"|
! colspan="7"| Energy (kJmol<sup>-1</sup>)
|-
! Reaction type !! SO<sub>2</sub> !! Xylylene!! Reactant total !! Transition State !! Activation Energy !! Product !! Reaction Energy
|-
!Exo
| rowspan="2" | -311.38
| rowspan="2" | 466.43
| rowspan="2" | 154.94
| 275.82
| 120.88
| 176.70
| 21.77
|-
!Endo
| 267.98
| 113.05
| 172.26
| 17.32
|-
|}

From the reaction energies shown in table 4 it can be seen that these reactions are endothermic and therefore not thermodynamically favourable, which is due to the lack of aromaticity to stabilise the products. The activation energy for both reactions is also very high compared to the previous Diels-Alder reactions, showing that the reactions are also kinetically unfavourable. The endo reaction is kinetically and preferred over the exo reaction, which is due to the stabilisation that comes from the orbital interaction of the p orbital of the oxygen with that of the diene, as before.

=Electrocyclic reaction=
The electrocyclic reaction of a diene was investigated at the PM6 level. Figure 16 shows the reaction scheme for this reaction. This is a thermal reaction rather than a photochemical reaction as at the PM6 level, the molecules are in the ground state, and for a photochemical reaction to occur, they would need to be able to reach an excited state. This means that as there are 4n electrons, therefore the groups on the diene will both rotate in the same direction (conrotation). This results in both hydrogens facing upwards as can be seen in the reaction path vibration (figure 17)
[[File:lo915_4_reaction_scheme.jpg|thumb|Figure 16. Reaction scheme for the thermal electrocyclic reaction|center|500px]]

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Figure 17. Vibration of reaction path
[[File:lo915_4_conrotation2.jpg|thumb|Figure 18. Controtation in electrocyclic reaction|center|500px]]

(Very close but you're using Ψ4 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:36, 4 April 2018 (BST))

Figure 18 shows the formation of the HOMO of the product, with the C<sub>2</sub> axis of symmetry labelled. This axis of symmetry is used to label the orbitals as either symmetric or asymmetric. Figure 19 shows the correlation diagram for the reaction, where it can be seen that the order of the occupied orbitals is reversed, with symmetric HOMO of the reactant forming the symmetric σ orbital formed in the product, while the HOMO orbital of the product (the π orbital) has the same symmetry as the HOMO-1 of the reactant. The same occurs with the unoccupied orbitals, with the asymmetric LUMO of the reactant forming the asymmetric LUMO+1 of the product (the σ<sup>*</sup> orbital), and the LUMO+1 orbitals of the reactant forming the LUMO of the product (the π<sup>*</sup> orbital)
[[File:lo915_4_MOs2.jpg|thumb|Figure 19. Correlation diagram|center|500px]]
The reaction goes through a mobius transition state, with a node in the phases of the orbitals. As it is a 4n electron reaction, the transition state is termed 'aromatic'.<ref>Dolbier, W. R''Acc. Chem. Res.'', '''1996''', ''29'', 471-477</ref> This can be seen in the visualisation of the transition state orbitals in figure 16.

{| style="margin-left: auto; margin-right: auto; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 20. Reactant, product and transition state MOs
|-
!colspan="4"|Reactant MOs
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!colspan="4"|Product MOs
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!colspan="4"|Transition State MOs
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=Conclusion=
For all of the reactions, the transition state was found and optimised successfully. It was found that the first Diels-Alder reaction was normal demand, while the second Diels-Alder was inverse electron demand, due to the electron rich nature of the dienophile. For both exercises 2 and 3, it was found that the endo Diels-Alder reaction was thermodynamically preferred to the exo reaction, due to the stabilising secondary orbital overlap. For exercise 3, the cheletropic product was the thermodynamically preferred product, while the alternate Diels-Alder reactions were thermodynamically unfavourable as there is no aromatic ring formation as for the original Diels-Alder reactions and the cheletropic reaction. In the electrocyclic reaction it was found to proceed in a conrotatory fashion, as expected for a thermal 4n eletron elecrocyclic reaction. This could be extended by investigated the photochemical reaction, which would preocceed in a disrotatory fashion, however the PM6 level could not be used for these calculations due to the need for excited states.

=Files=
===Exercise 1===
[[Media:Lo915_1_ETHENE.LOG|Log file of ethene (PM6)]]

[[Media:Lo915_1_BUTADIENE.LOG|Log file of butadiene]]

[[Media:LO915_REACTANTS_ENERGY.LOG||Log file of Single point energy of reactants]]

[[Media:Lo915_1_TS.LOG|Log file of transition state]]

[[Media:Lo915_1_TSIRC.LOG|Log file of IRC]]

[[Media:Lo915_1_IRC_PRODUCTS.LOG|Log file of product]]

===Exercise 2===
[[Media:Lo915_2_DIOXOLE_B3LYP.LOG|Log file of 1,3-dioxole ]]

[[Media:Lo915_2_CYCLOHEXADIENE_B3LYP.LOG|Log file of cyclohexadiene]]

[[Media:Lo915_2_TS_ENDO_B3LYP.LOG|Log file of endo transition state]]

[[Media:Lo915_2_TS_EXO_B3LYP.LOG|Log file of exo transition state]]

[[Media:Lo915_2_ENDO_IRC.LOG|Log file of endo IRC]]

[[Media:Lo915_2_EXO_IRC_PM6.LOG|Log file of exo IRC]]

[[Media:Lo915_2_ENDO_PRODUCTS_B3LYP.LOG|Log file of endo product]]

[[Media:Lo915_2_EXO_PRODUCTS_B3LYP.LOG|Log file of exo product]]

===Exercise 3===
[[Media:lo915_3_SO2.LOG|Log file of SO<sub>2</sub>]]

[[Media:lo915_3_XYLENE2.LOG|Log file of xylylene]]

[[Media:lo915_3_TS_ENDO.LOG|Log file of endo transition state]]

[[Media:lo915_3_TS_ENDO_IRC.LOG|Log file of endo IRC]]

[[Media:lo915_3_ENDO_PROD.LOG|Log file of endo product]]

[[Media:lo915_3_TS_EXO.LOG|Log file of exo transition state]]

[[Media:lo915_3_EXO_IRC.LOG|Log file of exo IRC]]

[[Media:lo915_3_EXO_PROD.LOG|Log file of exo product]]

[[Media:lo915_3_CHELETROPIC_TS.LOG|Log file of cheletropic transition state]]

[[Media:lo915_3_CHELETROPIC_IRC.LOG|Log file of cheletropic IRC]]

[[Media:lo915_3_CHELETROPIC_PROD.LOG|Log file of cheletropic product]]

[[Media:lo915_3_INT_ENDO_TS.LOG|Log file of internal endo transition state]]

[[Media:lo915_3_INT_ENDO_IRC.LOG|Log file of internal endo IRC]]

[[Media:lo915_3_INT_ENDO_PROD.LOG|Log file of internal endo product]]

[[Media:lo915_3_INT_EXO_TS.LOG|Log file of internal exo transition state]]

[[Media:lo915_3_INT_EXO_IRC.LOG|Log file of internal exo IRC]]

[[Media:lo915_3_INT_EXO_PROD.LOG|Log file of internal exo product]]

===Electrocyclic Reaction===
[[Media:lo915_4_TS.LOG|Log file of transition state]]

[[Media:lo915_4_IRC.LOG|Log file of IRC]]

[[Media:lo915_4_IRC_INITIAL.LOG|Log file of reactant]]

[[Media:lo915_4_IRC_FINAL.LOG|Log file of product]]

=References=

Rep:SJP115 Transition States And Reactivity By Sarah Patterson

2018-04-07T10:15:46Z

Fv611: /* Molecular Orbital Analysis */

==<u>Introduction</u>==

===<u> Potential Energy Surface </u>===

Potential energy surfaces depict the energy of a molecule as a function of its geometry across all dimensions. A non-linear molecule will have 3N degrees of freedom in three dimensional space. The degrees of freedom may be decomposed into translational, rotational and vibrational motion. The rotational and translational motions do not vary the internuclear distances of the molecule and will not affect its potential energy. This means an N-atom molecule will have 3N-6 degrees of freedom remaining, and this leads to a PES with 3N-6 geometric variables. A key approximation made upon generating a PES is that the Born-Oppenheimer approximation is valid and that the energy can be given as a function of the positions of the nuclei.

The potential energy landscape will contain stationary points, at such points the first derivative of the potential energy with respect to each geometric parameter (equivalent to the gradient) will be zero (eq 1.).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 TS Eq1.png|thumb| Equation 1: Equation for a stationary point on a general potential energy surface. R is the set of nuclear coordinates and R<sub>i</sub> refers to a specific member of the set <ref>Joseph J W McDouall ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'' Royal Society of Chemistry 2013 ISBN: 978-1-84973-608-4 http://dx.doi.org/10.1039/9781849737289-00001</ref> ]]
|}

This can be related to the force acting on the atoms. In one dimension this force will have a single value; in three dimensions the force will be the first derivative matrix (the gradient matrix), and the force constant will be the second derivative matrix, the Hessian matrix. Normal modes are the eigenvectors of this Hessian matrix. <ref>Joseph J W McDouall ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'' Royal Society of Chemistry 2013 ISBN: 978-1-84973-608-4 http://dx.doi.org/10.1039/9781849737289-00001</ref> Matrices provide an advantage over linear algebra, since they allow the Hamiltonian to be easily diagonalised and the eigenvectors and eigenvalues solved.

A stationary point may correspond to a minimum or saddle point transition structure. They are distinguished by the curvature surrounding the stationary point. The curvature of each dimension can be found by computing the force constant Hessian matrix eigenvalues for each normal mode (second derivative). At a minimum the second derivative will be positive in all dimensions and there are no negative force constants. Movement along any degree of freedom will raise the energy hence a minimum represents a stable or quasi configuration of a molecule. If the vibrational frequencies are real, then this confirms the structure is a minimum.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Eq2 Minima.png|thumb| Equation 2: Equation for the minima of stable reactant, products or intermediates]]
|}

A TS will have a single negative hessian eigenvalue and this unique normal coordinate corresponds to the reaction coordinate. In other words, a transition state (TS) is a maximum along a minimum energy path connecting two minima. The single negative hessian eigenvalue will lead to an imaginary frequency vibration which is indicative of the TS. The vibrational mode of the imaginary frequency should match the action of the reaction path. If there is more than one imaginary frequency, there will be a lower energy pathway connecting the minima.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Eq3 TS.png|thumb| Equation 3: Equation for second derivative of the TS along nuclear coordinates other than the reaction coordinate ]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Eq4 TS.png|thumb| Equation 4: Equation for the second derivative of the TS along the unique coordinate]]
|}

TS control reactivity since they are the highest energy point that must be overcome to go from reactant to products. In this experiment, Gaussian was used to locate the TS of a number of pericyclic reactions based on the local shape of the potential energy surface.

===<u> Computational Methods </u>===

Two electronic structure methods in Gaussian were used to solve the Schrödinger equation and generate the potential energy landscape for the reactions.

Method 1: The first method employed was the semi empirical quantum chemical PM6 (Parameterization Method 6) method which is based on the Hartree Fock Hamiltontian. Approximations are made in order to solve the Hamiltonitan matrix which consist of using experimental data. Parameterised corrections are also made to correct for the approximate quantum mechanical model.<ref>Jan Reza, Jindrich Fanfrlık, Dennis Salahub, and Pavel Hobza ''J. Chem. Theory Comput.'' 2009, 5, 1749–1760</ref> The PM6 method fails in accounting for non-covalent interactions such as the dispersion energy and hydrogen bonding. The vast number of approximations and use of experimental data makes this method less accurate. Nonetheless, this semi-empirical calculation remains much faster than its ab initio counterpart, allowing the system to be modeled in a reasonable amount of time.

Method 2: The B3YLP method is a hybrid method between Density Functional Theory (DFT) and the Hartree Fock theorem. The electronic wavefunction is given by the basis set 6-31(d)
<ref>J. P. Stewart ''Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements'' 2007 DOI: 10.1007/s00894-007-0233-4</ref>. Both of the hybrid methods are used to recover electron correlation. The Hartree Fock method accounts for the exchange correlation. The DFT method recovers the dynamic electron correlation and solves the DFT hamiltonian.

In this experiment PM6 was used as the primary calculation method. Exercise 1 and 2 were carried out solely using PM6, whereas in exercise 3 the PM6 results were further optimised using the B3YLP method.

====<u> The Hartree Fock approximation </u>====

The Hartree Fock (HF) approximation is central to finding solutions to the Schroginger equation by overcoming the many-electron problem. In order to describe the wavefunction of the ground state of an N-electron system, a Slater determinant is used. <ref>Attila Szabo, Neil S. Ostlund ''Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory'' Dover Books on Chemistry 1989 ISBN: 0486691861</ref> According to the variational principle the best wavefunction will be the one with the lowest energy. The energy can be lowered by changing the spin orbitals. <ref>Attila Szabo, Neil S. Ostlund ''Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory'' Dover Books on Chemistry 1989 ISBN: 0486691861</ref>This leads to the Hartree Fock equation, as seen in equation 5.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 HF Equation.PNG|thumb|500x500px| Equation 5: Simplified derivation for the Hartree Fock equation <ref>http://www.quimica.urv.es/~bo/MOLMOD/Mike_Colvin/qc/thm.html Last accessed 24th March 2018 </ref>]]
|}

The Hartree Fock approximation overcomes the complicated, many electron problem, by treating it as a one-electron problem and accounting for electron-electron repulsion in an average way. <ref>Attila Szabo, Neil S. Ostlund ''Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory'' Dover Books on Chemistry 1989 ISBN: 0486691861</ref> The Hartree Fock equation can then be solved using the self-consistent field (SCF) method. This method involves making an initial guess for the spin orbitals, calculating the average electron field, and solving the HF equation to obtain a new set of spin orbitals. This process is then repeated with the new set of spin orbitals until the basis sets lower the Hartree Fock energy to a limit called the Hartree Fock limit. <ref>Attila Szabo, Neil S. Ostlund ''Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory'' Dover Books on Chemistry 1989 ISBN: 0486691861</ref>

===<u> Methods for Locating and Characterising Transition States</u>===

There are three different methods for localising and characterising transition states:

Method 1: The structure of the transition state is estimated and a PM6 TS calculation is carried out. If successful the optimised transition state should have a single imaginary frequency and a successful IRC path with a gradient of zero at the TS. Further optimisation can then be carried out using a B3LYP/6-31g(d) calculation. Whilst this is the fastest method, it suffers from various drawbacks; it requires prior knowledge of the transition state and failure to adequately estimate the structure will result in a failed calculation or the wrong TS structure.

Method 2: Similarly to method 1, the initial step of method 2 is to estimate the structure of the transition state. However, the atom pairs involved in the bond forming reaction are frozen in space preceding optimisation to a minimum. This enables the rest of the structure to be optimised and the TS can then be calculated using PM6 (and B3LYP/6-31g(d)). The primary disadvantage of method 2 is that it requires knowledge of the TS, but it provides a more significant means of locating the TS compared to method 1.

Method 3: This is the most infallible method of locating the TS as it does not require knowledge of the TS. The downside of the method is that it is slow, requiring many steps. In addition difficulties can arise if the TS is located far from the reactant and product minima. In this method either the reactant or product geometries are optimised, and the bond lengths are then modified to resemble the TS. The atom pairs involved in the reaction are then frozen, and from the optimised structure a TS calculation can be carried out.

Method 2 was used for exercise 1 and 2. Exercise 3 was carried out using method 3.

==<u>Exercise 1: Reaction of Butadiene with Ethylene</u>==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Excellent work across the whole exercise - very well done!)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Exercise1 RX Scheme.PNG|thumb| Figure 1: Scheme for the Diels-Alder Cycloaddition of Butadiene and Ethene]]
|}

The conjugated butadiene undergoes a thermal [4+2] cycloaddition with ethene to form an unsaturated six-membered ring. There are 6 electrons moving in suprafacial fashion making the reaction pericyclic. The absence of substitution on the fragments avoids issues of stereoselectivity.

===<u> Molecular Orbital Analysis</u>===

Analysis of the molecular orbitals of ethene and butadiene enables the determination of how the orbitals interact to form the transition state. In a product molecular orbital diagram the reactants overlap to form bonding and anti-bonding MOs which are stabilised and destabilised more than the reactants respectively. Whilst a transition state MO diagram also shows stabilising and destabilising interactions, the orbitals remain raised in energy. This can be rationalised by the definition of a transition state as the maximum on the minimum energy path or a stationary point with a single negative Hessian eigenvalue. There is an activation barrier that must be surmounted to reach the transition state.

From the visualisation of the MOs in table 1 it can be seen that HOMO-1 is formed from a stabilising interaction between the HOMO of butadiene and the LUMO of ethene. Similarly, the HOMO TS is formed from the stabilising overlap of the HOMO of ethene and the LUMO of butadiene. The LUMO of the transition state is formed from a destabilising interaction between the overlap of the LUMO of butadiene with the HOMO of ethene. The destabilising overlap of the HOMO of butadiene and the LUMO of ethene affords the LUMO+1. The interaction between the orbitals is consistent with the observations made by Fukui ''et al.'' <ref>Kenichi Fukui, Teijiro Yonezawa, and Haruo Shingu A Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons ''The Journal of Chemical Physics'' 20, 722 (1952); doi: 10.1063/1.1700523</ref> ; the occupied orbitals of different molecules do not interact whilst the the occupied orbitals of one molecule and the unoccupied orbital of another will interact with each other causing attraction. Moreover, it can be deduced that interacting orbitals must be of the same symmetry. The symmetric HOMO of ethene and the symmetric LUMO of butadiene overlap to give a symmetric HOMO and LUMO whilst the antisymmetric HOMO of butadiene and the anti-symmetric LUMO of ethene give the anti-symmetric HOMO-1 and LUMO+1. The orbitals must be of the same symmetry in order to interact, and the overlap integral is a measure of their interaction. Orbitals of the same symmetry will interact strongly and have a non-zero value of the overlap integral. In a forbidden reaction such as that with an anti-symmetric and symmetric orbital combination, the overlap integral will be zero and there will be no interaction between the orbitals. The symmetry of the orbitals can be determined by a plane of symmetry passing vertically through the orbitals.

The Diels Alder reaction undergoes normal electron demand. The reactivity is controlled by the relative energies between the Frontier Molecular orbitals where the key interaction will be between the HOMO and LUMO that are closer in energy. From figure 2 it can be seen that the smallest energy gap will be between the HOMO of butadiene and the LUMO of ethene. The smaller energy gap will result in a better overlap in the transition state. The energies in the molecular orbital diagram (figure 2) were obtained by doing a single point energy calculation on the reactants obtained from the IRC. The TS energies were equally obtained by doing a single point energy calculation of the TS. Using these energies it can be seen quantitatively that the energy gap between the HOMO of butadiene and the LUMO of ethene is 0.398 Ha, whilst the energy gap between the HOMO of ethene and the LUMO of butadiene is 0.399 Ha. Although there is a small energy difference, the reaction is still expected to proceed via a normal electron demand Diels Alder.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Butadiene MO final.PNG|600x700px|thumb| Figure 2: Molecular Orbital Diagram for the Transition State formed during the Cycloaddition of Ethene and Butadiene]]
|}

The molecular orbital diagram for the transition state (figure 2) was constructed using the molecular orbitals in table 1.

{| class="wikitable"
|+ '''Table 1.''' The Molecular Orbitals For Ethene, Butadiene, the Transition State
|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visulisation of the Reactant Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Ethene HOMO
! style="background: #0D4F8B; color: white;" | Ethene LUMO
! style="background: #0D4F8B; color: white;" | Butadiene HOMO
! style="background: #0D4F8B; color: white;" | Butadiene LUMO
|-
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|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation Transition State Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Transition State HOMO -1
! style="background: #0D4F8B; color: white;" | Transition State HOMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO +1
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===<u>Bond Distance Changes</u>===

Table 2 illustrates the changes in bond length that occur throughout the reaction with two π bonds being broken and concomitant formation of two single bonds. Examination of the C1-C2 ethene double bond shows a clear elongation upon formation of the transition state and subsequent lengthening in the product to form a single bond. The change in bond length is consistent with the change in hybridisation from sp<sup>2</sup> to sp<sup>3</sup> for both C1 and C2 that occurs throughout the course of the Diels Alder reaction. The two double bonds of the butadiene fragment, C3-C4 and C5-C6, are equally progressively lengthened from double to single bonds. In this case C4 and C5 remain sp<sup>2</sup> hybridised whilst C3 and C6 change hybridisation state from sp<sup>2</sup> to sp<sup>3</sup>. The internal single bond of the butadiene fragment is shortened in the transition state to form a double bond in the product. Typical values for the interatomic distance between a carbon-carbon sp<sup>3</sup> single bond is 1.54 Å whilst that for a carbon-carbon sp<sup>2</sup> double bond is 1.34 Å <ref>Linus Pauling, and L. O. Brockway Carbon—Carbon Bond Distances. The Electron Diffraction Investigation of Ethane, Propane, Isobutane, Neopentane, Cyclopropane, Cyclopentane, Cyclohexane, Allene, Ethylene, Isobutene, Tetramethylethylene, Mesitylene, and Hexamethylbenzene. Revised Values of Covalent Radii ''J. Am. Chem. Soc.'', 1937, 59 (7), pp 1223–1236 DOI: 10.1021/ja01286a021</ref>. The literature values closely match the single and double bond lengths in the product. However, butadiene's internal single bond (C4-C5) appears slightly shorter than is expected for a single bond and this is a result of it being a conjugated diene with π electrons delocalised across the fragment. Similarly in cyclohexene the bonds adjacent from the double bond (C3-C4 and C5-C6) are slightly shorter than a typical single bond and this is a result of adjacent carbon being sp<sup>2</sup> hybridised thus benefiting from additional s character. The C2-C3 and C1-C6 interatomic distances represent the bonds that are formed between ethene and butadiene to form single bonds in the cyclohexene product. In the TS these bond lengths appear as approximately 2.115 Å, this is shorter than twice the Van der Waals radius of carbon which is indicative of interaction between the electron densities of the two carbon atoms <ref>S. S. Batsanov Van der Waals Radii of Elements ''Inorganic Materials'', Vol. 37, No. 9, 2001, pp. 871–885</ref>.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ '''Table 2. Bond length Changes throughout the Cycloaddition of Ethene and Butadiene'''
! colspan="1" style="border: none; background: none;"|
! colspan="4"| Bond Length (Å)
|-
!Carbon-Carbon Bond
!Ethene
!Butadiene
!Transition State
!Cyclohexene
|-
|C1-C2
|<nowiki>1.3273</nowiki>
|n/a
|1.3818
|1.5345
|-
|C2-C3
|<nowiki>n/a</nowiki>
|n/a
|2.1147
|1.5372
|-
|C3-C4
|<nowiki>n/a</nowiki>
|1.3352
|1.3798
|1.5008
|-
|C4-C5
|<nowiki>n/a</nowiki>
|<nowiki>1.4683</nowiki>
|1.4111
|1.3370
|-
|C5-C6
|n/a
|<nowiki>1.3352</nowiki>
|1.3798
|1.5008
|-
|C6-C1
|<nowiki>n/a</nowiki>
|<nowiki>n/a</nowiki>
|2.1149
|1.5372
|}

The changes in bond length during the course of the reaction are further illustrated by figure 3. The reaction coordinate shows the dissociation of the cyclohexene product into the ethene and butadiene reactants. The double bond in cyclohexene (C4-C5) is lengthened from a single to double bond. The neighbouring single bonds (C3-C4 and C5-C6) are shorthened to double bonds. C1-C2 is shorthened to reform the ethene double bond. The bond distances C2-C3 and C1-C6 show the single bonds between the two fragments being lengthened and the bonds being broken.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Bond Distance Graph.PNG|thumb|500x500px|Figure 3: Graph showing the variation in internuclear distance for the dissociation of ethene and butadiene]]
|}

===<u> Reaction Path Vibrations </u>===

The animation below shows the vibrational mode of the imaginary frequency of the TS which occurs at 948.5i cm<sup>-1</sup>. This vibrational mode matches the action of the reaction path. The animation shows that the reaction is both synchronous and concerted with two new bonds forming simultaneously. Table 2 provides further evidence for a synchronous reaction path since the two forming bonds have the same length.

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<br />

==<u>Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole</u>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Scheme EX2.PNG|thumb|500x500px|Figure 4: Scheme for the reaction of cyclohexadiene and 1,3-Dioxole]]
|}

The Diels-Alder between cyclohexadiene and 1,3-dioxane can proceed in an exo and endo manner. The different pathways rely on the approach of the 1,3-dioxole towards the cyclohexadiene. If the dioxole approaches the diene with the oxygen atoms lying beneath the ring then the endo product will result. Conversely, if the dioxole ring oxygens point away from the diene, the exo product will predominate.

===<u> Molecular Orbital Analysis </u>===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very nice MO diagrams.)

MO diagrams were constructed for both the exo and endo transition states, these can be seen in figure 5 and 6 respectively. The MO diagrams show the same observation as made in exercise 1; orbitals can only overlap if they are of the same symmetry. The anti-symmetric diene HOMO and dienophile LUMO generate the anti-symmetric TS HOMO-1 and LUMO+1. The symmetric HOMO dienophile and LUMO diene afford the symmetric HOMO and LUMO.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Exercise2 Exo Mo.PNG|thumb|600x700px|Figure 5: Molecular Orbital Diagram for the Exo Transition State]]
![[File:SJP115 Exercise2 Endo Mo.PNG|thumb| 600x700px|Figure 6: Molecular Orbital Diagram for the Endo Transition State]]
|}

A normal electron demand Diels Alder reaction typically proceeds between an electron rich diene and an electron poor dienophile. The smallest energy gap controls the reactivity and for a normal electron demand Diels Alder reaction this will be between the HOMO of the diene and the LUMO of the dienophile. The small energy gap will enable strong overlap between the orbitals. Inverse electron demand Diels Alder reactions are typical of an electron poor diene, with an electron withdrawing group that lowers the energy of the HOMO and LUMO, and an electron rich dienophile, with electron donating groups that raise the energy of the HOMO and LUMO. The HOMO of the dienophile will lie above the diene’s HOMO and the smallest energy gap will be between the HOMO of the dienophile and the LUMO of the diene. The energy gap between the HOMO and LUMO frontier molecular orbitals in both normal and inverse electron demand can be seen in figure 7.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Normal Inverse Electron Demand.PNG|thumb|500x500px|Figure 7: Scheme showing the frontier molecular orbitals for both a normal electron demand Diels Alder and an inverse electron demand Diels Alder<ref>Radleigh A. A. Foster and Michael C. Willis Tandem inverse-electron-demand hetero-/retro-Diels–Alder reactions for aromatic nitrogen heterocycle synthesis ''Chem. Soc. Rev.'', 2013, 42, 63-76 DOI: 10.1039/C2CS35316D </ref>]]
|}

From the MO diagrams (figure 5 and 6) it can be seen that both the endo and exo reactions undergo inverse electron demand Diels Alder. There is a smaller energy gap between the 1,3-dioxole HOMO and the cyclohexadiene LUMO than the 1,3-dioxole LUMO and cyclohexadiene HOMO. The 1,3-dioxole has two electron donating oxygen substituents which raise the energy of the HOMO and LUMO, such that the HOMO of the dienophile is higher in energy than the cyclohexadiene HOMO. The HOMO of the dienophile will hence interact more strongly with the LUMO cyclohexadiene. The energies reported in the MO diagrams are those from the B3YLP optimisations of the reactants and the transition state. In order to quantify the energy gap between the HOMO and LUMOs of the two reactants, a single point energy calculation was carried out from the IRC for both the endo and exo reactants. The results are summarised in table 3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ '''Table 3. Single point energy calculations of the reactants from the IRC output'''
! colspan="1" style="border: none; background: none;"|
|-
!Endo
!Ha
!Exo
!Ha
|-
|1,3 Dioxole HOMO
|<nowiki>-0.317</nowiki>
|1,3 Dioxole HOMO
| -0.322
|-
|1,3 Dioxole LUMO
|<nowiki>0.032</nowiki>
|1,3 Dioxole LUMO
|0.030
|-
|1,3 Cyclohexadiene HOMO
|<nowiki>-0.321</nowiki>
|1,3 Cyclohexadiene HOMO
| -0.322
|-
|1,3 Cyclohexadiene LUMO
|<nowiki>0.023</nowiki>
|1,3 Cyclohexadiene LUMO
|0.021
|}

From table 3 it can be seen that the energy gap between the cyclohexadiene LUMO and 1,3 dioxole HOMO is approximately 0.34 Ha whilst the energy gap between the cyclohexadiene HOMO and 1,3 dioxole LUMO is approximately 0.35 Ha. This provides further, quantitative evidence for an inverse electron demand Diels Alder.

{| class="wikitable"
|+ '''Table 4.''' The Molecular Orbitals For the Endo and Exo Transition State
|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation of the Exo Transition State Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Transition State HOMO-1
! style="background: #0D4F8B; color: white;" | Transition State HOMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO+1
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! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation of the Endo Transition State Molecular Orbitals
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! style="background: #0D4F8B; color: white;" | Transition State HOMO -1
! style="background: #0D4F8B; color: white;" | Transition State HOMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO +1
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===<u> Thermochemistry </u>===

Under the thermochemistry section of the log file, the “sum of electronic and thermal free energies” was extracted for the reactants, TS and the product. The activation energy was then was computed by doing the energy difference between the TS and the reactants. The reaction energies were calculated by calculating the energy difference between the product and the reactants. The results are summarised in table 5.

<center>
{| class="wikitable"
|+ '''Table 5. Thermochemistry Data for the Endo and Exo Diels Alder reaction between 1,3 Dioxole and 1,3 Cyclohexadiene '''
|-
! rowspan="3" style="background: #0D4F8B; color: white;" | Reaction Type
! colspan="7" style="background: #0D4F8B; color: white;" | Energy (kJ/mol)
|-
! colspan="3" style="background: #0D4F8B; color: white;" | Reactants
! rowspan="2" style="background: #0D4F8B; color: white;" | Transition State
! rowspan="2" style="background: #0D4F8B; color: white;" | Product
! rowspan="2" style="background: #0D4F8B; color: white;" | Activation Energy
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diene
! style="background: #0D4F8B; color: white;" | Dienophile
! style="background: #0D4F8B; color: white;" | Total
|-
| style="text-align: center;" | '''Exo'''
| rowspan="2" style="text-align: center;" | -612593.146
| rowspan="2" style="text-align: center;" | -701188.7353
| rowspan="2" style="text-align: center;" | -1313781.88
| style="text-align: center;" | -1313614.23
| style="text-align: center;" | -1313845.68
| style="text-align: center;" | 167.65
| style="text-align: center;" | -63.80
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | -1313622.07
| style="text-align: center;" | -1313849.27
| style="text-align: center;" | 159.23
| style="text-align: center;" | -67.39
|}
</center>

Examination of the activation energies in table 5 shows that there is a larger activation barrier to reach the exo TS than the endo TS. The endo TS is thus more stable than the exo TS. In order to reach the exo TS, the reactants will require additional energy to surmount the larger activation barrier. The fastest formed, kinetically favoured product, with the lower activation barrier will hence be the endo product.

The reaction energies show that whilst both the endo and exo reactions are exothermic and thermodynamically favourable, the endo product is lower in energy and thermodynamically more stable than the exo. The reaction energy for the endo is more negative, more exothermic and presents the thermodynamically most stable product. The endo product is thus not only kinetically favoured but also thermodynamically favoured. The exo product is higher in energy as a result of the steric clash between the bridging carbons and the 5 membered dioxole ring.

===<u> Secondary Orbital Interactions </u>===

The lower energy of the endo TS can be rationalised on the basis of secondary, non-bonding, interactions between the dioxole oxygen p orbitals and the π system of the diene. Such interactions lower the energy of the TS HOMO promoting faster formation of the kinetic product. The exo TS only has primary orbital interactions and this is a result of the oxygen p orbitals of the dioxole pointing away from the diene p orbtials making them too far apart to interact. The HOMO of both the exo and endo TS are given in table 5 wherein the isovalue has been set to 0.01, this has the effect of shortening the radial extension of the orbitals making the stabilising interactions of the endo clearer.

{| class="wikitable"
|+ '''Table 5.''' Visualisation of the Exo and Endo HOMO secondary orbital interactions
! style="background: #0D4F8B; color: white;" | Exo Secondary Orbital Interactions
! style="background: #0D4F8B; color: white;" | Endo Secondary Orbital Interactions
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In the exo TS HOMO the p orbitals of the dioxole do not interact with the diene p orbitals, whereas in the endo TS HOMO the p orbitals of the dioxole do interact with those of the diene.

==<u>Exercise 3: Diels-Alder vs Cheletropic</u>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Scheme Ex3.PNG|thumb|500x500px| Figure 8: Scheme for the Diels Alder and Cheletropic reaction between sulphur dioxide and xylyene ]]
|}

The reaction scheme shows the potential pathways for the reaction between o-xylyene and sulphur dioxide. The Diels-Alder reaction can proceed in an endo or exo fashion. The cheletropic reaction is characterised by two σ bonds forming in concert at a single atom. <ref>Angew. Chem. Int. Ed. Engl. 1969, 8, 781–853</ref>

===<u> Intrinsic Reaction Coordinate (IRC) </u>===

The IRC for the exo/endo Diels Alder pathways and the Cheletropic reaction are shown in figure 9, 10, 11 respectively. The IRCs show the progression of the reaction, from the SO<sub>2</sub> and o-xylyene fragments, to the TS, and finally to the products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 EXO Correct Order Exercise 3 2.gif|thumb|500x500px| Figure 9: IRC for the Exo Diels Alder pathway]]
![[File:SJP115 ENDO Correct Order Exercise 3.gif|thumb|500x500px|Figure 10: IRC for the Endo Diels Alder pathway]]
![[File:SJP115 Cheleo Correct Order Exercise 3.gif|thumb|500x500px|Figure 11: IRC for the Cheletropic pathway]]
|}

The exo and endo reactions show asynchronous bond formation, with the bonds forming at different times due to asymmetry. For both Diels Alder reactions the C-O bond between the diene and dienophile are formed before the bond between the diene and sulphur atom (C-S). The cheletropic reaction proceeds with synchronous bond formation; both ends of the diene form new C-S bonds with the sulphur atom of SO<sub>2</sub> at the same time. The three reactions all show a fully delocalised 6-membered aromatic ring intermediate and in all three products the six membered ring is aromatic. This illustrates the high instability of xylyene; there is a strong driving force for aromatisation which will drive product formation. Indeed, from the IRCs it can be seen that aromatisation occurs before bond formation.

===<u> Thermochemistry </u>===

Table 6 was constructed in the same was as in exercise 2, the "sum of the electronic and thermal free energies" were extracted from the log files of the reactants, TS and products and used to calculate the activation and reaction energies. Using the data from table 6 a reaction profile was constructed (figure 12).

<center>
{| class="wikitable"
|+ '''Table 6. Thermochemistry Data for the Cheletropic, endo and exo Diels Alder reaction between Xylyene and Sulphur Dioxide'''
|-
! rowspan="3" style="background: #0D4F8B; color: white;" | Reaction Type
! colspan="7" style="background: #0D4F8B; color: white;" | Energy (kJ/mol)
|-
! colspan="3" style="background: #0D4F8B; color: white;" | Reactants
! rowspan="2" style="background: #0D4F8B; color: white;" | Transition State
! rowspan="2" style="background: #0D4F8B; color: white;" | Product
! rowspan="2" style="background: #0D4F8B; color: white;" | Activation Energy
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Sulphur Dioxide
! style="background: #0D4F8B; color: white;" | Xylyene
! style="background: #0D4F8B; color: white;" | Total
|-
| style="text-align: center;" | '''Exo'''
| rowspan="3" style="text-align: center;" | -313.14
| rowspan="3" style="text-align: center;" | 467.33
| rowspan="3" style="text-align: center;" | 154.19
| style="text-align: center;" | 241.75
| style="text-align: center;" | 56.32
| style="text-align: center;" | 87.56
| style="text-align: center;" | -97.87
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | 237.76
| style="text-align: center;" | 56.98
| style="text-align: center;" | 83.57
| style="text-align: center;" | -97.21
|-
| style="text-align: center;" | '''Cheletropic'''
| style="text-align: center;" | 260.09
| style="text-align: center;" | 0
| style="text-align: center;" | 105.9
| style="text-align: center;" | -154.2
|}
</center>

The reaction profile clearly illustrates that the endo TS has the lowest energy activation barrier, requiring less energy than the exo or cheletropic to be surmounted. The endo product is hence the kinetic product since it will be formed fastest. The stability of the endo TS could be due to secondary orbital interactions between the p orbitals of the non-bonding oxygen atom of the SO<sub>2</sub> dienophile and the π system of the xylene diene. This interaction is not possible for the exo Diels-Alder reaction since the sulphur dioxide approaches the diene with one of its oxygen pointed away from xylyene. The exo TS thus lies slightly higher in energy than the endo. The cheletropic TS has the largest activation energy and this is a result of the ring and angle strain of the 5-membered ring formed. The 6-membered ring in the exo and endo TS are conformationally less strained minimising 1,3 diaxial repulsions and angle strain. The reaction profile highlights that the reactions are all exothermic. The endo and exo products are similar in energy with the endo product being slightly higher in energy. However, the cheletropic product has the lowest reaction energy and it is the thermodynamically favoured product. This can be rationalised by the high bond energy of the two S=O bonds <ref>D. P. Stevenson The Strengths of Chemical Bonds J. Am. Chem. Soc., 1955, 77 (8), pp 2350–2350 DOI: 10.1021/ja01613a116</ref>.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Energies Exercise 3.PNG|thumb|500x500px|Figure 12: Reaction Profile for the different reactions between sulphur dioxide and xylyene]]
|}

===<u> An alternative Diels Alder Site </u>===

There is an alternative Diels-Alder reaction which can occur at the cis-butadiene fragment in the 6-membered ring of xylyene. This [4+2] cycloaddition can be exo or endo and the IRCs for both pathways are shown in figures 13 and 14 respectively.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Alternative Path Exo EX3.gif|Figure 13:IRC for the alternative exo Diels Alder pathway]]
![[File:SJP115 Alternative Path Endo EX3.gif|Figure 14: IRC for the alternative endo Diels Alder pathway]]
|}

A thermochemical analysis of these reactions shows that they possess large activation barriers making them less favourable than the previously described Diels-Alder pathways. Not only are these reactions kinetically unfavourable, but they are endothermic with positive reaction energies. The products lie higher in energy than the reactants and require an input of energy to be formed making these reactions thermodynamically unfavourable. This can be accounted for by the absence of aromaticity in the TS or product. Moreover, there is loss of the conjugation between the two butadiene fragments which is present in xylyene. Whilst both pathways are unfavourable, the endo remains more favourable than the exo since it posses a lower activation energy. This could be due to secondary orbital interactions. The reaction energy is also lower for the endo. The endo pathway hence presents both the kinetically and thermodynamically favoured Diels-Alder reaction for this alternative site.

<center>
{| class="wikitable"
|+ '''Table 7. Thermochemistry Data for the Alternative Exo and Endo Diels Alder Reactions'''
|-
! rowspan="3" style="background: #0D4F8B; color: white;" | Reaction Type
! colspan="7" style="background: #0D4F8B; color: white;" | Energy (kJ/mol)
|-
! colspan="3" style="background: #0D4F8B; color: white;" | Reactants
! rowspan="2" style="background: #0D4F8B; color: white;" | Transition State
! rowspan="2" style="background: #0D4F8B; color: white;" | Product
! rowspan="2" style="background: #0D4F8B; color: white;" | Activation Energy
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Sulphur Dioxide
! style="background: #0D4F8B; color: white;" | Xylyene
! style="background: #0D4F8B; color: white;" | Total
|-
| style="text-align: center;" | '''Exo'''
| rowspan="2" style="text-align: center;" | -313.14
| rowspan="2" style="text-align: center;" | 467.33
| rowspan="2" style="text-align: center;" | 154.19
| style="text-align: center;" | 275.82
| style="text-align: center;" | 176.71
| style="text-align: center;" | 121.63
| style="text-align: center;" | 22.52
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | 267.98
| style="text-align: center;" | 172.26
| style="text-align: center;" | 113.79
| style="text-align: center;" | 18.07
|}
</center>

==<u>Extension 1: Electrocyclic Ring Closing</u>==

Electrocyclic reactions are characterised by the net transformation of a pi bond into a sigma bond. The thermal electrocyclic ring closing of a substituted cyclobutene is a 4nπ electron process which proceeds with conrotatory motion of the groups on the terminal carbons in order to bring the lobes of the orbitals of the same phase together. The stabilising, attractive interaction of bringing two lobes of the same phase together will form a sigma bond.

The reaction path is illustrated by the gif in figure 15.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Extension IRC Path.gif|500x500px| thumb| Figure 15: IRC path for the electrocyclic ring closing of a substituted butadiene]]
|}

Figure 16 illustrates the effect of conrotatory motion on the orbitals of the HOMO ψ2 for the thermal electrocylcic ring closing.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Extension Con Motion.PNG|thumb|500x500px| Figure 16: Scheme showing the conrotatory motion of the orbitals]]
|}

(This is where you have to be careful about symmetry. In the products, the orbitals must have rough rotational and reflective symmetry. The product orbitals above have rotational symmetry (symmetric) but an undefined reflective symmetry (antisymmetric at back, symmetric at front). Either the front or the back should rearrange or cancel out to maintain these symmetry requirements. Later in your correlation diagram you show the back as having cancelled out [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:19, 4 April 2018 (BST))

Throughout the rehybridisation reaction the C2 (two-fold) axis of symmetry is maintained. If the phases of the orbitals are preserved under the symmetry transformation they are described as being symmetric.<ref>Prof. R. B. Woodward Prof. Roald Hoffmann The Conservation of Orbital Symmetry ''Angew. Chem. internat. Edit.'' 1 Vol. 8 (1969) 1 No. II </ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Extension C2 Axis.PNG|thumb|500x500px|Figure 17: Scheme showing the effect of a C2 axis on the symmetric ψ2 HOMO orbital ]]
|}

A correlation diagram can be constructed to connect molecular orbitals of the same symmetry in the reactants and products (figure 18). This diagram shows that the Ψ2 orbital of butadiene and the sigma orbital of cyclobutene, which are both symmetric with respect to the C2 axis, are correlated. The antisymmetric Ψ1 and π orbitals will be correlated. Similiar considerations apply for the LUMO orbitals in which the antisymmetric sigma star and Ψ3 are correlated. Finally, the Ψ4 and π* will be correlated. The conrotatory process is symmetry-allowed because the bonding orbitals of the reactants correlate with the bonding orbitals of the product with the same symmetry. According to Woodward et al. <ref>Prof. R. B. Woodward Prof. Roald Hoffmann The Conservation of Orbital Symmetry ''Angew. Chem. internat. Edit.'' 1 Vol. 8 (1969) 1 No. II </ref> the highest occupied orbitals dominate these correlations and they can be considered as valence electrons that can be easily perturbed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Extension Correlation Diagram.PNG|thumb| 500x500px|Figure 18: Correlation Diagram for the Conrotatory Ring Closing of Butadiene]]
|}

(Show the symmetry axis here for clarity [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:19, 4 April 2018 (BST))

The transition state will have an odd number of phase inversions hence will proceed with a Möbius topology. <ref>Rainer Herges Topology in Chemistry: Designing Mo1bius Molecules ''Chem. Rev.'' 2006, 106, 4820−4842</ref> This TS can be seen in table 8 wherein the π electrons resulting from the 2p atomic orbitals are distributed around a Möbius strip bearing a single half-twist. <ref>Henry S. Rzepa The Aromaticity of Pericyclic Reaction Transition States ''Journal of Chemical Education'' Vol. 84 No. 9 September 2007 •</ref>

{| class="wikitable"
|+ '''Table 8.''' The Molecular Orbitals For Cyclobutene and Butadiene
|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visulisation of the Reactant Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Butadiene σ
! style="background: #0D4F8B; color: white;" | Butadiene π
! style="background: #0D4F8B; color: white;" | Butadiene π*
! style="background: #0D4F8B; color: white;" | Butadiene σ*
|-
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|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation the Product Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Cyclobutene σ
! style="background: #0D4F8B; color: white;" | Cyclobutene π
! style="background: #0D4F8B; color: white;" | Cyclobutene π*
! style="background: #0D4F8B; color: white;" | Cyclobutene σ*
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|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation the Transition State Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | HOMO-1
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
! style="background: #0D4F8B; color: white;" | LUMO+1
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The stereochemistry of the reactant and product molecular orbitals provide further evidence for a conrotatory electrocyclic reaction. From the reactant MO in table 8 it can be seen that one of the double bonds is trans whilst the other is cis and following a conrotatory motion the hydrogens originating from the double bond will end up on the same side of the cyclobutene ring.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Stereochemistry.PNG|500x500px|thumb| Figure 19: Stereochemical Evidence for Conrotatory Electrocyclic Reaction]]
|}

Under photochemical conditions, electronic promotion causes the ψ3 orbital to become the HOMO. The electrocyclic ring closing can only proceed via a disrotatory mechanism and in this case an invariant plane of symmetry will be present. In order to be carry out the photochemical disrotatory electrocyclyic ring closing, Gaussian cannot use single reference calculations. Hartree Fock and density functional theory are not adequate in this case and the multiconfigurational method is required to enable mixing of the various electronically excited states. This method uses a linear combination of configuration states (CSF) to determine the electronic wavefunction. In such calculations the Complete Active Space Multiconfiguration SCF (CAS) is defined to include the approximate spin orbit coupling between the various spin states of the first excited state.

The multiconfigurational method was applied to the substituted butadiene in order to observe the electronic ground state of the photochemical ring closing pathway. The number of electrons and orbitals in the active space were both defined to be four such that the CAS corresponds to the first excited state of butadiene. The output will hence be a minimum on the excited state. Examination of the log file revealed that the excited state is mainly composed of the ground electronic state (1100) and an excited singlet state (a1b0). The geometric configuration of this excited state is twisted making it harder for butadiene to react in this configuration. Although there may be alternative geometric configurations that may react more easily it is envisioned that the disrotatory electrocyclic ring closing will remain more disfavoured than the thermal conrotatory path. This is evidenced by the correlation diagram for the photochemical pathway in which the TS lies higher in energy.

==<u> Extension 2: Electrocyclic Ring Opening </u>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Scheme EXtension2.PNG|thumb|500x500px| Figure 20: IRC for the ring opening of a substituted butadiene]]
|}

The electrocyclic ring opening reaction illustrated in figure 20 reacts antrafacially according to the Woodward Hoffman rules. This system is also a 4nπ electron system that will proceed with conrotation. The TS shows the intermediate step in the formation of the butadiene double bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115_Extension2_GIF.gif|thumb|500x500px| Figure 21: IRC for the ring opening of a substituted butadiene]]
|}

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!HOMO of TS
!HOMO of Product
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==<u>Conclusion</u>==

A number of pericyclic reactions were successfully modeled in Gaussian. PM6 was used as the primary method of carrying out calculations as a compromise between rapidity and accuracy. B3YLP was used when it was necessary to probe reactions with a higher level of accuracy. For example, in exercise 2 the transition state geometries of the exo and endo Diels Alder pathways were elucidated using B3YLP.

Gaussian not only provides a means of locating and characterising transition states, but it also enables the visualization of molecular orbitals. The energies of these molecular orbitals can be used to gain insight into the mechanistic pathway behind the reaction; for example, whether a Diels Alder proceeds via normal or inverse electron demand. The Diels Alder reaction between ethene and butadiene (exercise 1) was found to proceed via a normal electron demand, whilst the Diels Alder between the electron rich 1,3 dioxole and the cyclohexadiene was found to occur via inverse electron demand. Further mechanistic insights can be obtained by animation of the imaginary frequency vibration. This gave an insight into how bond formation occurred, whether bond formation was synchronous or asynchronous. Finally, analysis of the thermochemical data aided in identifying the kinetic and thermodynamic pathways and products.

==<u> Files </u>==

===<u>Reaction of Butadiene with Ethylene</u>===

[[Media:SJP115_ETHENE.LOG|Log file of ethene]]

[[Media:SJP115 BUTADIENE2.LOG| Log file of butadiene]]

[[Media:SJP115 EX1 ETHENE AND BUTADIENE SAME FRAME.LOG| Log file of butadiene and ethene in the same frame PM6]]

[[Media: SJP115 Ex1 TS IRC INITIAL SINGLE POINT ENERGY.LOG| Log file of single point energy of ethene and butadiene]]

[[Media:SJP115 TS PM6.LOG| Log file of TS PM6 Optimised]]

[[Media: SJP115 TS IRC.LOG|Log file of the IRC PM6]]

[[Media: SJP115 TS PM6 SYMBROKEN2.LOG| Log file of the PM6 product ]]

===<u>Reaction of Cyclohexadiene and 1,3-Dioxole</u>===

[[Media:SJP115 DIOXANE BY3.LOG|Log file of 1,3 Dioxole B3YLP]]

[[Media:SJP115 DIENE B3LYP 631GD.LOG|Log file of 1,3 Cyclohexadiene B3YLP]]

[[Media:SJP115 Ex2 Exo TS B3LYP 631GD.LOG|Log file of Exo TS B3YLP]]

[[Media:SJP115_Ex3_Endo_TS_B3LYP_631GD_NOPTEIGEN.LOG|Log file of Endo TS B3YLP]]

[[Media: SJP115 Ex2 Exo TS IRC.LOG|Log file of Exo IRC PM6]]

[[Media:SJP115 Ex2 Endo TS PM6 IRC.LOG|Log file of Endo IRC PM6]]

[[Media:SJP115 Ex2 Exo PRODUCT B3LYP6 31GSD.LOG| Log file of Exo Product B3YLP]]

[[Media:SJP115 Ex2 ENDO PRODUCT B3LYP 631GD.LOG| Log file of Endo Product B3YLP]]

===<u>Diels-Alder vs Cheletropic</u>===

[[Media:SJP115 SO2 2 PM6.LOG|Log file of SO<sub>2</sub>]]

[[Media:SJP115 O-XYLYENE PM6.LOG|Log file of o-Xylyene]]

[[Media:SJP115 Exercise3 TS PM6.LOG| Log file of Exo TS PM6]]

[[Media:SJP115 Exercise3 TS IRC PM6.LOG| Log file of Exo IRC PM6]]

[[Media:SJP115 Exercise3 EXO PRODUCT PM6.LOG| Log file of Exo Product]]

[[Media:SJP115 Exercise3 Endo TS PM6.LOG|Log file of Endo TS PM6]]

[[Media: SJP115 Exercise3 Endo TS IRC.LOG|Log file of Endo IRC PM6]]

[[Media:SJP115 Exercise3 Endo PRODUCT PM6.LOG|Log file of Endo Product]]

[[Media:SJP115 CHELE TS PM6.LOG|Log file of Cheletropic TS PM6]]

[[Media:SJP115 chele IRC 2.LOG|Log file of Cheletropic IRC PM6]]

[[Media:SJP115 CHELE PRODUCT 2 PM6.LOG| Log file of Cheletopic Product]]

[[Media: SJP115 EX3 AP Endo TS PM6.LOG|Log file of Alternative Path Endo TS PM6]]

[[Media:SJP115 EX3 AP Endo TS IRC.LOG| Log file of Alternative Path Endo IRC PM6]]

[[Media:SJP115 EX3 AP ENDO PRODUCT PM6.LOG| Log file of Alternative Path Endo Product PM6]]

[[Media:SJP115 Ex3 AP Exo TS PM6.LOG| Log file of Alternative Path Exo TS PM6]]

[[Media:SJP115 Ex3 AP Exo TS IRC.LOG| Log file of Alternative Path Exo IRC PM6]]

[[Media:SJP115 Ex3 AP Exo PRODUCT PM6.LOG| Log file of Alternative Path Exo Product PM6]]

===<u>Electrocyclic Ring Closing Reaction</u>===

[[Media:SJP115 EXTENSION PRODUCTS FROM IRC.LOG| Log file of Electrocyclic Ring Closing Reactants PM6]]

[[Media: SJP115 Extension1 TS IRC FINAL.LOG| Log file of Electrocyclic Ring Closing IRC PM6]]

[[Media: SJP115 Extension TS PM6 2.LOG| Log file of Electrocyclic Ring Closing TS PM6]]

[[Media:SJP115 EXTENSION REACTANTS FROM IRC.LOG| Log file of Electrocyclic Ring Closing Products PM6]]

[[Media:SJP115 Extension HF OPT.LOG| Log file of Electrocyclic Ring Closing Reactant HF]]

[[Media:SJP115 Extension CAS S1 opt.log| Log File of Electrocyclic Ring Closing CAS of first excited state]]

===<u> Electrocyclic Ring Opening Reaction </u>===

[[Media: SJP115 EXTENSION2 REACTANTS.LOG| Log file of Electrocyclic Ring Opening Reactants]]

[[Media: SJP115 Extension2 TS PM6.LOG| Log file of Electrocyclic Ring Opening TS PM6]]

[[Media: SJP115 Extension2 TS IRC.LOG| Log file of Electrocyclic Ring Opening IRC PM6]]

[[Media: SJP115 EXTENSION2 PRODUCT.LOG| Log file of Electrocyclic Ring Opening Product]]

==<u>References</u>==

Rep:SJP115 Transition States And Reactivity By Sarah Patterson

2018-04-07T10:13:45Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene */

==<u>Introduction</u>==

===<u> Potential Energy Surface </u>===

Potential energy surfaces depict the energy of a molecule as a function of its geometry across all dimensions. A non-linear molecule will have 3N degrees of freedom in three dimensional space. The degrees of freedom may be decomposed into translational, rotational and vibrational motion. The rotational and translational motions do not vary the internuclear distances of the molecule and will not affect its potential energy. This means an N-atom molecule will have 3N-6 degrees of freedom remaining, and this leads to a PES with 3N-6 geometric variables. A key approximation made upon generating a PES is that the Born-Oppenheimer approximation is valid and that the energy can be given as a function of the positions of the nuclei.

The potential energy landscape will contain stationary points, at such points the first derivative of the potential energy with respect to each geometric parameter (equivalent to the gradient) will be zero (eq 1.).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 TS Eq1.png|thumb| Equation 1: Equation for a stationary point on a general potential energy surface. R is the set of nuclear coordinates and R<sub>i</sub> refers to a specific member of the set <ref>Joseph J W McDouall ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'' Royal Society of Chemistry 2013 ISBN: 978-1-84973-608-4 http://dx.doi.org/10.1039/9781849737289-00001</ref> ]]
|}

This can be related to the force acting on the atoms. In one dimension this force will have a single value; in three dimensions the force will be the first derivative matrix (the gradient matrix), and the force constant will be the second derivative matrix, the Hessian matrix. Normal modes are the eigenvectors of this Hessian matrix. <ref>Joseph J W McDouall ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'' Royal Society of Chemistry 2013 ISBN: 978-1-84973-608-4 http://dx.doi.org/10.1039/9781849737289-00001</ref> Matrices provide an advantage over linear algebra, since they allow the Hamiltonian to be easily diagonalised and the eigenvectors and eigenvalues solved.

A stationary point may correspond to a minimum or saddle point transition structure. They are distinguished by the curvature surrounding the stationary point. The curvature of each dimension can be found by computing the force constant Hessian matrix eigenvalues for each normal mode (second derivative). At a minimum the second derivative will be positive in all dimensions and there are no negative force constants. Movement along any degree of freedom will raise the energy hence a minimum represents a stable or quasi configuration of a molecule. If the vibrational frequencies are real, then this confirms the structure is a minimum.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Eq2 Minima.png|thumb| Equation 2: Equation for the minima of stable reactant, products or intermediates]]
|}

A TS will have a single negative hessian eigenvalue and this unique normal coordinate corresponds to the reaction coordinate. In other words, a transition state (TS) is a maximum along a minimum energy path connecting two minima. The single negative hessian eigenvalue will lead to an imaginary frequency vibration which is indicative of the TS. The vibrational mode of the imaginary frequency should match the action of the reaction path. If there is more than one imaginary frequency, there will be a lower energy pathway connecting the minima.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Eq3 TS.png|thumb| Equation 3: Equation for second derivative of the TS along nuclear coordinates other than the reaction coordinate ]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Eq4 TS.png|thumb| Equation 4: Equation for the second derivative of the TS along the unique coordinate]]
|}

TS control reactivity since they are the highest energy point that must be overcome to go from reactant to products. In this experiment, Gaussian was used to locate the TS of a number of pericyclic reactions based on the local shape of the potential energy surface.

===<u> Computational Methods </u>===

Two electronic structure methods in Gaussian were used to solve the Schrödinger equation and generate the potential energy landscape for the reactions.

Method 1: The first method employed was the semi empirical quantum chemical PM6 (Parameterization Method 6) method which is based on the Hartree Fock Hamiltontian. Approximations are made in order to solve the Hamiltonitan matrix which consist of using experimental data. Parameterised corrections are also made to correct for the approximate quantum mechanical model.<ref>Jan Reza, Jindrich Fanfrlık, Dennis Salahub, and Pavel Hobza ''J. Chem. Theory Comput.'' 2009, 5, 1749–1760</ref> The PM6 method fails in accounting for non-covalent interactions such as the dispersion energy and hydrogen bonding. The vast number of approximations and use of experimental data makes this method less accurate. Nonetheless, this semi-empirical calculation remains much faster than its ab initio counterpart, allowing the system to be modeled in a reasonable amount of time.

Method 2: The B3YLP method is a hybrid method between Density Functional Theory (DFT) and the Hartree Fock theorem. The electronic wavefunction is given by the basis set 6-31(d)
<ref>J. P. Stewart ''Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements'' 2007 DOI: 10.1007/s00894-007-0233-4</ref>. Both of the hybrid methods are used to recover electron correlation. The Hartree Fock method accounts for the exchange correlation. The DFT method recovers the dynamic electron correlation and solves the DFT hamiltonian.

In this experiment PM6 was used as the primary calculation method. Exercise 1 and 2 were carried out solely using PM6, whereas in exercise 3 the PM6 results were further optimised using the B3YLP method.

====<u> The Hartree Fock approximation </u>====

The Hartree Fock (HF) approximation is central to finding solutions to the Schroginger equation by overcoming the many-electron problem. In order to describe the wavefunction of the ground state of an N-electron system, a Slater determinant is used. <ref>Attila Szabo, Neil S. Ostlund ''Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory'' Dover Books on Chemistry 1989 ISBN: 0486691861</ref> According to the variational principle the best wavefunction will be the one with the lowest energy. The energy can be lowered by changing the spin orbitals. <ref>Attila Szabo, Neil S. Ostlund ''Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory'' Dover Books on Chemistry 1989 ISBN: 0486691861</ref>This leads to the Hartree Fock equation, as seen in equation 5.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 HF Equation.PNG|thumb|500x500px| Equation 5: Simplified derivation for the Hartree Fock equation <ref>http://www.quimica.urv.es/~bo/MOLMOD/Mike_Colvin/qc/thm.html Last accessed 24th March 2018 </ref>]]
|}

The Hartree Fock approximation overcomes the complicated, many electron problem, by treating it as a one-electron problem and accounting for electron-electron repulsion in an average way. <ref>Attila Szabo, Neil S. Ostlund ''Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory'' Dover Books on Chemistry 1989 ISBN: 0486691861</ref> The Hartree Fock equation can then be solved using the self-consistent field (SCF) method. This method involves making an initial guess for the spin orbitals, calculating the average electron field, and solving the HF equation to obtain a new set of spin orbitals. This process is then repeated with the new set of spin orbitals until the basis sets lower the Hartree Fock energy to a limit called the Hartree Fock limit. <ref>Attila Szabo, Neil S. Ostlund ''Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory'' Dover Books on Chemistry 1989 ISBN: 0486691861</ref>

===<u> Methods for Locating and Characterising Transition States</u>===

There are three different methods for localising and characterising transition states:

Method 1: The structure of the transition state is estimated and a PM6 TS calculation is carried out. If successful the optimised transition state should have a single imaginary frequency and a successful IRC path with a gradient of zero at the TS. Further optimisation can then be carried out using a B3LYP/6-31g(d) calculation. Whilst this is the fastest method, it suffers from various drawbacks; it requires prior knowledge of the transition state and failure to adequately estimate the structure will result in a failed calculation or the wrong TS structure.

Method 2: Similarly to method 1, the initial step of method 2 is to estimate the structure of the transition state. However, the atom pairs involved in the bond forming reaction are frozen in space preceding optimisation to a minimum. This enables the rest of the structure to be optimised and the TS can then be calculated using PM6 (and B3LYP/6-31g(d)). The primary disadvantage of method 2 is that it requires knowledge of the TS, but it provides a more significant means of locating the TS compared to method 1.

Method 3: This is the most infallible method of locating the TS as it does not require knowledge of the TS. The downside of the method is that it is slow, requiring many steps. In addition difficulties can arise if the TS is located far from the reactant and product minima. In this method either the reactant or product geometries are optimised, and the bond lengths are then modified to resemble the TS. The atom pairs involved in the reaction are then frozen, and from the optimised structure a TS calculation can be carried out.

Method 2 was used for exercise 1 and 2. Exercise 3 was carried out using method 3.

==<u>Exercise 1: Reaction of Butadiene with Ethylene</u>==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Excellent work across the whole exercise - very well done!)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Exercise1 RX Scheme.PNG|thumb| Figure 1: Scheme for the Diels-Alder Cycloaddition of Butadiene and Ethene]]
|}

The conjugated butadiene undergoes a thermal [4+2] cycloaddition with ethene to form an unsaturated six-membered ring. There are 6 electrons moving in suprafacial fashion making the reaction pericyclic. The absence of substitution on the fragments avoids issues of stereoselectivity.

===<u> Molecular Orbital Analysis</u>===

Analysis of the molecular orbitals of ethene and butadiene enables the determination of how the orbitals interact to form the transition state. In a product molecular orbital diagram the reactants overlap to form bonding and anti-bonding MOs which are stabilised and destabilised more than the reactants respectively. Whilst a transition state MO diagram also shows stabilising and destabilising interactions, the orbitals remain raised in energy. This can be rationalised by the definition of a transition state as the maximum on the minimum energy path or a stationary point with a single negative Hessian eigenvalue. There is an activation barrier that must be surmounted to reach the transition state.

From the visualisation of the MOs in table 1 it can be seen that HOMO-1 is formed from a stabilising interaction between the HOMO of butadiene and the LUMO of ethene. Similarly, the HOMO TS is formed from the stabilising overlap of the HOMO of ethene and the LUMO of butadiene. The LUMO of the transition state is formed from a destabilising interaction between the overlap of the LUMO of butadiene with the HOMO of ethene. The destabilising overlap of the HOMO of butadiene and the LUMO of ethene affords the LUMO+1. The interaction between the orbitals is consistent with the observations made by Fukui ''et al.'' <ref>Kenichi Fukui, Teijiro Yonezawa, and Haruo Shingu A Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons ''The Journal of Chemical Physics'' 20, 722 (1952); doi: 10.1063/1.1700523</ref> ; the occupied orbitals of different molecules do not interact whilst the the occupied orbitals of one molecule and the unoccupied orbital of another will interact with each other causing attraction. Moreover, it can be deduced that interacting orbitals must be of the same symmetry. The symmetric HOMO of ethene and the symmetric LUMO of butadiene overlap to give a symmetric HOMO and LUMO whilst the antisymmetric HOMO of butadiene and the anti-symmetric LUMO of ethene give the anti-symmetric HOMO-1 and LUMO+1. The orbitals must be of the same symmetry in order to interact, and the overlap integral is a measure of their interaction. Orbitals of the same symmetry will interact strongly and have a non-zero value of the overlap integral. In a forbidden reaction such as that with an anti-symmetric and symmetric orbital combination, the overlap integral will be zero and there will be no interaction between the orbitals. The symmetry of the orbitals can be determined by a plane of symmetry passing vertically through the orbitals.

The Diels Alder reaction undergoes normal electron demand. The reactivity is controlled by the relative energies between the Frontier Molecular orbitals where the key interaction will be between the HOMO and LUMO that are closer in energy. From figure 2 it can be seen that the smallest energy gap will be between the HOMO of butadiene and the LUMO of ethene. The smaller energy gap will result in a better overlap in the transition state. The energies in the molecular orbital diagram (figure 2) were obtained by doing a single point energy calculation on the reactants obtained from the IRC. The TS energies were equally obtained by doing a single point energy calculation of the TS. Using these energies it can be seen quantitatively that the energy gap between the HOMO of butadiene and the LUMO of ethene is 0.398 Ha, whilst the energy gap between the HOMO of ethene and the LUMO of butadiene is 0.399 Ha. Although there is a small energy difference, the reaction is still expected to proceed via a normal electron demand Diels Alder.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Butadiene MO final.PNG|600x700px|thumb| Figure 2: Molecular Orbital Diagram for the Transition State formed during the Cycloaddition of Ethene and Butadiene]]
|}

The molecular orbital diagram for the transition state (figure 2) was constructed using the molecular orbitals in table 1.

{| class="wikitable"
|+ '''Table 1.''' The Molecular Orbitals For Ethene, Butadiene, the Transition State
|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visulisation of the Reactant Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Ethene HOMO
! style="background: #0D4F8B; color: white;" | Ethene LUMO
! style="background: #0D4F8B; color: white;" | Butadiene HOMO
! style="background: #0D4F8B; color: white;" | Butadiene LUMO
|-
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|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation Transition State Molecular Orbitals
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! style="background: #0D4F8B; color: white;" | Transition State HOMO -1
! style="background: #0D4F8B; color: white;" | Transition State HOMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO +1
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===<u>Bond Distance Changes</u>===

Table 2 illustrates the changes in bond length that occur throughout the reaction with two π bonds being broken and concomitant formation of two single bonds. Examination of the C1-C2 ethene double bond shows a clear elongation upon formation of the transition state and subsequent lengthening in the product to form a single bond. The change in bond length is consistent with the change in hybridisation from sp<sup>2</sup> to sp<sup>3</sup> for both C1 and C2 that occurs throughout the course of the Diels Alder reaction. The two double bonds of the butadiene fragment, C3-C4 and C5-C6, are equally progressively lengthened from double to single bonds. In this case C4 and C5 remain sp<sup>2</sup> hybridised whilst C3 and C6 change hybridisation state from sp<sup>2</sup> to sp<sup>3</sup>. The internal single bond of the butadiene fragment is shortened in the transition state to form a double bond in the product. Typical values for the interatomic distance between a carbon-carbon sp<sup>3</sup> single bond is 1.54 Å whilst that for a carbon-carbon sp<sup>2</sup> double bond is 1.34 Å <ref>Linus Pauling, and L. O. Brockway Carbon—Carbon Bond Distances. The Electron Diffraction Investigation of Ethane, Propane, Isobutane, Neopentane, Cyclopropane, Cyclopentane, Cyclohexane, Allene, Ethylene, Isobutene, Tetramethylethylene, Mesitylene, and Hexamethylbenzene. Revised Values of Covalent Radii ''J. Am. Chem. Soc.'', 1937, 59 (7), pp 1223–1236 DOI: 10.1021/ja01286a021</ref>. The literature values closely match the single and double bond lengths in the product. However, butadiene's internal single bond (C4-C5) appears slightly shorter than is expected for a single bond and this is a result of it being a conjugated diene with π electrons delocalised across the fragment. Similarly in cyclohexene the bonds adjacent from the double bond (C3-C4 and C5-C6) are slightly shorter than a typical single bond and this is a result of adjacent carbon being sp<sup>2</sup> hybridised thus benefiting from additional s character. The C2-C3 and C1-C6 interatomic distances represent the bonds that are formed between ethene and butadiene to form single bonds in the cyclohexene product. In the TS these bond lengths appear as approximately 2.115 Å, this is shorter than twice the Van der Waals radius of carbon which is indicative of interaction between the electron densities of the two carbon atoms <ref>S. S. Batsanov Van der Waals Radii of Elements ''Inorganic Materials'', Vol. 37, No. 9, 2001, pp. 871–885</ref>.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ '''Table 2. Bond length Changes throughout the Cycloaddition of Ethene and Butadiene'''
! colspan="1" style="border: none; background: none;"|
! colspan="4"| Bond Length (Å)
|-
!Carbon-Carbon Bond
!Ethene
!Butadiene
!Transition State
!Cyclohexene
|-
|C1-C2
|<nowiki>1.3273</nowiki>
|n/a
|1.3818
|1.5345
|-
|C2-C3
|<nowiki>n/a</nowiki>
|n/a
|2.1147
|1.5372
|-
|C3-C4
|<nowiki>n/a</nowiki>
|1.3352
|1.3798
|1.5008
|-
|C4-C5
|<nowiki>n/a</nowiki>
|<nowiki>1.4683</nowiki>
|1.4111
|1.3370
|-
|C5-C6
|n/a
|<nowiki>1.3352</nowiki>
|1.3798
|1.5008
|-
|C6-C1
|<nowiki>n/a</nowiki>
|<nowiki>n/a</nowiki>
|2.1149
|1.5372
|}

The changes in bond length during the course of the reaction are further illustrated by figure 3. The reaction coordinate shows the dissociation of the cyclohexene product into the ethene and butadiene reactants. The double bond in cyclohexene (C4-C5) is lengthened from a single to double bond. The neighbouring single bonds (C3-C4 and C5-C6) are shorthened to double bonds. C1-C2 is shorthened to reform the ethene double bond. The bond distances C2-C3 and C1-C6 show the single bonds between the two fragments being lengthened and the bonds being broken.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Bond Distance Graph.PNG|thumb|500x500px|Figure 3: Graph showing the variation in internuclear distance for the dissociation of ethene and butadiene]]
|}

===<u> Reaction Path Vibrations </u>===

The animation below shows the vibrational mode of the imaginary frequency of the TS which occurs at 948.5i cm<sup>-1</sup>. This vibrational mode matches the action of the reaction path. The animation shows that the reaction is both synchronous and concerted with two new bonds forming simultaneously. Table 2 provides further evidence for a synchronous reaction path since the two forming bonds have the same length.

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<br />

==<u>Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole</u>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Scheme EX2.PNG|thumb|500x500px|Figure 4: Scheme for the reaction of cyclohexadiene and 1,3-Dioxole]]
|}

The Diels-Alder between cyclohexadiene and 1,3-dioxane can proceed in an exo and endo manner. The different pathways rely on the approach of the 1,3-dioxole towards the cyclohexadiene. If the dioxole approaches the diene with the oxygen atoms lying beneath the ring then the endo product will result. Conversely, if the dioxole ring oxygens point away from the diene, the exo product will predominate.

===<u> Molecular Orbital Analysis </u>===

MO diagrams were constructed for both the exo and endo transition states, these can be seen in figure 5 and 6 respectively. The MO diagrams show the same observation as made in exercise 1; orbitals can only overlap if they are of the same symmetry. The anti-symmetric diene HOMO and dienophile LUMO generate the anti-symmetric TS HOMO-1 and LUMO+1. The symmetric HOMO dienophile and LUMO diene afford the symmetric HOMO and LUMO.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Exercise2 Exo Mo.PNG|thumb|600x700px|Figure 5: Molecular Orbital Diagram for the Exo Transition State]]
![[File:SJP115 Exercise2 Endo Mo.PNG|thumb| 600x700px|Figure 6: Molecular Orbital Diagram for the Endo Transition State]]
|}

A normal electron demand Diels Alder reaction typically proceeds between an electron rich diene and an electron poor dienophile. The smallest energy gap controls the reactivity and for a normal electron demand Diels Alder reaction this will be between the HOMO of the diene and the LUMO of the dienophile. The small energy gap will enable strong overlap between the orbitals. Inverse electron demand Diels Alder reactions are typical of an electron poor diene, with an electron withdrawing group that lowers the energy of the HOMO and LUMO, and an electron rich dienophile, with electron donating groups that raise the energy of the HOMO and LUMO. The HOMO of the dienophile will lie above the diene’s HOMO and the smallest energy gap will be between the HOMO of the dienophile and the LUMO of the diene. The energy gap between the HOMO and LUMO frontier molecular orbitals in both normal and inverse electron demand can be seen in figure 7.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Normal Inverse Electron Demand.PNG|thumb|500x500px|Figure 7: Scheme showing the frontier molecular orbitals for both a normal electron demand Diels Alder and an inverse electron demand Diels Alder<ref>Radleigh A. A. Foster and Michael C. Willis Tandem inverse-electron-demand hetero-/retro-Diels–Alder reactions for aromatic nitrogen heterocycle synthesis ''Chem. Soc. Rev.'', 2013, 42, 63-76 DOI: 10.1039/C2CS35316D </ref>]]
|}

From the MO diagrams (figure 5 and 6) it can be seen that both the endo and exo reactions undergo inverse electron demand Diels Alder. There is a smaller energy gap between the 1,3-dioxole HOMO and the cyclohexadiene LUMO than the 1,3-dioxole LUMO and cyclohexadiene HOMO. The 1,3-dioxole has two electron donating oxygen substituents which raise the energy of the HOMO and LUMO, such that the HOMO of the dienophile is higher in energy than the cyclohexadiene HOMO. The HOMO of the dienophile will hence interact more strongly with the LUMO cyclohexadiene. The energies reported in the MO diagrams are those from the B3YLP optimisations of the reactants and the transition state. In order to quantify the energy gap between the HOMO and LUMOs of the two reactants, a single point energy calculation was carried out from the IRC for both the endo and exo reactants. The results are summarised in table 3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ '''Table 3. Single point energy calculations of the reactants from the IRC output'''
! colspan="1" style="border: none; background: none;"|
|-
!Endo
!Ha
!Exo
!Ha
|-
|1,3 Dioxole HOMO
|<nowiki>-0.317</nowiki>
|1,3 Dioxole HOMO
| -0.322
|-
|1,3 Dioxole LUMO
|<nowiki>0.032</nowiki>
|1,3 Dioxole LUMO
|0.030
|-
|1,3 Cyclohexadiene HOMO
|<nowiki>-0.321</nowiki>
|1,3 Cyclohexadiene HOMO
| -0.322
|-
|1,3 Cyclohexadiene LUMO
|<nowiki>0.023</nowiki>
|1,3 Cyclohexadiene LUMO
|0.021
|}

From table 3 it can be seen that the energy gap between the cyclohexadiene LUMO and 1,3 dioxole HOMO is approximately 0.34 Ha whilst the energy gap between the cyclohexadiene HOMO and 1,3 dioxole LUMO is approximately 0.35 Ha. This provides further, quantitative evidence for an inverse electron demand Diels Alder.

{| class="wikitable"
|+ '''Table 4.''' The Molecular Orbitals For the Endo and Exo Transition State
|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation of the Exo Transition State Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Transition State HOMO-1
! style="background: #0D4F8B; color: white;" | Transition State HOMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO+1
|-
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|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation of the Endo Transition State Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Transition State HOMO -1
! style="background: #0D4F8B; color: white;" | Transition State HOMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO
! style="background: #0D4F8B; color: white;" | Transition State LUMO +1
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===<u> Thermochemistry </u>===

Under the thermochemistry section of the log file, the “sum of electronic and thermal free energies” was extracted for the reactants, TS and the product. The activation energy was then was computed by doing the energy difference between the TS and the reactants. The reaction energies were calculated by calculating the energy difference between the product and the reactants. The results are summarised in table 5.

<center>
{| class="wikitable"
|+ '''Table 5. Thermochemistry Data for the Endo and Exo Diels Alder reaction between 1,3 Dioxole and 1,3 Cyclohexadiene '''
|-
! rowspan="3" style="background: #0D4F8B; color: white;" | Reaction Type
! colspan="7" style="background: #0D4F8B; color: white;" | Energy (kJ/mol)
|-
! colspan="3" style="background: #0D4F8B; color: white;" | Reactants
! rowspan="2" style="background: #0D4F8B; color: white;" | Transition State
! rowspan="2" style="background: #0D4F8B; color: white;" | Product
! rowspan="2" style="background: #0D4F8B; color: white;" | Activation Energy
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diene
! style="background: #0D4F8B; color: white;" | Dienophile
! style="background: #0D4F8B; color: white;" | Total
|-
| style="text-align: center;" | '''Exo'''
| rowspan="2" style="text-align: center;" | -612593.146
| rowspan="2" style="text-align: center;" | -701188.7353
| rowspan="2" style="text-align: center;" | -1313781.88
| style="text-align: center;" | -1313614.23
| style="text-align: center;" | -1313845.68
| style="text-align: center;" | 167.65
| style="text-align: center;" | -63.80
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | -1313622.07
| style="text-align: center;" | -1313849.27
| style="text-align: center;" | 159.23
| style="text-align: center;" | -67.39
|}
</center>

Examination of the activation energies in table 5 shows that there is a larger activation barrier to reach the exo TS than the endo TS. The endo TS is thus more stable than the exo TS. In order to reach the exo TS, the reactants will require additional energy to surmount the larger activation barrier. The fastest formed, kinetically favoured product, with the lower activation barrier will hence be the endo product.

The reaction energies show that whilst both the endo and exo reactions are exothermic and thermodynamically favourable, the endo product is lower in energy and thermodynamically more stable than the exo. The reaction energy for the endo is more negative, more exothermic and presents the thermodynamically most stable product. The endo product is thus not only kinetically favoured but also thermodynamically favoured. The exo product is higher in energy as a result of the steric clash between the bridging carbons and the 5 membered dioxole ring.

===<u> Secondary Orbital Interactions </u>===

The lower energy of the endo TS can be rationalised on the basis of secondary, non-bonding, interactions between the dioxole oxygen p orbitals and the π system of the diene. Such interactions lower the energy of the TS HOMO promoting faster formation of the kinetic product. The exo TS only has primary orbital interactions and this is a result of the oxygen p orbitals of the dioxole pointing away from the diene p orbtials making them too far apart to interact. The HOMO of both the exo and endo TS are given in table 5 wherein the isovalue has been set to 0.01, this has the effect of shortening the radial extension of the orbitals making the stabilising interactions of the endo clearer.

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|+ '''Table 5.''' Visualisation of the Exo and Endo HOMO secondary orbital interactions
! style="background: #0D4F8B; color: white;" | Exo Secondary Orbital Interactions
! style="background: #0D4F8B; color: white;" | Endo Secondary Orbital Interactions
|-
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In the exo TS HOMO the p orbitals of the dioxole do not interact with the diene p orbitals, whereas in the endo TS HOMO the p orbitals of the dioxole do interact with those of the diene.

==<u>Exercise 3: Diels-Alder vs Cheletropic</u>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Scheme Ex3.PNG|thumb|500x500px| Figure 8: Scheme for the Diels Alder and Cheletropic reaction between sulphur dioxide and xylyene ]]
|}

The reaction scheme shows the potential pathways for the reaction between o-xylyene and sulphur dioxide. The Diels-Alder reaction can proceed in an endo or exo fashion. The cheletropic reaction is characterised by two σ bonds forming in concert at a single atom. <ref>Angew. Chem. Int. Ed. Engl. 1969, 8, 781–853</ref>

===<u> Intrinsic Reaction Coordinate (IRC) </u>===

The IRC for the exo/endo Diels Alder pathways and the Cheletropic reaction are shown in figure 9, 10, 11 respectively. The IRCs show the progression of the reaction, from the SO<sub>2</sub> and o-xylyene fragments, to the TS, and finally to the products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 EXO Correct Order Exercise 3 2.gif|thumb|500x500px| Figure 9: IRC for the Exo Diels Alder pathway]]
![[File:SJP115 ENDO Correct Order Exercise 3.gif|thumb|500x500px|Figure 10: IRC for the Endo Diels Alder pathway]]
![[File:SJP115 Cheleo Correct Order Exercise 3.gif|thumb|500x500px|Figure 11: IRC for the Cheletropic pathway]]
|}

The exo and endo reactions show asynchronous bond formation, with the bonds forming at different times due to asymmetry. For both Diels Alder reactions the C-O bond between the diene and dienophile are formed before the bond between the diene and sulphur atom (C-S). The cheletropic reaction proceeds with synchronous bond formation; both ends of the diene form new C-S bonds with the sulphur atom of SO<sub>2</sub> at the same time. The three reactions all show a fully delocalised 6-membered aromatic ring intermediate and in all three products the six membered ring is aromatic. This illustrates the high instability of xylyene; there is a strong driving force for aromatisation which will drive product formation. Indeed, from the IRCs it can be seen that aromatisation occurs before bond formation.

===<u> Thermochemistry </u>===

Table 6 was constructed in the same was as in exercise 2, the "sum of the electronic and thermal free energies" were extracted from the log files of the reactants, TS and products and used to calculate the activation and reaction energies. Using the data from table 6 a reaction profile was constructed (figure 12).

<center>
{| class="wikitable"
|+ '''Table 6. Thermochemistry Data for the Cheletropic, endo and exo Diels Alder reaction between Xylyene and Sulphur Dioxide'''
|-
! rowspan="3" style="background: #0D4F8B; color: white;" | Reaction Type
! colspan="7" style="background: #0D4F8B; color: white;" | Energy (kJ/mol)
|-
! colspan="3" style="background: #0D4F8B; color: white;" | Reactants
! rowspan="2" style="background: #0D4F8B; color: white;" | Transition State
! rowspan="2" style="background: #0D4F8B; color: white;" | Product
! rowspan="2" style="background: #0D4F8B; color: white;" | Activation Energy
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Sulphur Dioxide
! style="background: #0D4F8B; color: white;" | Xylyene
! style="background: #0D4F8B; color: white;" | Total
|-
| style="text-align: center;" | '''Exo'''
| rowspan="3" style="text-align: center;" | -313.14
| rowspan="3" style="text-align: center;" | 467.33
| rowspan="3" style="text-align: center;" | 154.19
| style="text-align: center;" | 241.75
| style="text-align: center;" | 56.32
| style="text-align: center;" | 87.56
| style="text-align: center;" | -97.87
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | 237.76
| style="text-align: center;" | 56.98
| style="text-align: center;" | 83.57
| style="text-align: center;" | -97.21
|-
| style="text-align: center;" | '''Cheletropic'''
| style="text-align: center;" | 260.09
| style="text-align: center;" | 0
| style="text-align: center;" | 105.9
| style="text-align: center;" | -154.2
|}
</center>

The reaction profile clearly illustrates that the endo TS has the lowest energy activation barrier, requiring less energy than the exo or cheletropic to be surmounted. The endo product is hence the kinetic product since it will be formed fastest. The stability of the endo TS could be due to secondary orbital interactions between the p orbitals of the non-bonding oxygen atom of the SO<sub>2</sub> dienophile and the π system of the xylene diene. This interaction is not possible for the exo Diels-Alder reaction since the sulphur dioxide approaches the diene with one of its oxygen pointed away from xylyene. The exo TS thus lies slightly higher in energy than the endo. The cheletropic TS has the largest activation energy and this is a result of the ring and angle strain of the 5-membered ring formed. The 6-membered ring in the exo and endo TS are conformationally less strained minimising 1,3 diaxial repulsions and angle strain. The reaction profile highlights that the reactions are all exothermic. The endo and exo products are similar in energy with the endo product being slightly higher in energy. However, the cheletropic product has the lowest reaction energy and it is the thermodynamically favoured product. This can be rationalised by the high bond energy of the two S=O bonds <ref>D. P. Stevenson The Strengths of Chemical Bonds J. Am. Chem. Soc., 1955, 77 (8), pp 2350–2350 DOI: 10.1021/ja01613a116</ref>.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Energies Exercise 3.PNG|thumb|500x500px|Figure 12: Reaction Profile for the different reactions between sulphur dioxide and xylyene]]
|}

===<u> An alternative Diels Alder Site </u>===

There is an alternative Diels-Alder reaction which can occur at the cis-butadiene fragment in the 6-membered ring of xylyene. This [4+2] cycloaddition can be exo or endo and the IRCs for both pathways are shown in figures 13 and 14 respectively.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Alternative Path Exo EX3.gif|Figure 13:IRC for the alternative exo Diels Alder pathway]]
![[File:SJP115 Alternative Path Endo EX3.gif|Figure 14: IRC for the alternative endo Diels Alder pathway]]
|}

A thermochemical analysis of these reactions shows that they possess large activation barriers making them less favourable than the previously described Diels-Alder pathways. Not only are these reactions kinetically unfavourable, but they are endothermic with positive reaction energies. The products lie higher in energy than the reactants and require an input of energy to be formed making these reactions thermodynamically unfavourable. This can be accounted for by the absence of aromaticity in the TS or product. Moreover, there is loss of the conjugation between the two butadiene fragments which is present in xylyene. Whilst both pathways are unfavourable, the endo remains more favourable than the exo since it posses a lower activation energy. This could be due to secondary orbital interactions. The reaction energy is also lower for the endo. The endo pathway hence presents both the kinetically and thermodynamically favoured Diels-Alder reaction for this alternative site.

<center>
{| class="wikitable"
|+ '''Table 7. Thermochemistry Data for the Alternative Exo and Endo Diels Alder Reactions'''
|-
! rowspan="3" style="background: #0D4F8B; color: white;" | Reaction Type
! colspan="7" style="background: #0D4F8B; color: white;" | Energy (kJ/mol)
|-
! colspan="3" style="background: #0D4F8B; color: white;" | Reactants
! rowspan="2" style="background: #0D4F8B; color: white;" | Transition State
! rowspan="2" style="background: #0D4F8B; color: white;" | Product
! rowspan="2" style="background: #0D4F8B; color: white;" | Activation Energy
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Sulphur Dioxide
! style="background: #0D4F8B; color: white;" | Xylyene
! style="background: #0D4F8B; color: white;" | Total
|-
| style="text-align: center;" | '''Exo'''
| rowspan="2" style="text-align: center;" | -313.14
| rowspan="2" style="text-align: center;" | 467.33
| rowspan="2" style="text-align: center;" | 154.19
| style="text-align: center;" | 275.82
| style="text-align: center;" | 176.71
| style="text-align: center;" | 121.63
| style="text-align: center;" | 22.52
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | 267.98
| style="text-align: center;" | 172.26
| style="text-align: center;" | 113.79
| style="text-align: center;" | 18.07
|}
</center>

==<u>Extension 1: Electrocyclic Ring Closing</u>==

Electrocyclic reactions are characterised by the net transformation of a pi bond into a sigma bond. The thermal electrocyclic ring closing of a substituted cyclobutene is a 4nπ electron process which proceeds with conrotatory motion of the groups on the terminal carbons in order to bring the lobes of the orbitals of the same phase together. The stabilising, attractive interaction of bringing two lobes of the same phase together will form a sigma bond.

The reaction path is illustrated by the gif in figure 15.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Extension IRC Path.gif|500x500px| thumb| Figure 15: IRC path for the electrocyclic ring closing of a substituted butadiene]]
|}

Figure 16 illustrates the effect of conrotatory motion on the orbitals of the HOMO ψ2 for the thermal electrocylcic ring closing.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Extension Con Motion.PNG|thumb|500x500px| Figure 16: Scheme showing the conrotatory motion of the orbitals]]
|}

(This is where you have to be careful about symmetry. In the products, the orbitals must have rough rotational and reflective symmetry. The product orbitals above have rotational symmetry (symmetric) but an undefined reflective symmetry (antisymmetric at back, symmetric at front). Either the front or the back should rearrange or cancel out to maintain these symmetry requirements. Later in your correlation diagram you show the back as having cancelled out [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:19, 4 April 2018 (BST))

Throughout the rehybridisation reaction the C2 (two-fold) axis of symmetry is maintained. If the phases of the orbitals are preserved under the symmetry transformation they are described as being symmetric.<ref>Prof. R. B. Woodward Prof. Roald Hoffmann The Conservation of Orbital Symmetry ''Angew. Chem. internat. Edit.'' 1 Vol. 8 (1969) 1 No. II </ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Extension C2 Axis.PNG|thumb|500x500px|Figure 17: Scheme showing the effect of a C2 axis on the symmetric ψ2 HOMO orbital ]]
|}

A correlation diagram can be constructed to connect molecular orbitals of the same symmetry in the reactants and products (figure 18). This diagram shows that the Ψ2 orbital of butadiene and the sigma orbital of cyclobutene, which are both symmetric with respect to the C2 axis, are correlated. The antisymmetric Ψ1 and π orbitals will be correlated. Similiar considerations apply for the LUMO orbitals in which the antisymmetric sigma star and Ψ3 are correlated. Finally, the Ψ4 and π* will be correlated. The conrotatory process is symmetry-allowed because the bonding orbitals of the reactants correlate with the bonding orbitals of the product with the same symmetry. According to Woodward et al. <ref>Prof. R. B. Woodward Prof. Roald Hoffmann The Conservation of Orbital Symmetry ''Angew. Chem. internat. Edit.'' 1 Vol. 8 (1969) 1 No. II </ref> the highest occupied orbitals dominate these correlations and they can be considered as valence electrons that can be easily perturbed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Extension Correlation Diagram.PNG|thumb| 500x500px|Figure 18: Correlation Diagram for the Conrotatory Ring Closing of Butadiene]]
|}

(Show the symmetry axis here for clarity [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:19, 4 April 2018 (BST))

The transition state will have an odd number of phase inversions hence will proceed with a Möbius topology. <ref>Rainer Herges Topology in Chemistry: Designing Mo1bius Molecules ''Chem. Rev.'' 2006, 106, 4820−4842</ref> This TS can be seen in table 8 wherein the π electrons resulting from the 2p atomic orbitals are distributed around a Möbius strip bearing a single half-twist. <ref>Henry S. Rzepa The Aromaticity of Pericyclic Reaction Transition States ''Journal of Chemical Education'' Vol. 84 No. 9 September 2007 •</ref>

{| class="wikitable"
|+ '''Table 8.''' The Molecular Orbitals For Cyclobutene and Butadiene
|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visulisation of the Reactant Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Butadiene σ
! style="background: #0D4F8B; color: white;" | Butadiene π
! style="background: #0D4F8B; color: white;" | Butadiene π*
! style="background: #0D4F8B; color: white;" | Butadiene σ*
|-
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|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation the Product Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | Cyclobutene σ
! style="background: #0D4F8B; color: white;" | Cyclobutene π
! style="background: #0D4F8B; color: white;" | Cyclobutene π*
! style="background: #0D4F8B; color: white;" | Cyclobutene σ*
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|-
! colspan="4" style="background: #0D4F8B; color: white;" | Visualisation the Transition State Molecular Orbitals
|-
! style="background: #0D4F8B; color: white;" | HOMO-1
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
! style="background: #0D4F8B; color: white;" | LUMO+1
|-
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The stereochemistry of the reactant and product molecular orbitals provide further evidence for a conrotatory electrocyclic reaction. From the reactant MO in table 8 it can be seen that one of the double bonds is trans whilst the other is cis and following a conrotatory motion the hydrogens originating from the double bond will end up on the same side of the cyclobutene ring.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Stereochemistry.PNG|500x500px|thumb| Figure 19: Stereochemical Evidence for Conrotatory Electrocyclic Reaction]]
|}

Under photochemical conditions, electronic promotion causes the ψ3 orbital to become the HOMO. The electrocyclic ring closing can only proceed via a disrotatory mechanism and in this case an invariant plane of symmetry will be present. In order to be carry out the photochemical disrotatory electrocyclyic ring closing, Gaussian cannot use single reference calculations. Hartree Fock and density functional theory are not adequate in this case and the multiconfigurational method is required to enable mixing of the various electronically excited states. This method uses a linear combination of configuration states (CSF) to determine the electronic wavefunction. In such calculations the Complete Active Space Multiconfiguration SCF (CAS) is defined to include the approximate spin orbit coupling between the various spin states of the first excited state.

The multiconfigurational method was applied to the substituted butadiene in order to observe the electronic ground state of the photochemical ring closing pathway. The number of electrons and orbitals in the active space were both defined to be four such that the CAS corresponds to the first excited state of butadiene. The output will hence be a minimum on the excited state. Examination of the log file revealed that the excited state is mainly composed of the ground electronic state (1100) and an excited singlet state (a1b0). The geometric configuration of this excited state is twisted making it harder for butadiene to react in this configuration. Although there may be alternative geometric configurations that may react more easily it is envisioned that the disrotatory electrocyclic ring closing will remain more disfavoured than the thermal conrotatory path. This is evidenced by the correlation diagram for the photochemical pathway in which the TS lies higher in energy.

==<u> Extension 2: Electrocyclic Ring Opening </u>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Scheme EXtension2.PNG|thumb|500x500px| Figure 20: IRC for the ring opening of a substituted butadiene]]
|}

The electrocyclic ring opening reaction illustrated in figure 20 reacts antrafacially according to the Woodward Hoffman rules. This system is also a 4nπ electron system that will proceed with conrotation. The TS shows the intermediate step in the formation of the butadiene double bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115_Extension2_GIF.gif|thumb|500x500px| Figure 21: IRC for the ring opening of a substituted butadiene]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
!HOMO of Reactant
!HOMO of TS
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==<u>Conclusion</u>==

A number of pericyclic reactions were successfully modeled in Gaussian. PM6 was used as the primary method of carrying out calculations as a compromise between rapidity and accuracy. B3YLP was used when it was necessary to probe reactions with a higher level of accuracy. For example, in exercise 2 the transition state geometries of the exo and endo Diels Alder pathways were elucidated using B3YLP.

Gaussian not only provides a means of locating and characterising transition states, but it also enables the visualization of molecular orbitals. The energies of these molecular orbitals can be used to gain insight into the mechanistic pathway behind the reaction; for example, whether a Diels Alder proceeds via normal or inverse electron demand. The Diels Alder reaction between ethene and butadiene (exercise 1) was found to proceed via a normal electron demand, whilst the Diels Alder between the electron rich 1,3 dioxole and the cyclohexadiene was found to occur via inverse electron demand. Further mechanistic insights can be obtained by animation of the imaginary frequency vibration. This gave an insight into how bond formation occurred, whether bond formation was synchronous or asynchronous. Finally, analysis of the thermochemical data aided in identifying the kinetic and thermodynamic pathways and products.

==<u> Files </u>==

===<u>Reaction of Butadiene with Ethylene</u>===

[[Media:SJP115_ETHENE.LOG|Log file of ethene]]

[[Media:SJP115 BUTADIENE2.LOG| Log file of butadiene]]

[[Media:SJP115 EX1 ETHENE AND BUTADIENE SAME FRAME.LOG| Log file of butadiene and ethene in the same frame PM6]]

[[Media: SJP115 Ex1 TS IRC INITIAL SINGLE POINT ENERGY.LOG| Log file of single point energy of ethene and butadiene]]

[[Media:SJP115 TS PM6.LOG| Log file of TS PM6 Optimised]]

[[Media: SJP115 TS IRC.LOG|Log file of the IRC PM6]]

[[Media: SJP115 TS PM6 SYMBROKEN2.LOG| Log file of the PM6 product ]]

===<u>Reaction of Cyclohexadiene and 1,3-Dioxole</u>===

[[Media:SJP115 DIOXANE BY3.LOG|Log file of 1,3 Dioxole B3YLP]]

[[Media:SJP115 DIENE B3LYP 631GD.LOG|Log file of 1,3 Cyclohexadiene B3YLP]]

[[Media:SJP115 Ex2 Exo TS B3LYP 631GD.LOG|Log file of Exo TS B3YLP]]

[[Media:SJP115_Ex3_Endo_TS_B3LYP_631GD_NOPTEIGEN.LOG|Log file of Endo TS B3YLP]]

[[Media: SJP115 Ex2 Exo TS IRC.LOG|Log file of Exo IRC PM6]]

[[Media:SJP115 Ex2 Endo TS PM6 IRC.LOG|Log file of Endo IRC PM6]]

[[Media:SJP115 Ex2 Exo PRODUCT B3LYP6 31GSD.LOG| Log file of Exo Product B3YLP]]

[[Media:SJP115 Ex2 ENDO PRODUCT B3LYP 631GD.LOG| Log file of Endo Product B3YLP]]

===<u>Diels-Alder vs Cheletropic</u>===

[[Media:SJP115 SO2 2 PM6.LOG|Log file of SO<sub>2</sub>]]

[[Media:SJP115 O-XYLYENE PM6.LOG|Log file of o-Xylyene]]

[[Media:SJP115 Exercise3 TS PM6.LOG| Log file of Exo TS PM6]]

[[Media:SJP115 Exercise3 TS IRC PM6.LOG| Log file of Exo IRC PM6]]

[[Media:SJP115 Exercise3 EXO PRODUCT PM6.LOG| Log file of Exo Product]]

[[Media:SJP115 Exercise3 Endo TS PM6.LOG|Log file of Endo TS PM6]]

[[Media: SJP115 Exercise3 Endo TS IRC.LOG|Log file of Endo IRC PM6]]

[[Media:SJP115 Exercise3 Endo PRODUCT PM6.LOG|Log file of Endo Product]]

[[Media:SJP115 CHELE TS PM6.LOG|Log file of Cheletropic TS PM6]]

[[Media:SJP115 chele IRC 2.LOG|Log file of Cheletropic IRC PM6]]

[[Media:SJP115 CHELE PRODUCT 2 PM6.LOG| Log file of Cheletopic Product]]

[[Media: SJP115 EX3 AP Endo TS PM6.LOG|Log file of Alternative Path Endo TS PM6]]

[[Media:SJP115 EX3 AP Endo TS IRC.LOG| Log file of Alternative Path Endo IRC PM6]]

[[Media:SJP115 EX3 AP ENDO PRODUCT PM6.LOG| Log file of Alternative Path Endo Product PM6]]

[[Media:SJP115 Ex3 AP Exo TS PM6.LOG| Log file of Alternative Path Exo TS PM6]]

[[Media:SJP115 Ex3 AP Exo TS IRC.LOG| Log file of Alternative Path Exo IRC PM6]]

[[Media:SJP115 Ex3 AP Exo PRODUCT PM6.LOG| Log file of Alternative Path Exo Product PM6]]

===<u>Electrocyclic Ring Closing Reaction</u>===

[[Media:SJP115 EXTENSION PRODUCTS FROM IRC.LOG| Log file of Electrocyclic Ring Closing Reactants PM6]]

[[Media: SJP115 Extension1 TS IRC FINAL.LOG| Log file of Electrocyclic Ring Closing IRC PM6]]

[[Media: SJP115 Extension TS PM6 2.LOG| Log file of Electrocyclic Ring Closing TS PM6]]

[[Media:SJP115 EXTENSION REACTANTS FROM IRC.LOG| Log file of Electrocyclic Ring Closing Products PM6]]

[[Media:SJP115 Extension HF OPT.LOG| Log file of Electrocyclic Ring Closing Reactant HF]]

[[Media:SJP115 Extension CAS S1 opt.log| Log File of Electrocyclic Ring Closing CAS of first excited state]]

===<u> Electrocyclic Ring Opening Reaction </u>===

[[Media: SJP115 EXTENSION2 REACTANTS.LOG| Log file of Electrocyclic Ring Opening Reactants]]

[[Media: SJP115 Extension2 TS PM6.LOG| Log file of Electrocyclic Ring Opening TS PM6]]

[[Media: SJP115 Extension2 TS IRC.LOG| Log file of Electrocyclic Ring Opening IRC PM6]]

[[Media: SJP115 EXTENSION2 PRODUCT.LOG| Log file of Electrocyclic Ring Opening Product]]

==<u>References</u>==

Rep:BT1215 CP3MD Lab

2018-04-07T09:58:23Z

Fv611: /* Molecular Orbital Discussion */

== Introduction ==
The ability to model reactions using computational simulations is something of great interest, particularly with regard to understanding experimental mechanisms or molecular properties<ref>R. Breslow et. al., Beyond the Molecular Frontier: Challenges for Chemistry and Chemical Engineering, National Research Council, 2003.</ref>. Modern computational software, such as Gaussian, is able to use a series of quantum mechanical calculations to optimise a reaction system and determine a lowest energy reaction pathway, as well as the predicted energies and structures of any reactants, transition states, and products involved. Within these calculations, there are two important theoretical considerations to take into account:

''1. Potential Energy Surface (PES)'' - The potential energy of a system given as a function of molecular geometry. By changing the molecular geometry (e.g. bond lengths during a reaction), the change in energy and transition state can be computed.

''2. Computational Method'' - Defines the approximations made within the quantum mechanics, balancing accuracy (fewer approximations lead to more precise results) with computational cost (fewer assumptions mean more resource-intensive calculations).

=== Potential Energy Surface (PES) ===
[[File:BT1215 PES Example.JPG|right|thumb|210x205px|'''''Figure 1 - An example PES surface, AB<sup>+</sup> and A<sup>+</sup> + B represent local minima, which are separated by a labelled saddle point<ref>L. Sleno and D. A. Volmer, J. Mass Spectrom., 2004, 39, 1091–1112.</ref>.''''']]
As mentioned before, the PES is a representation of the relationship between the potential energy of a system and its molecular geometry. Given that non-linear molecules have a geometrical freedom of 3N-6 modes (or 3N-5 for linear molecules), where N = the number of atoms in the molecule, the PES therefore has the same dependency, relying on the internal coordinates of the atoms in the system. In order to model a reaction PES, the number of degrees of freedom that are varied is often reduced in order to make the calculation computationally feasible. When plotted graphically, the PES represents a landscape of high and low energy configurations that correspond to turning or stationary points on the surface, with an example plot shown in '''Figure 1'''<sup>[2]</sup>. Low energy turning points correspond to an energetically stable molecular geometry, which are mathematically characterised by having a first derivative equal to 0 ('''Eq 1'''), and a positive second derivative ('''Eq 2'''), where <math>{V}</math> is potential energy and <math>{x}</math> represents an atomic or reaction coordinate:
<br>
<br>
<div style="text-align: center;"><math>\frac{\partial V}{\partial x}= 0 </math> '''Eq 1'''</div>
<br>
<div style="text-align: center;"><math>\frac{\partial^{2} V}{\partial x^{^{2}}}> 0</math> '''Eq 2'''</div>
<br>
[[File:BT1215 2D PES to TS Example.gif|right|thumb|313x553px|'''''Figure 2 - A PES diagram of ozone which has been mapped to an IRC along a reaction coordinate, showing the transition state, reactants and products<ref>1 E. G. Lewars, in Computational Chemistry, 2011, vol. 26, pp. 9–43.</ref>.''''']]
The potential energy well surrounding the minimum can be modelled as a Simple Harmonic Oscillator, where the lowest energy point is described by a Taylor expansion. Assuming a harmonic motion modelled by Hooke's law, force constant <math>{k}</math> can be equated to the second derivative in '''Eq 2'''. Since the vibrational wavenumber, <math>{v}</math>, is directly proportional to <math>\sqrt{k}</math>, it can therefore be seen that the molecular configurations corresponding to minimum turning points will '''''only''''' have positive vibrations<ref>P. Atkins and J. De Paula, Atkins’ physical chemistry, 2009.</ref>.

The transition state of a reaction corresponds to a saddle point which separates two local minima in the PES, and is essentially a maximum turning point along a particular reaction coordinate of the surface. This can be modelled as a barrier separating two wells, shown in '''Figure 2'''<sup>[2]</sup>. An activation energy is required to overcome this transition state and thus interconvert between the two wells, often denoted reactants and products. The saddle point on the PES surface can be mathematically described as being a local minimum in all directions except for one, where it is equivalent to a maximum turning point. This leads to one reaction coordinate where the second derivative of potential energy is '''negative'''. Following the same key discussion above, '''''one negative vibration frequency will be observed in the transition state''''', while all other frequencies observed will be positive.

It is important to note that, while this discussion of a singular force constant holds true for one-dimentional systems, polyatomic systems require more complicated treatment, since there are multiple force constants and vibrational motions within the system that can actually couple (i.e. one vibration could affect the likelihood of another happening). The general form of these force constants is shown below in '''Eq 3''', where ''i'' and ''j'' represent degrees of freedom (or coordinates) up to 3N-6:
<br>
<br>
<div style="text-align: center;"><math>\frac{\partial^{2} V}{\partial x_i x_j} = k_{ij} </math> '''Eq 3'''</div>

Software such as Gaussian simplifies these complicated raw motions by first converting the internal coordinates into mass-weighted coordinates to make the coupled force constants equally weighted, before creating a large Hessian matrix of all the coupled force constants. The software then diagonalises the Hessian matrix to give the decoupled, vibrational modes of the molecule<ref>A. Ghysels, V. Van Speybroeck, E. Pauwels, S. Catak, B. R. Brooks, D. Van Neck and M. Waroquier, J. Comput. Chem., 2010, 31, 994–1007./</ref>. A simplified example of the Hessian matrix that is diagonalised is shown below in '''Figure 3''', where <math>K_{ij}</math> represents the force constants with respect to the mass-weighted coordinates.
<br>
<br>
[[File:BT1215 Hessian Matrix.JPG|centre|thumb|799x169px|'''''Figure 3 - A simplified example of the Hessian matrix which is solved to give the vibrational modes''''']]

=== Computational Method ===

In order to compute the potential energy surface and obtain molecular energies, Gaussian uses quantum mechanical calculations based on the Linear Combination of Atomic Orbitals (LCAO) method. As implied by the existence of the PES, the Born-Oppenheimer approximation is used to separate the electron and nuclear timescales, meaning the nuclei are effectively static on an electron timescale and can be manipulated as such. If this approximation was not true then it would be impossible to calculate the PES, since the electronic energies would constantly be affected by nuclear motion. The LCAO method is essentially a sum of atomic orbitals, <math>\phi_i</math>, which combine with a weighting coefficient, <math>c_i</math>, to give the overall molecular orbital wavefunction, <math>\psi_m</math>, shown below in '''Eqn 4''':
<br>
<br>
<div style="text-align: center;"><math>\psi_m = \sum_{i}^N c_i \phi_i</math> '''Eq 4'''</div>
<br>
The number of atomic orbitals used to ''build'' the LCAO is called the '''Basis Set''', which will be discussed further below. The total energy of the molecule is then calculated as a sum of the orbital energies, using the Hamiltonian Operator to solve the Schrödinger equation, where '''Eqn 5''' shows the general form, and '''Eqn 6''' shows the same equation but with the sum of atomic orbitals:
<br>
<br>
<div style="text-align: center;"><math><\psi|\widehat{H}|\psi> = E</math> '''Eq 5'''</div>
<br>
<div style="text-align: center;"><math>\sum_{i}^N \sum_{j}^N<\phi_i|\widehat{H}|\phi_j>c_i c_j = E</math> '''Eq 6'''</div>
<br>
Gaussian represents these equations in matrix form and solves to give the molecular orbital energies, as well as the overall molecule energy. Both the method of calculation and the size of the basis set used to construct the molecular orbital are fundamental factors in determining the accuracy of the computed MOs and energy output, but also in the amount of computational power required. A variety of methods and basis sets can be used to perform optimisations and energy calculations, depending on the computational method chosen. The two methods chosen for all of the following calculations are PM6 and B3LYP (with a 6-31G (d) basis set).

'''PM6''' is a Semi-Empirical method based on the Hartree-Fock method, however it utilises experimental data and/or DFT results (where experimental data is not available) to help speed up the calculation time. Naturally, these assumptions require the system to be modelled by the experimental data used, which may not be an accurate representation. As with the Hartree-Fock method, it also treats electrons as largely independent, and does not account for electron correlation. As a result it represents a rough approximation of the system, although its speed does make it useful for very large systems which would require far too much computational power with a more accurate method. <ref>J. Řezáč, J. Fanfrlík, D. Salahub and P. Hobza, J. Chem. Theory Comput., 2009, 5, 1749–1760.</ref>

'''B3LYP''' is a hybrid method based on both the Hartree-Fock and Density Functional Theory (DFT) techniques. The Hartree-Fock method is employed in the calculation of the exchange-correlation energy, while DFT is used elsewhere due to its improved efficiency. This is because it only depends on a 3-coordinate system describing the electron, and thus scales 3-dimensionally with the number of basis functions, versus the four-dimensional scaling of the Hartree-Fock method. The smaller scaling results in faster computation, though it is still a lot slower than Semi-Empirical methods. A 6-31G (d) Pople basis set used for the B3LYP calculations, where the numbers represent the basis functions used in the calculation. In general terms, a larger basis set corresponds to a more accurate calculation<sup>[4]</sup>.

To localise the transition state in the reaction systems below, three main methods are possible in Gaussian. The first method is adequate when there is previous knowledge surrounding the reaction mechanism, meaning it is possible to guess the transition state structure and then optimise it. Unfortunately this is very difficult to correctly guess, often missing the transition state. The second method has a higher level of accuracy, and involves optimising the reactants, before setting and freezing the distance between the atoms involved in the reaction. Optimisation to a minima is then performed, followed by a transition state optimisation. This approach provides Gaussian with more information surrounding the reaction pathway, and thus helps guide the optimisation to the correct result. This method was used for Exercise 1.

For Exercises 2, 3, and 4, a third, more complex method was chosen. This involves optimising the product, before breaking the bonds that are formed in the reaction. The distance between the atoms that form these bonds is set and frozen at a specific distance that resembles the transition state. The same calculations as in the second method are then used to identify and optimise the transition state structure. This method is the longest, but is also the most reliable, which was the main reason for its use in more complicated reaction systems.

== Exercise 1: Diels-Alder Reaction of Butadiene + Ethylene - PM6 Level ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) very good job overall, just a little hiccup on the bond length discussion.)

=== Reaction Overview ===
Butadiene and ethylene can react to form cyclohexene, shown below in '''Scheme 1'''. The reaction occurs via a type of [4+2] cycloaddition, commonly known as a Diels-Alder reaction, through a concerted syn addition<ref>K. N. Houk, Y. T. Lin and F. K. Brown, J. Am. Chem. Soc., 1986, 108, 554–556.</ref>. In the case of butadiene and ethylene, since butadiene (the diene) is more electron rich than ethylene (the dienophile), the reaction represents a ''normal electron demand'' Diels-Alder cycloaddition.

[[File:BT1215 Diels-Alder RS Butadiene Ethylene.jpg|centre|thumb|757x757px|'''''Scheme 1 - Diels-Alder reaction between butadiene and ethylene''''']]

=== Molecular Orbital Discussion ===
The frontier molecular orbital (MO) diagram for the reaction between butadiene and ethylene is shown below in '''Figure 1''', and was generated using the calculated Gaussian energies of the transition state and reactants. The transition state and reactants were used in the MO diagram for clarity, since conformational changes and significant orbital mixing in the product make the connection more complicated. As a result, the energies computed for the overlapping MOs are significantly higher than those of the optimised product, especially since the transition state represents a strained conformation. It is also important to note that these energies can only be considered relative to each other due to the inaccuracy of the PM6 optimisation method.

[[File:BT1215 Diels-Alder TS Butadiene Ethylene Y3TS.jpg|centre|thumb|783x783px|'''''Figure 4 - MO diagram showing frontier orbital interactions in the Diels-Alder reaction between butadiene and ethylene.''''']]

Interactive JMOLs of the two starting materials, as well as the orbitals involved in the bonding interaction can be seen below in '''Table 1''', labelled with both their number, computed energy and occupancy. It is possible to toggle through the generated frontier MOs using the drop down box. Please note that they may not appear to work correctly until after all of the Jmols on the page have loaded.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 1 - Frontier orbitals in the Diels-Alder Reaction between butadiene + ethylene'''''
!Reactant Orbitals
!Transition State Orbitals
!Product Orbitals
|-
|<jmol>
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<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 SPE REACT PM6.LOG </uploadedFileContents>
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<target>ButadieneEthyleneR</target>
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<item>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_BEDIELSALDER_ORB_COMB_REACT_TS_PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneDielsAlder</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneDielsAlder</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneDielsAlder</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 PROD CYCLOHEXENE OPT PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneP</target>
</item>
</jmolmenu>
</jmol>
|}

Orbitals can form stabilising overlap interactions when their associated overlap integral is '''''non-zero'''''. The integral is a quantitative representation of the spatial overlap of the orbitals, and thus an integral equal to 0 is equivalent to '''''no''''' spatial overlap. In order for the overlap integral to be non-zero, the overall integral of the interacting orbital wavefunctions must be a symmetric function. As a result, only orbitals which are '''''both''''' symmetric (S × S = S) or '''''both''''' antisymmetric (AS × AS = S) result in a non-zero overlap integral that allows for a stabilising orbital overlap. Interaction between a symmetric and antisymmetric orbital would lead to an overall antisymmetric function (S × AS = AS) and an integral equal to 0 (representing no interaction). <sup>[4]</sup> This can also be seen in the MO diagram above, where only orbitals of the same symmetry interact in the Diels-Alder reaction.

=== Bond Length Discussion ===
Diels-Alder reactions involve the creation of two new σ-bonds between the diene and dienophile, while three π-bonds are lost and another one is created to complete the cycloaddition. The curly-arrow mechanism for the cycloaddition between butadiene and ethylene is shown below in '''Figure 5''', where each carbon has been numbered so as to allow for the discussion of how each bond length changes throughout the course of the reaction.

[[File:BT1215_Diels-Alder_Curly_Arrows.jpg|centre|thumb|584x129px|'''''Figure 5 - Currly arrow mechanism for the Diels-Alder Reaction between Butadiene + Ethylene''''']]

The changes in bond lengths with the reaction coordinate are shown below in '''Graph 1''', and were extracted from the PM6 optimised IRC reaction pathway. The typical values for bond lengths between two sp<sup>3</sup> hybridised carbon atoms, two sp<sup>2</sup> carbon atoms (both single and double bonds), and sp<sup>3</sup> and sp<sup>2</sup> carbon atoms is shown in '''Table 2''', where all values were obtained from the CRC Handbook of Chemistry and Physics<ref>D. R. Lide, CRC Handbook of Chemistry and Physics, 2003, 53, 2616.</ref>. The calculated bond lengths for the PM6 optimised reactants, products, and transition state can be seen in '''Table 3'''. While there are several slightly distinct values for the van der waals radius of a carbon atom, the overall consensus corresponds to a value of 1.70 Å<ref>1 S. S. Batsanov, Inorg. Mater., 2001, 37, 871–885.</ref>.

[[File:BT1215 Exercise 1 C-C Bond Length Change IRC.jpg|thumb|650x650px|'''''Graph 1 - Change of bond lengths with the reaction coordinate in the Diels-Alder reaction between butadiene and ethylene'''''|left]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 2 - Typical C-C bond lengths'''''
!Bond Type
!Bond Length (Å)
|-
|C-C (sp<sup>3</sup>-sp<sup>3</sup>)
|1.530
|-
|C-C (sp<sup>2</sup>-sp<sup>2</sup>)
|1.460
|-
|C=C (sp<sup>2</sup>-sp<sup>2</sup>)
|1.316
|-
|C-C (sp<sup>3</sup>-sp<sup>2</sup>)
|1.503
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 3 - Optimised bond length values (PM6)'''''
!
! colspan="3" |Bond Length (Å)
|-
!Bond
!Reactants
!Transition State
!Products
|-
|C<sup>1</sup>-C<sup>2</sup>
|1.327
|1.382
|1.541
|-
|C<sup>2</sup>-C<sup>3</sup>
|3.413*
|2.115
|1.540
|-
|C<sup>3</sup>-C<sup>4</sup>
|1.335
|1.380
|1.501
|-
|C<sup>4</sup>-C<sup>5</sup>
|1.468
|1.411
|1.338
|-
|C<sup>5</sup>-C<sup>6</sup>
|1.335
|1.380
|1.501
|-
|C<sup>6</sup>-C<sup>1</sup>
|3.414*
|2.115
|1.540
|}

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) The Van der Waals radius is indeed 1.7A, but for each carbon, meaning the two atoms can be considered to be interacting as soon as their bond length becomes smaller than 2 x 1.7 i.e. 3.4. Incidentally, this is why the "infinite" distance for two carbons is set to be 3.414.)

It is important to note for the reactant values marked with an asterisk that as C<sup>2</sup>-C<sup>3</sup> and C<sup>6</sup>-C<sup>1</sup> are bonds formed during the reaction, the bond length can essentially be assumed as infinite, since there is no interaction between the carbon atoms. The same bonds in the transition state have a length of 2.115 Å, which is significantly larger than the van der waal radius for carbon atoms, suggesting a very weak interaction that still does not have a significant bonding character. In the products these bonds represent C-C (sp<sup>3</sup>-sp<sup>3</sup>) bonds, however the optimised value of 1.540 Å shows significant deviation to the typical bond value of 1.530 Å. Comparison with experimentally determined bond lengths of cyclohexene showed reasonable agreement with literature values<ref>V. A. Naumov, V. G. Dashevskii and N. M. Zaripov, J. Struct. Chem., 1971, 11, 736–742.</ref>, highlighting the limitation that treating bonds individually from a valence bond theory perspective does not take into account complex orbital interactions that can affect bond length.

C<sup>3</sup>-C<sup>4</sup> and C<sup>5</sup>-C<sup>6</sup> represent the sp<sup>2</sup>-sp<sup>2</sup> double bonds of butadiene in the reactants, while C<sup>4</sup>-C<sup>5</sup> represents the sp<sup>2</sup>-sp<sup>2</sup> single bond connecting them. Their deviation from typical bond length values can be explained by delocalisation through the overlapping p-orbitals, which lengthens the double bonds (due to loss of electron density in the stabilised bonding orbitals) and shortens the single bond (as it gains partial double bond character). Throughout the reaction, the two double bonds lengthen to form sp<sup>3</sup>-sp<sup>2</sup> single bonds, while the single bond shortens to become a sp<sup>2</sup>-sp<sup>2</sup> double bond in cyclohexene.

Finally C<sup>1</sup>-C<sup>2</sup> represents the ethylene sp<sup>2</sup>-sp<sup>2</sup> double bond in the reactants, which again lengthens to form a sp<sup>3</sup>-sp<sup>3</sup> single bond in the cyclohexene product. Once again, the values obtained all agree strongly with literature values for the cyclohexene product<sup>[10]</sup>.

From the bond length data, the transition state appears to have a structure similar to the reactants. Following on from Hammond's postulate, it can be suggested that this reaction must have an ''early'' transition state, whereby there is little difference in structure and therefore energy between the reactants and transition state, but a large difference between the transition state and products. This suggestion was confirmed by the IRC calculation, which follows the lowest energy pathway to determine the 1D PES, similar to that seen in '''Figure 2'''. The resultant plot, as well as the animated .gif file are shown below in '''Table 4'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 4 - IRC plot and .gif file for the Diels-Alder reaction between Butadiene + Ethylene'''
!IRC Plot
!IRC .gif File
|-
|[[File:BT1215_Butadiene_Ethylene_IRC.png|490x340px]]
|[[File:BT1215_Buteth.gif]]
|}

=== Transition State Vibration Discussion ===
As mentioned before, the Diels-Alder reaction between butadiene and ethylene has been experimentally and theoretically proven through various experimental and theoretical studies, however the '''''concerted''' ''nature of the pathway can also be formed by looking at the vibration which corresponds to the transition state formation. As can be seen below, the vibration shows the key C<sup>1</sup>-C<sup>6</sup> and C<sup>2</sup>-C<sup>3</sup> bonds forming at the same time, hence identifying a synchronous reaction mechanism.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>BT1215_BEDIELSALDER_ORB_COMB_REACT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 17; frank off </script>
<name>VibTSBT1215</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibrate</text>
<target>VibTSBT1215</target>
</jmolbutton>
</jmol>

=== Output Calculation Files ===

SM: [[File:BT1215 CIS BUTADIENE OPT PM6.LOG]]
<br>
IRC: [[File:BT1215 COMB REACT IRC PM6.LOG]]
<br>
PRETS OPT: [[File:BT1215 COMB REACT PM6 PRETS OPT.LOG]]
<br>
TS: [[File:BT1215 BEDIELSALDER ORB COMB REACT TS PM6.LOG]]
<br>
SM: [[File:BT1215 ETHYLENE OPT PM6.LOG]]
<br>
PROD: [[File:BT1215 PROD CYCLOHEXENE OPT PM6.LOG]]
<br>
SINGLE POINT ENERGY REACT: [[File:BT1215 SPE REACT PM6.LOG]]

== Exercise 2: Cyclohexadiene + 1,3-Dioxole - PM6 & B3LYP Level ==

=== Reaction Overview ===
As with Exercise 1, cyclohexadiene and 1,3-dioxole can undergo a [4+2] Diels-Alder cycloaddition reaction, however in this example there are two fundamental points to be aware of. Firstly, by having two disubstituted alkene components, stereoselectivity is introduced whereby the orientation of the alkenes affect the reaction product. The two products formed are denominated endo and exo and are a function of their orientation in the cyclic product. The endo product corresponds to an axially fused ring system (where the extra ring faces downwards), while the exo product represents the equatorial equivalent. For this reaction, the two possible stereoisomers are shown below in '''Scheme 2'''.

[[File:BT1215 Cyclodioxone Reaction Scheme.jpg|centre|thumb|843x418px|'''''Scheme 2 - Reaction scheme showing the stereoselectivity of the Diels-Alder reaction between cyclohexadiene + 1,3-dioxole''''']]

The second key point is that the presence of two electron-donating oxygen atoms adjacent to the dienophile results in an '''''inverse electron demand''''' for the reaction, whereby the electron rich dienophile has a higher energy HOMO and essentially acts as the electron donor. This interacts with the lower energy LUMO of cyclohexadiene to result in an apparent 'reverse' electron flow, and thus generates the HOMO of the transition state. This can be seen qualitatively by comparing the relative reactant MO positions of the normal electron demand reaction above ('''Figure 4''') with those shown below in '''Figure 6 '''and '''Figure 7'''. The comparative energy gap between HOMO-LUMO overlap interactions in both the normal and inverse demand cases was also compared by looking at the computed orbitals in the optimised PM6 structures, and is shown below in '''Table 5'''. As can be seen, the energy gap between the Dienophile HOMO and Diene LUMO is smaller in the Diels-Alder reacton between cyclohexadiene and 1,3-dioxole, leading to the perceived inverse flow. This is confirmed by experimental data with 1,3-dioxole Diels-Alder reactions<ref>M. A. Mckervey, Alicyclic Chemistry, The Chemical Society, 1978.</ref>. The reaction is still thermally allowed following the Woodward-Hoffman rules, since the diene is a (4q+2)<sub>s</sub> component, and there is no (4r)<sub>a</sub> component, thus yielding an odd number which corresponds to a thermal reaction<ref>R. Hoffmann and R. B. Woodward, Acc. Chem. Res., 1968, 1, 17–22.</ref>.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 5 - Comparison of diene and dienophile HOMO-LUMO energy gaps for normal and inverse electron demands'''
!Diels-Alder Reaction
!Diene''' HOMO-Dienophile LUMO Energy gap / Hartrees'''
!Dienophile HOMO-Diene LUMO Energy gap''' / Hartrees'''
!Reaction Type
|-
|Butadiene + Ethylene (PM6)
|'''0.39770'''
|0.39854
|Normal Electron Demand
|-
|Cyclohexadiene + 1,3-Dioxole (PM6)
|0.35354
|'''0.33984'''
|Inverse Electron Demand
|}

It should be noted that the values shown in '''Table 5 '''represent the values obtained from single point energy PM6 calculations, since the B3LYP single point energy optimisations of butadiene + ethylene actually suggest an Inverse Electron Demand reaction. This is likely due to the fact that the butadiene + ethylene case is borderline, making it very difficult to distinguish which pathway the reaction undergoes. In addition, there are several different definitions for normal and inverse electron demand, meaning that while the discussion regarding the HOMO-LUMO gap is still important, it does not always accurately predict the electron demand of the reaction.

Unlike in the previous exercise, the reactants, products, and transition states were all optimised with the more accurate B3LYP method (and 6-31G basis set) after an initial PM6 optimisation, giving a more precise comparison of the orbital interactions in the transition state.

=== Molecular Orbital Discussion ===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very good MO diagrams. Well done!)

The MO diagrams for both the endo and exo transition states are shown below in '''Figure 6''' and '''Figure 7'''. As with the MO diagram in Exercise 1, the occupied orbitals shown for the transition state are significantly destabilised compared to the expected orbitals in the product, since the transition state represents a significantly constrained and therefore high-energy conformation. While the order of the MO interactions is the same in both cases, the relative stability of the orbitals is significantly different for the endo and exo forms. For the frontier HOMO, the endo equivalent is significantly more stable, which can be explained by the involvement of secondary orbital interactions between the two oxygen p-orbitals and the two p-orbitals of the diene which are not directly involved in the diene-dienophile orbital overlap.

[[File:BT1215 cyclodioxone endo MO diagram.jpg|thumb|786x786px|'''''Figure 7 - Frontier MO diagram of the endo stereoisomer in the cyclohexadiene + (1,3)-dioxole Diels-Alder reaction.''''']]
[[File:BT1215 cyclodioxone exo MO diagram.jpg|left|thumb|771x771px|'''''Figure 6 - Frontier MO diagram of the exo stereoisomer in the cyclohexadiene + (1,3)-dioxole Diels-Alder reaction.''''']]

A more thorough discussion of the difference in stabilities is given below in the '''''Energy Discussion''''' section, but secondary orbital interactions can be seen below in the interactive Jmols of the endo orbitals (particularly orbitals 41 and 43). The endo pathway orbitals are shown in '''Table 6''', while those of the exo pathway are given in '''Table 7'''. As before, it is possible to toggle through all of the generated frontier MOs using the drop down box.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 6 - Frontier orbitals in the ENDO Diels-Alder Reaction between cyclohexadiene + 1,3-dioxole'''''
!ENDO Reactant Orbitals
!ENDO Transition State Orbitals
!ENDO Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_SPE_ENDO_OXONE_SM_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCDR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCDR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_OPT_TS_B3LYP_2ND.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCD</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCD</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCD</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCD</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_PROD_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCDP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCDP</target>
</item>
</jmolmenu>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 7 - Frontier orbitals in the EXO Diels-Alder Reaction between cyclohexadiene + 1,3-dioxole'''''
!EXO Reactant Orbitals
!EXO Transition State Orbitals
!EXO Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_SPE_EXO_OXONE_SM_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCDR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCDR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_OPT_TS_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCD</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCD</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCD</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCD</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_PROD_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 14; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCDP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 14; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCDP</target>
</item>
</jmolmenu>
</jmol>
|}

=== Energy Discussion ===
The thermochemical data for the activation and reaction energy of both the endo and exo pathway is given below in '''Table 8''', while the reaction profile is shown below in '''Figure 8'''. As can be seen, the endo reaction represents not only the kinetic product for the reaction (by having a lower activation energy) but also the thermodynamic product, as it has a lower energy than the exo form. The reactant, product, and transition state energies are given in Hartrees in '''Table 9''' for comparison. The reactant energies were summed from separate optimisations to ensure there was no interaction between the two that would affect the computed energy.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 8 - Thermochemical data for both stereochemical routes in the cyclohexadiene + 1,3-dioxole Diels-Alder reaction'''
!Reaction Pathway
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|'''Exo Pathway'''
|0.063853
|167.65
|<nowiki>-0.024302</nowiki>
|<nowiki>-63.81</nowiki>
|-
|'''Endo Pathway'''
|0.060871
|159.82
|<nowiki>-0.025671</nowiki>
|<nowiki>-67.40</nowiki>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 9 - Reactant, transition state, and product energies for the 1,3-dioxole + cyclohexadiene Diels-Alder reaction'''
!Reaction Pathway
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|'''Exo Pathway'''
|<nowiki>-500.393020</nowiki>
|<nowiki>-500.329167</nowiki>
|<nowiki>-500.417322</nowiki>
|-
|'''Endo Pathway'''
|<nowiki>-500.393020</nowiki>
|<nowiki>-500.332149</nowiki>
|<nowiki>-500.418691</nowiki>
|}
[[File:BT1215 cyclodioxone reaction pathway diagram.jpg|centre|thumb|499x499px|'''''Figure 8 - Reaction coordinate of the cyclohexadiene + 1,3-dioxole Diels-Alder reaction showing the activation and reaction energies for both the endo and exo stereoisomers''''']]
Generally, for alkenes containing substituents that are able to form secondary orbital interactions, the endo product is formed under kinetic control due to a lower energy transition state and therefore a lower activation energy. As mentioned before, these secondary orbital interactions consist of the involvement of the oxygen p-orbitals in the 1,3-dioxole ring which form constructive, symmetry allowed overlaps with the cyclohexadiene frontier orbitals. This increase in overlap leads to a greater stabilisation of the HOMO in the product and transition state, thus also lowering the overall energy of both. These interactions are 'secondary' as their contribution to the bonding is not essential for the reaction to occur, however their impact is significant in determining the stereochemistry of the product. The key secondary orbital interaction between oxygen and cyclohexadiene is shown below in '''Figure 9''', while an interactive Jmol of the endo transition state HOMO with a higher isovalue is shown below to highlight the interaction.
[[File:BT1215 Stabilising Orbital Interaction dioxone.jpg|centre|thumb|735x735px|'''''Figure 9 - Stabilising secondary orbital interactions observed in the endo conformer of the 1,3-dioxole + cyclohexadiene Diels-Alder reaction ''''']]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
!ENDO TS HOMO Showing Secondary Orbital Interactions
!EXO TS HOMO (No Secondary Interaction)
|-
|<jmol>
<jmolApplet>
<size>500</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_OPT_TS_B3LYP_2ND.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat "" rotate x -20; frank off</script>
<name>EndoDielsAlderCDO</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDO</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDO</target>
</jmolbutton>
</jmol>
|<jmol>
<jmolApplet>
<size>500</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_OPT_TS_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 20; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat "" rotate x -20; frank off</script>
<name>ExoDielsAlderCDO</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDO</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDO</target>
</jmolbutton>
</jmol>
|}

While secondary orbital interactions are important in determining kinetic control, the endo stereosiomer may not be the thermodynamic product if there is a significant steric clash. In this case, the endo form is actually also thermodynamically more stable than the exo form, due to fewer steric interactions between the bridge of the cyclohexene ring and the -CH<sub>2</sub> group in the 1,3-dioxole ring. A comparison of the steric interactions is shown below in '''Figure 10'''.
[[File:BT1215 Steric Clash Dioxone Diels-Alder.jpg|centre|thumb|649x649px|'''''Figure 10 - Steric clash observed in both stereoisomer products of the Diels-Alder reaction''''']]

=== Output Calculation Files ===

SM: [[File:BT1215 CYCLOHEXADIENE OPT PM6.LOG]]
<br>
SM: [[File:BT1215 CYCLOHEXADIENE OPT B3LYP 2.LOG]]
<br>
SM: [[File:BT1215 DIOXONE OPT PM6.LOG]]
<br>
SM: [[File:BT1215 DIOXONE OPT B3LYP.LOG]]
<br>
ENDO IRC: [[File:BT1215 ENDO OXONE IRC PM6.LOG]]
<br>
ENDO PRETS OPT: [[File:BT1215 ENDO OXONE PREOPT TS PM6.LOG]]
<br>
ENDO TS: [[File:BT1215 ENDO OXONE OPT TS B3LYP 2ND.LOG]]
<br>
ENDO PROD: [[File:BT1215 ENDO OXONE PROD OPT PM6.LOG]]
<br>
ENDO PROD: [[File:BT1215 ENDO OXONE PROD OPT B3LYP.LOG]]
<br>
ENDO SINGLE POINT ENERGY REACT: [[File:BT1215_SPE_ENDO_OXONE_SM.LOG]]
<br>
EXO IRC: [[File:BT1215 EXO OXONE IRC PM6.LOG]]
<br>
EXO PRETS OPT: [[File:BT1215 EXO OXONE PREOPT TS PM6.LOG]]
<br>
EXO TS: [[File:BT1215 EXO OXONE OPT TS B3LYP.LOG]]
<br>
EXO PROD: [[File:BT1215 EXO OXONE PROD OPT PM6.LOG]]
<br>
EXO PROD: [[File:BT1215 EXO OXONE PROD OPT B3LYP.LOG]]
<br>
EXO SINGLE POINT ENERGY REACT: [[File:BT1215 EXO OXONE SM OPT PM6.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic Reactions (Xylylene + SO<sub>2</sub>) - PM6 Level ==

=== Reaction Overview ===
The reaction of xylylene with SO<sub>2</sub> is of particular interest, since the involvement of an electron-rich atom such as sulphur, which can easily become hypervalent, allows for new pericyclic reactions. As before, a [4+2] Diels-Alder cycloaddition an occur between the two exocyclic double bonds and the S=O double bond to give two fused six-membered rings with an either endo or exo stereoselectivity. Alternatively, it is possible for the sulphur atom alone to react with the exocyclic diene to give a 5-membered ring fused to the aromatic phenyl ring, in what is called a cheletropic reaction. The reaction with xylylene also introduces an interesting regioselectivity discussion; as well as the cheletropic reaction, a second endocyclic cis-diene is available to react with the SO<sub>2</sub> to yield alternative products. This pathway is highly disfavoured compared to the exocyclic Diels-Alder, the reasons of which are explained in the '''''Energy Discussion Section'''''. All of the discussed reaction routes are shown below in '''Scheme 3'''

[[File:BT1215 Chele vs Diels Alder React Scheme.jpg|centre|thumb|800x418px|'''''Scheme 3 - Reaction scheme showing all of the Diels-Alder and cheletropic reactions between Xylylene + SO<sub>2</sub>''''']]

=== Energy Discussion ===
As for '''<u>Exercise 2</u>''', the activation and reaction energies for all of the possible routes are given below in '''Table 10''', while a visual representation of the reaction profile can be seen below in '''Figure 11'''. For comparison, the reactant, transition state, and product energies are given in Hartrees below in '''Table 11'''.

Comparing the activation energies, the endo pathway of the exocyclic Diels-Alder reaction appears to be the kinetic product of the reaction, since it has the lowest energy transition state compared to the reactants. The thermodynamic product for the reaction is clearly the '''cheletropic''' product, since it is significantly more stable than any of the Diels-Alder reaction products. This is in agreement with literature results<ref>D. Suárez, T. L. Sordo and J. A. Sordo, J. Org. Chem., 1995, 60, 2848–2852.</ref>, and is likely due to the fact that the cheletropic transition state suffers a higher level of ring strain due to the formation of a 5-membered fused ring, compared to the 6-membered ring formed in the Diels-Alder reactions, which makes the Diels-Alder route kinetically faster. Conversely, the retention of the highly stable S=O bond in the cheletropic product makes this the thermodynamic product. Indeed, as a result of this, the cheletropic product is significantly more accessible experimentally when compared to the reversible Diels-Alder routes. Both the exocyclic Diels-Alder reactions and the cheletropic reaction are all thermodynamically stable compared to the reactants, and can be explained by the formation of the highly stabilised aromatic phenyl ring which lowers the product energy.

In comparison, xylylene is destabilised as it does not possess any aromaticity. The same discussion can be applied to the unfavourable, high-energy endocyclic Diels-Alder reactions; their significantly higher activation barriers and reaction energies compared to the other routes can be explained by the fact there is no aromatic ring in the products, which are also destabilised compared to the reactants due to the creation of a strained bi-fused ring system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 10 - Thermochemical data for all possible reactions between xylylene and SO<sub>2</sub>'''
!Reaction Pathway
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|Cheletropic
|0.040671
|106.78
|<nowiki>-0.058385</nowiki>
|<nowiki>-153.29</nowiki>
|-
|'''Exo'''cyclic '''Exo '''Diels-Alder
|0.033694
|88.46
|<nowiki>-0.036928</nowiki>
|<nowiki>-96.95</nowiki>
|-
|'''Exo'''cyclic '''Endo '''Diels-Alder
|0.032177
|84.48
|<nowiki>-0.036685</nowiki>
|<nowiki>-96.32</nowiki>
|-
|'''Endo'''cyclic '''Exo '''Diels-Alder
|0.046672
|122.54
|0.008922
|23.42
|-
|'''Endo'''cyclic '''Endo '''Diels-Alder
|0.043687
|114.70
|0.007226
|18.97
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 11 - Reactant, transition state, and product energies for all possible reactions between xylylene + SO<sub>2</sub>'''
!Reaction Pathway
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|Cheletropic
|0.058383
|0.099054
|<nowiki>-0.000002</nowiki>
|-
|'''Exo'''cyclic '''Exo '''Diels-Alder
|0.058383
|0.092077
|0.021455
|-
|'''Exo'''cyclic '''Endo '''Diels-Alder
|0.058383
|0.090560
|0.021698
|-
|'''Endo'''cyclic '''Exo '''Diels-Alder
|0.058383
|0.105055
|0.067305
|-
|'''Endo'''cyclic '''Endo '''Diels-Alder
|0.058383
|0.102070
|0.065609
|}
[[File:BT1215 Exercise 3 Reaction Diagram.jpg|centre|thumb|869x869px|'''''Figure 11 - Reaction profile for the key cycloadditions between xylylene + SO<sub>2</sub>''''']]

The .gif files for the IRC calculations of the reaction routes are shown below. Please note that they may not play smoothly until the interactive Jmols above load. A variety of interesting results can be seen from the animations. All of the Diels-Alder reactions occur via an asynchronous bond formation, where the C-O bond forms before the C-S bond. This could be due to the fact that the smaller, more electron dense oxygen atom can get closer to the xylylene ring to form the C-O bond more quickly than the larger, more diffuse sulphur atom. However, this is merely observational and further calculations would be required to confirm this. In contrast, since only the sulphur atom is involved in the cheletropic reaction, both sigma bonds are formed in a synchronous manner. The IRC plots for all of the reactions are shown below, adjacent to the .gif files. It should be noted that for the Exocyclic Exo route the IRC ran from products to reactants, meaning the reactants are on the right side and the products are on the left side. When compared to the other plots the graph should be reversed.

(Be careful here: you can't use GaussView to decide when precisely a "bond" is formed, as it uses a cutoff distance to decide when to draw a bond [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:15, 4 April 2018 (BST))

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Cheletropic IRC Plot
!Cheletropic IRC .gif
|-
|[[File:BT1215_CheletropicIRC_(2).png|490x370px]]
|[[File:BT1215_Cheletropic.gif]]
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Exocyclic Exo IRC Plot
!Exocyclic Exo IRC .gif
!Exocyclic Endo IRC Plot
!Exocyclic Endo IRC .gif
|-
|[[File:BT1215 Exo Exo DA.png|320x330px]]
|[[File:BT1215 Exo Exo.gif]]
|[[File:BT1215 Exo Endo DA png.png|320x330px]]
|[[File:BT1215_Exo_Endo_DA.gif]]
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Endocyclic Exo IRC Plot
!Endocyclic Exo IRC .gif
!Endocyclic Endo IRC Plot
!Endocyclic Endo IRC .gif
|-
|[[File:BT1215 Endo Exo DA 2.png|320x330px]]
|[[File:BT1215_Endo_Exo.gif]]
|[[File:BT1215 Endo Endo DA 2.png|320x330px]]
|[[File:BT1215_Endo_Endo.gif]]
|}

=== Output Calculation Files ===

SM: [[File:BT1215 SO2 SM PM6.LOG]]
<br>
SM: [[File:BT1215 XYLYLENE SM PM6.LOG]]
<br>
CHELO IRC: [[File:BT1215 CHELO XYLYLENE IRC PM6.LOG]]
<br>
CHELO PRETS OPT: [[File:BT1215 CHELO XYLYLENE REDUNDANT OPT.LOG]]
<br>
CHELO TS: [[File:BT1215 CHELO XYLYLENE TS PM6.LOG]]
<br>
CHELO PROD: [[File:BT1215 CHELO XYLYLENE REOPT PM6.LOG]]
<br>
DA EXOCYCLIC ENDO IRC: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE IRC PM6.LOG]]
<br>
DA EXOCYCLIC ENDO PRETS: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE PRETS OPT PM6.LOG]]
<br>
DA EXOCYCLIC ENDO TS: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE TS PM6.LOG]]
<br>
DA EXOCYCLIC ENDO PROD: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE OPT.LOG]]
<br>
DA EXOCYCLIC EXO IRC: [[File:BT1215 DIELS-ALDER XYLYLENE IRC PM6.LOG]]
<br>
DA EXOCYCLIC EXO PRETS: [[File:BT1215 DIELS-ALDER XYLYLENE REDUNDANT OPT.LOG]]
<br>
DA EXOCYCLIC EXO TS: [[File:BT1215 DIELS-ALDER XYLYLENE TS PM6.LOG]]
<br>
DA EXOCYCLIC EXO PROD: [[File:BT1215 DIELS-ALDER XYLYLENE REOPT PM6.LOG]]
<br>
DA ENDOCYCLIC ENDO IRC: [[File:BT1215 HIGH ENERGY IRC.LOG]]
<br>
DA ENDOCYCLIC ENDO PRETS: [[File:BT1215 HIGH ENERGY PREOPT TS PM6 2.LOG]]
<br>
DA ENDOCYCLIC ENDO TS: [[File:BT1215 HIGH ENERGY TS PM6.LOG]]
<br>
DA ENDOCYCLIC ENDO TS: [[File:BT1215 HIGH ENERGY TS CHECK ORB.LOG]]
<br>
DA ENDOCYCLIC ENDO PROD: [[File:BT1215 HIGH ENERGY PRODUCT OPT PM6.LOG]]
<br>
DA ENDOCYCLIC EXO IRC: [[File:BT1215 DA EXO HIGH ENERGY IRC PM6.LOG]]
<br>
DA ENDOCYCLIC EXO PRETS: [[File:BT1215 DA EXO HIGH ENERGY RED OPT PM6.LOG]]
<br>
DA ENDOCYCLIC EXO TS: [[File:BT1215 DA EXO HIGH ENERGY TS PM6.LOG]]
<br>
DA ENDOCYCLIC EXO PROD: [[File:BT1215 DA EXO HIGH ENERGY PROD OPT PM6.LOG]]

== 4π Electrocyclic Reactions: [1,1']-bicyclohexene - PM6 Level ==

=== Reaction Overview ===
The Woodward-Hoffman rules are also essential in predicting the stereochemistry of other pericyclic reactions, including electrocyclic reactions which involve the loss of a π bond and the creation of a σ bond that causes the cyclisation of the molecule. The mechanism for this reaction, shown in '''Scheme 4''', is shown below. For this investigation, [1,1']-bicyclohexene was chosen, with a core diene structure analogous to that of butadiene. This electrocyclic reaction is denoted 4π as 4π electrons are involved in the cyclisation.
<br>
[[File:BT1215 Extension RS 1.jpg|centre|thumb|847x120px|'''''Scheme 4 - Reaction scheme showing the 4π electrocyclic reaction of [1,1']-bicyclohexene''''']]
<br>
The stereoselectivity concerns of this reaction are very important, as shown by the Woodward-Hoffman rules<sup>[13]</sup>, since two possible reactions can occur depending on the conditions that the diene is reacting under. [1,1']-bicyclohexene can cyclise under thermal conditions via a '''''conrotatory''' ''mechanism, shown below in '''Figure 12'''. This is allowed due to the presence of a <sub>π</sub>4<sub>a</sub> orbital component which, when 'pulled together', causes the Hydrogen atoms to rotate in the same direction. An alternative possibility is a '''''disrotatory''''' mechanism with a <sub>π</sub>4<sub>s</sub> orbital component; this is '''thermally disallowed''', but can occur under photochemical conditions to yield a trans-alkene product.
<br>
[[File:BT1215 WH Thermal Vs Photo.jpg|centre|thumb|475x400px|'''''Figure 12 - Symmetry Woodward-Hoffmann rules for both the thermal and photochemical reactions of dienes''''']]
<br>
The full explanation as to whether a reaction is thermally allowed or disallowed can be explained by looking at the frontier orbital overlaps in both a conrotatory and disrotatory mechanism. For simplicity, the orbitals of the analogous butadiene will be used, however the explanation can be directly applied to [1,1']-bicyclohexene. In a conrotatory mechanism, the two terminal symmetry orbitals of butadiene (on the top left of the diagram) shown in '''Figure 12''' can be superimposed using a C2 axis perpendicular to the plane of the screen. For a disrotatory mechanism however, the same orbitals are reflected in a σ symmetry plane that is perpendicular to the screen and runs through the centre of the butadiene. It is important to note that while the symmetry based orbitals often used to describe WH rules cannot be directly compared to the frontier molecular orbitals, the symmetry linking both sets of orbitals remains the same here.

The symmetry of the frontier orbitals of butadiene can then be determined based on these two operators, and a correlation diagram composed to identify which orbitals can overlap in the reaction to make the product. The correlation diagrams for the conrotatory and disrotatory mechanisms are shown below in '''Figure 13'''. As can be seen, the conrotatory mechanism involves the transfer of electrons from the ground state orbitals of the butadiene into the ground state orbitals of the cyclobutene, resulting in a small energy barrier for the reaction. In contrast, the disrotatory mechanism requires the excitation of electrons into an excited state antibonding orbital, giving it a much larger energy barrier and making the reaction thermally disallowed.

'''While this provides an elegant way of explaining the WH rules, it must be stated that it ''cannot'' provide significant insight into the structure of the product orbital, since the reaction proceeds via a 4n Mobius transition state and this allows all of the orbitals to rotate and switch symmetry. The actual frontier orbitals can be seen below in the MO/Energy Discussion'''.
<br>
[[File:BT1215 Extension FO Symmetry.jpg|centre|thumb|1458x415px|'''''Figure 13 - Frontier orbital symmetry of butadiene for conrotatory & disrotatory mechanisms''''']]
<br>

(Good intro, and you have labelled your symmetry axis [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:04, 4 April 2018 (BST))

=== MO/Energy Discussion ===

In this discussion, the thermally allowed pathway will be focused on due to time limitations that meant that the full calculation of the photochemical route could not be performed. All optimisations were performed at the PM6 level, with the key MOs for the reactant, transition state, and product, given below in '''Table 12'''. As can be seen, MO 32 of the product is different to the WH predicted frontier orbital. The expected bonding interaction appears as part of MO 31, along with a more complicated bonding interaction from the alkene of the cyclobutene that appears to be the same symmetry. This is likely a consequence of reacting through a twisted Mobius transition state. It is recommended that further calculations be performed with a more accurate method to confirm the orbital ordering. The rest of the orbitals are as expected in the '''Reaction Overview''' section.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 12 - Frontier orbitals in the 4π electrocyclic reaction of [1,1']-bicyclohexene'''''
!Reactant Orbitals
!Transition State Orbitals
!Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 DIENE SM PM6 OPT 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; mo 32; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 22; mo 32; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 33; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 34; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 35; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 DIENE TS OPT PM6 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 32; mo nodots nomesh fill translucent; mo cutoff 0.04; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneT</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneT</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneT</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 8; mo 32; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 33; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 34; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 35; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneT</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 PRODUCT ALKENE PM6 OPT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 48; mo 31; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 22; mo 31; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 31</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 32; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 33; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 34; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 35; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneP</target>
</item>
</jmolmenu>
</jmol>
|}

The thermochemical data for the reaction is shown below in '''Table 13''', while the energies of the reactant, transition state, and product are given in '''Table 14'''. The computed energies reveal that the starting diene is more stable, and therefore the predominant form. This is likely due to the high levels of ring strain in the cyclobutene ring destabilising the product. Kinetically this reaction is also highly unfavourable, with a much higher activation energy than the previous reaction systems discussed. It is possible that the complexity of the cyclohexene rings means a large amount of bond rearrangement is required in order to form the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 13 - Thermochemical data for the 4π electrocyclic reaction of [1,1']-bicyclohexene'''
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|0.104375
|274.04
|0.028329
|74.3777952
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 14 - Reactant, transition state, and product energies for the electrocyclic reaction of [1,1']-bicyclohexene'''
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|0.199543
|0.303918
|0.227872
|}

An IRC calculation was performed and both the plot and .gif file are shown below. As before, the reaction was computed from products to reactants in the IRC, so the graph should appear reversed. It is also important to note that in the IRC calculation the reactant energy appears to be higher energy than the product, likely due to it converging to a metastable minima where the diene is planar, and not the most stable form of the reactants.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!IRC Plot
!IRC .gif File
|-
|[[File:BT1215 Diene Extension.png|490x375px]]
|[[File:BT1215 Ext Diene.gif]]
|}

Finally, the imaginary vibration corresponding to the transition state can be seen below. As suggested by the vibration and the IRC, the bond formation in the electrocyclic reaction appears to be synchronous, with the hydrogen atoms rotating in a concerted manner.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>BT1215 DIENE TS OPT PM6 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 9; frank off </script>
<name>VibTS2BT1215</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibrate</text>
<target>VibTS2BT1215</target>
</jmolbutton>
</jmol>

=== Output Calculation Files ===

SM: [[File:BT1215 DIENE SM PM6 OPT 2.LOG]]
<br>
IRC: [[File:BT1215 DIENE IRC PM6.LOG]]
<br>
PRETS OPT: [[File:BT1215 DIENE TS PREOPT PM6 2.LOG]]
<br>
TS: [[File:BT1215 DIENE TS OPT PM6 2.LOG]]
<br>
PROD: [[File:BT1215 PRODUCT ALKENE PM6 OPT.LOG]]
<br>

== Conclusion ==
Computational analysis of 4 different pericyclic systems was performed with a large degree of success, both with the Semi-Empirical PM6 and DFT B3LYP methods. In all cases, it was possible to model and correctly predict experimentally determined reaction mechanisms and transition states. The use of Gaussian was also able to provide insight into the change in bond lengths throughout the reaction, the type of transition state, the electron demand of the reaction, and which routes represent the thermodynamic or kinetic product. The computation of molecular orbitals was crucial in justifying the observed stereoselectivities, providing an elegant visual representation of secondary orbital interactions, as well as other factors affecting product formation. Unfortunately, the complexity of the calculations, along with time constraints, meant that the majority of reaction systems could only be optimised using the PM6 method, and so can only yield qualitative results due to the limitations discussed in the introduction. Conclusions for the individual exercises were as follows:

*<u>Exercise 1 - PM6</u> - The Diels-Alder reaction of butadiene + ethylene was modelled and shown to occur via a synchronous 4+2 cycloaddition, with a normal electron demand for the reaction. The transition state was correctly identified and confirmed by the presence of a single imaginary vibration frequency, corresponding to product formation, and an IRC calculation was performed to determine an early transition state. This was also confirmed by modelling the change in bond lengths throughout the course of the reaction, showing a transition state structure close to that of the reactants. Despite the inaccuracies of the PM6 method, bond lengths were in reasonable agreement with the literature.

*<u>Exercise 2 - PM6 & B3LYP</u> - The stereoselectivity of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole was investigated in order to determine whether the endo or exo product represented kinetic and/or thermodynamic control. All structures were optimised first with the PM6 method, before being reoptimised with the B3LYP method in order to give a more accurate depiction of the reaction system and its energies. Relative HOMO-LUMO energy gaps were compared with butadiene + ethylene to determine an inverse electron demand reaction, caused by the electron rich atoms on the dienophile. An MO diagram was constructed, and the kinetic stability of the endo product was explained by the involvement of oxygen p-orbitals in secondary orbital interactions that help to stabilise the transition state. The endo product was also determined to be the thermodynamic product due to the absence of steric clash between the bridged ring and the 1,3-dioxole group.

*<u>Exercise 3 - PM6</u> - The relative stabilities of five different pericyclic routes for the reaction between Xylylene + SO<sub>2</sub> were probed. Optimisations of reactants, products, and transition states were all carried out with the PM6 method. The cheletropic reaction yielded the thermodynamic product via a synchronous bond formation, likely due to the preservation of both S=O bonds. The exocyclic endo Diels-Alder reaction, occurring through asynchronous bond formation, represented kinetic control, due to the fact that the transition state contains a 6-membered fused ring compared to the relatively strained 5-membered cheletropic transition state. An alternative, endocyclic Diels-Alder reaction was investigated and shown to be highly disfavoured due to the fact that no aromatic ring was formed in the product, and the resultant fused ring product had large steric interactions making it thermodynamically unstable compared to the reactants.

*<u>Exercise 4 - PM6</u> - The thermally allowed, conrotatory 4π electrocyclic reaction of [1,1']-bicylcohexene was investigated, with all optimisations taking place at the PM6 level. The reaction was determined to proceed via a 4n Mobius transition state, which could explain discrepancies between the predicted orbital overlap using orbital symmetry and the observed product orbitals. An IRC calculation was performed and showed a concerted bond formation, while the imaginary transition state frequency observed for the transition state also suggested a concerted, conrotatory mechanism. Due to time constraints, the photochemical disrotatory reaction could not be calculated.

Further work could be explored not only in the computation of the photochemical reaction route in Exercise 4, but also by further modelling more obscure pericyclic reaction routes, similar to computational research performed by W. Grimme et al into cheletropic ene reactions<ref>W. Grimme, M. W. Harter, C. A. Sklorz, J. Chem. Soc., Perkin Trans. 2, 1999, 9.</ref>. Alternatively, higher level calculations could be performed to further understand more complex systems, such as ''ab initio'' calculations by F. Monnatt et al into the cheletropic and hetero Diels-Alder additions of SO<sub>2</sub> to (E)-Methoxybutadiene.<ref>F. Monnat, P. Vogel, V. M. Rayón and J. A. Sordo, J. Org. Chem., 2002, 67, 1882–1889.</ref>

== References ==

Rep:BT1215 CP3MD Lab

2018-04-07T09:56:47Z

Fv611: /* Exercise 1: Diels-Alder Reaction of Butadiene + Ethylene - PM6 Level */

== Introduction ==
The ability to model reactions using computational simulations is something of great interest, particularly with regard to understanding experimental mechanisms or molecular properties<ref>R. Breslow et. al., Beyond the Molecular Frontier: Challenges for Chemistry and Chemical Engineering, National Research Council, 2003.</ref>. Modern computational software, such as Gaussian, is able to use a series of quantum mechanical calculations to optimise a reaction system and determine a lowest energy reaction pathway, as well as the predicted energies and structures of any reactants, transition states, and products involved. Within these calculations, there are two important theoretical considerations to take into account:

''1. Potential Energy Surface (PES)'' - The potential energy of a system given as a function of molecular geometry. By changing the molecular geometry (e.g. bond lengths during a reaction), the change in energy and transition state can be computed.

''2. Computational Method'' - Defines the approximations made within the quantum mechanics, balancing accuracy (fewer approximations lead to more precise results) with computational cost (fewer assumptions mean more resource-intensive calculations).

=== Potential Energy Surface (PES) ===
[[File:BT1215 PES Example.JPG|right|thumb|210x205px|'''''Figure 1 - An example PES surface, AB<sup>+</sup> and A<sup>+</sup> + B represent local minima, which are separated by a labelled saddle point<ref>L. Sleno and D. A. Volmer, J. Mass Spectrom., 2004, 39, 1091–1112.</ref>.''''']]
As mentioned before, the PES is a representation of the relationship between the potential energy of a system and its molecular geometry. Given that non-linear molecules have a geometrical freedom of 3N-6 modes (or 3N-5 for linear molecules), where N = the number of atoms in the molecule, the PES therefore has the same dependency, relying on the internal coordinates of the atoms in the system. In order to model a reaction PES, the number of degrees of freedom that are varied is often reduced in order to make the calculation computationally feasible. When plotted graphically, the PES represents a landscape of high and low energy configurations that correspond to turning or stationary points on the surface, with an example plot shown in '''Figure 1'''<sup>[2]</sup>. Low energy turning points correspond to an energetically stable molecular geometry, which are mathematically characterised by having a first derivative equal to 0 ('''Eq 1'''), and a positive second derivative ('''Eq 2'''), where <math>{V}</math> is potential energy and <math>{x}</math> represents an atomic or reaction coordinate:
<br>
<br>
<div style="text-align: center;"><math>\frac{\partial V}{\partial x}= 0 </math> '''Eq 1'''</div>
<br>
<div style="text-align: center;"><math>\frac{\partial^{2} V}{\partial x^{^{2}}}> 0</math> '''Eq 2'''</div>
<br>
[[File:BT1215 2D PES to TS Example.gif|right|thumb|313x553px|'''''Figure 2 - A PES diagram of ozone which has been mapped to an IRC along a reaction coordinate, showing the transition state, reactants and products<ref>1 E. G. Lewars, in Computational Chemistry, 2011, vol. 26, pp. 9–43.</ref>.''''']]
The potential energy well surrounding the minimum can be modelled as a Simple Harmonic Oscillator, where the lowest energy point is described by a Taylor expansion. Assuming a harmonic motion modelled by Hooke's law, force constant <math>{k}</math> can be equated to the second derivative in '''Eq 2'''. Since the vibrational wavenumber, <math>{v}</math>, is directly proportional to <math>\sqrt{k}</math>, it can therefore be seen that the molecular configurations corresponding to minimum turning points will '''''only''''' have positive vibrations<ref>P. Atkins and J. De Paula, Atkins’ physical chemistry, 2009.</ref>.

The transition state of a reaction corresponds to a saddle point which separates two local minima in the PES, and is essentially a maximum turning point along a particular reaction coordinate of the surface. This can be modelled as a barrier separating two wells, shown in '''Figure 2'''<sup>[2]</sup>. An activation energy is required to overcome this transition state and thus interconvert between the two wells, often denoted reactants and products. The saddle point on the PES surface can be mathematically described as being a local minimum in all directions except for one, where it is equivalent to a maximum turning point. This leads to one reaction coordinate where the second derivative of potential energy is '''negative'''. Following the same key discussion above, '''''one negative vibration frequency will be observed in the transition state''''', while all other frequencies observed will be positive.

It is important to note that, while this discussion of a singular force constant holds true for one-dimentional systems, polyatomic systems require more complicated treatment, since there are multiple force constants and vibrational motions within the system that can actually couple (i.e. one vibration could affect the likelihood of another happening). The general form of these force constants is shown below in '''Eq 3''', where ''i'' and ''j'' represent degrees of freedom (or coordinates) up to 3N-6:
<br>
<br>
<div style="text-align: center;"><math>\frac{\partial^{2} V}{\partial x_i x_j} = k_{ij} </math> '''Eq 3'''</div>

Software such as Gaussian simplifies these complicated raw motions by first converting the internal coordinates into mass-weighted coordinates to make the coupled force constants equally weighted, before creating a large Hessian matrix of all the coupled force constants. The software then diagonalises the Hessian matrix to give the decoupled, vibrational modes of the molecule<ref>A. Ghysels, V. Van Speybroeck, E. Pauwels, S. Catak, B. R. Brooks, D. Van Neck and M. Waroquier, J. Comput. Chem., 2010, 31, 994–1007./</ref>. A simplified example of the Hessian matrix that is diagonalised is shown below in '''Figure 3''', where <math>K_{ij}</math> represents the force constants with respect to the mass-weighted coordinates.
<br>
<br>
[[File:BT1215 Hessian Matrix.JPG|centre|thumb|799x169px|'''''Figure 3 - A simplified example of the Hessian matrix which is solved to give the vibrational modes''''']]

=== Computational Method ===

In order to compute the potential energy surface and obtain molecular energies, Gaussian uses quantum mechanical calculations based on the Linear Combination of Atomic Orbitals (LCAO) method. As implied by the existence of the PES, the Born-Oppenheimer approximation is used to separate the electron and nuclear timescales, meaning the nuclei are effectively static on an electron timescale and can be manipulated as such. If this approximation was not true then it would be impossible to calculate the PES, since the electronic energies would constantly be affected by nuclear motion. The LCAO method is essentially a sum of atomic orbitals, <math>\phi_i</math>, which combine with a weighting coefficient, <math>c_i</math>, to give the overall molecular orbital wavefunction, <math>\psi_m</math>, shown below in '''Eqn 4''':
<br>
<br>
<div style="text-align: center;"><math>\psi_m = \sum_{i}^N c_i \phi_i</math> '''Eq 4'''</div>
<br>
The number of atomic orbitals used to ''build'' the LCAO is called the '''Basis Set''', which will be discussed further below. The total energy of the molecule is then calculated as a sum of the orbital energies, using the Hamiltonian Operator to solve the Schrödinger equation, where '''Eqn 5''' shows the general form, and '''Eqn 6''' shows the same equation but with the sum of atomic orbitals:
<br>
<br>
<div style="text-align: center;"><math><\psi|\widehat{H}|\psi> = E</math> '''Eq 5'''</div>
<br>
<div style="text-align: center;"><math>\sum_{i}^N \sum_{j}^N<\phi_i|\widehat{H}|\phi_j>c_i c_j = E</math> '''Eq 6'''</div>
<br>
Gaussian represents these equations in matrix form and solves to give the molecular orbital energies, as well as the overall molecule energy. Both the method of calculation and the size of the basis set used to construct the molecular orbital are fundamental factors in determining the accuracy of the computed MOs and energy output, but also in the amount of computational power required. A variety of methods and basis sets can be used to perform optimisations and energy calculations, depending on the computational method chosen. The two methods chosen for all of the following calculations are PM6 and B3LYP (with a 6-31G (d) basis set).

'''PM6''' is a Semi-Empirical method based on the Hartree-Fock method, however it utilises experimental data and/or DFT results (where experimental data is not available) to help speed up the calculation time. Naturally, these assumptions require the system to be modelled by the experimental data used, which may not be an accurate representation. As with the Hartree-Fock method, it also treats electrons as largely independent, and does not account for electron correlation. As a result it represents a rough approximation of the system, although its speed does make it useful for very large systems which would require far too much computational power with a more accurate method. <ref>J. Řezáč, J. Fanfrlík, D. Salahub and P. Hobza, J. Chem. Theory Comput., 2009, 5, 1749–1760.</ref>

'''B3LYP''' is a hybrid method based on both the Hartree-Fock and Density Functional Theory (DFT) techniques. The Hartree-Fock method is employed in the calculation of the exchange-correlation energy, while DFT is used elsewhere due to its improved efficiency. This is because it only depends on a 3-coordinate system describing the electron, and thus scales 3-dimensionally with the number of basis functions, versus the four-dimensional scaling of the Hartree-Fock method. The smaller scaling results in faster computation, though it is still a lot slower than Semi-Empirical methods. A 6-31G (d) Pople basis set used for the B3LYP calculations, where the numbers represent the basis functions used in the calculation. In general terms, a larger basis set corresponds to a more accurate calculation<sup>[4]</sup>.

To localise the transition state in the reaction systems below, three main methods are possible in Gaussian. The first method is adequate when there is previous knowledge surrounding the reaction mechanism, meaning it is possible to guess the transition state structure and then optimise it. Unfortunately this is very difficult to correctly guess, often missing the transition state. The second method has a higher level of accuracy, and involves optimising the reactants, before setting and freezing the distance between the atoms involved in the reaction. Optimisation to a minima is then performed, followed by a transition state optimisation. This approach provides Gaussian with more information surrounding the reaction pathway, and thus helps guide the optimisation to the correct result. This method was used for Exercise 1.

For Exercises 2, 3, and 4, a third, more complex method was chosen. This involves optimising the product, before breaking the bonds that are formed in the reaction. The distance between the atoms that form these bonds is set and frozen at a specific distance that resembles the transition state. The same calculations as in the second method are then used to identify and optimise the transition state structure. This method is the longest, but is also the most reliable, which was the main reason for its use in more complicated reaction systems.

== Exercise 1: Diels-Alder Reaction of Butadiene + Ethylene - PM6 Level ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) very good job overall, just a little hiccup on the bond length discussion.)

=== Reaction Overview ===
Butadiene and ethylene can react to form cyclohexene, shown below in '''Scheme 1'''. The reaction occurs via a type of [4+2] cycloaddition, commonly known as a Diels-Alder reaction, through a concerted syn addition<ref>K. N. Houk, Y. T. Lin and F. K. Brown, J. Am. Chem. Soc., 1986, 108, 554–556.</ref>. In the case of butadiene and ethylene, since butadiene (the diene) is more electron rich than ethylene (the dienophile), the reaction represents a ''normal electron demand'' Diels-Alder cycloaddition.

[[File:BT1215 Diels-Alder RS Butadiene Ethylene.jpg|centre|thumb|757x757px|'''''Scheme 1 - Diels-Alder reaction between butadiene and ethylene''''']]

=== Molecular Orbital Discussion ===
The frontier molecular orbital (MO) diagram for the reaction between butadiene and ethylene is shown below in '''Figure 1''', and was generated using the calculated Gaussian energies of the transition state and reactants. The transition state and reactants were used in the MO diagram for clarity, since conformational changes and significant orbital mixing in the product make the connection more complicated. As a result, the energies computed for the overlapping MOs are significantly higher than those of the optimised product, especially since the transition state represents a strained conformation. It is also important to note that these energies can only be considered relative to each other due to the inaccuracy of the PM6 optimisation method.

[[File:BT1215 Diels-Alder TS Butadiene Ethylene Y3TS.jpg|centre|thumb|783x783px|'''''Figure 4 - MO diagram showing frontier orbital interactions in the Diels-Alder reaction between butadiene and ethylene.''''']]

Interactive JMOLs of the two starting materials, as well as the orbitals involved in the bonding interaction can be seen below in '''Table 1''', labelled with both their number, computed energy and occupancy. It is possible to toggle through the generated frontier MOs using the drop down box. Please note that they may not appear to work correctly until after all of the Jmols on the page have loaded.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 1 - Frontier orbitals in the Diels-Alder Reaction between butadiene + ethylene'''''
!Reactant Orbitals
!Transition State Orbitals
!Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 SPE REACT PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_BEDIELSALDER_ORB_COMB_REACT_TS_PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneDielsAlder</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneDielsAlder</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneDielsAlder</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 PROD CYCLOHEXENE OPT PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneP</target>
</item>
</jmolmenu>
</jmol>
|}

Orbitals can form stabilising overlap interactions when their associated overlap integral is '''''non-zero'''''. The integral is a quantitative representation of the spatial overlap of the orbitals, and thus an integral equal to 0 is equivalent to '''''no''''' spatial overlap. In order for the overlap integral to be non-zero, the overall integral of the interacting orbital wavefunctions must be a symmetric function. As a result, only orbitals which are '''''both''''' symmetric (S × S = S) or '''''both''''' antisymmetric (AS × AS = S) result in a non-zero overlap integral that allows for a stabilising orbital overlap. Interaction between a symmetric and antisymmetric orbital would lead to an overall antisymmetric function (S × AS = AS) and an integral equal to 0 (representing no interaction). <sup>[4]</sup> This can also be seen in the MO diagram above, where only orbitals of the same symmetry interact in the Diels-Alder reaction.

=== Bond Length Discussion ===
Diels-Alder reactions involve the creation of two new σ-bonds between the diene and dienophile, while three π-bonds are lost and another one is created to complete the cycloaddition. The curly-arrow mechanism for the cycloaddition between butadiene and ethylene is shown below in '''Figure 5''', where each carbon has been numbered so as to allow for the discussion of how each bond length changes throughout the course of the reaction.

[[File:BT1215_Diels-Alder_Curly_Arrows.jpg|centre|thumb|584x129px|'''''Figure 5 - Currly arrow mechanism for the Diels-Alder Reaction between Butadiene + Ethylene''''']]

The changes in bond lengths with the reaction coordinate are shown below in '''Graph 1''', and were extracted from the PM6 optimised IRC reaction pathway. The typical values for bond lengths between two sp<sup>3</sup> hybridised carbon atoms, two sp<sup>2</sup> carbon atoms (both single and double bonds), and sp<sup>3</sup> and sp<sup>2</sup> carbon atoms is shown in '''Table 2''', where all values were obtained from the CRC Handbook of Chemistry and Physics<ref>D. R. Lide, CRC Handbook of Chemistry and Physics, 2003, 53, 2616.</ref>. The calculated bond lengths for the PM6 optimised reactants, products, and transition state can be seen in '''Table 3'''. While there are several slightly distinct values for the van der waals radius of a carbon atom, the overall consensus corresponds to a value of 1.70 Å<ref>1 S. S. Batsanov, Inorg. Mater., 2001, 37, 871–885.</ref>.

[[File:BT1215 Exercise 1 C-C Bond Length Change IRC.jpg|thumb|650x650px|'''''Graph 1 - Change of bond lengths with the reaction coordinate in the Diels-Alder reaction between butadiene and ethylene'''''|left]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 2 - Typical C-C bond lengths'''''
!Bond Type
!Bond Length (Å)
|-
|C-C (sp<sup>3</sup>-sp<sup>3</sup>)
|1.530
|-
|C-C (sp<sup>2</sup>-sp<sup>2</sup>)
|1.460
|-
|C=C (sp<sup>2</sup>-sp<sup>2</sup>)
|1.316
|-
|C-C (sp<sup>3</sup>-sp<sup>2</sup>)
|1.503
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 3 - Optimised bond length values (PM6)'''''
!
! colspan="3" |Bond Length (Å)
|-
!Bond
!Reactants
!Transition State
!Products
|-
|C<sup>1</sup>-C<sup>2</sup>
|1.327
|1.382
|1.541
|-
|C<sup>2</sup>-C<sup>3</sup>
|3.413*
|2.115
|1.540
|-
|C<sup>3</sup>-C<sup>4</sup>
|1.335
|1.380
|1.501
|-
|C<sup>4</sup>-C<sup>5</sup>
|1.468
|1.411
|1.338
|-
|C<sup>5</sup>-C<sup>6</sup>
|1.335
|1.380
|1.501
|-
|C<sup>6</sup>-C<sup>1</sup>
|3.414*
|2.115
|1.540
|}

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) The Van der Waals radius is indeed 1.7A, but for each carbon, meaning the two atoms can be considered to be interacting as soon as their bond length becomes smaller than 2 x 1.7 i.e. 3.4. Incidentally, this is why the "infinite" distance for two carbons is set to be 3.414.)

It is important to note for the reactant values marked with an asterisk that as C<sup>2</sup>-C<sup>3</sup> and C<sup>6</sup>-C<sup>1</sup> are bonds formed during the reaction, the bond length can essentially be assumed as infinite, since there is no interaction between the carbon atoms. The same bonds in the transition state have a length of 2.115 Å, which is significantly larger than the van der waal radius for carbon atoms, suggesting a very weak interaction that still does not have a significant bonding character. In the products these bonds represent C-C (sp<sup>3</sup>-sp<sup>3</sup>) bonds, however the optimised value of 1.540 Å shows significant deviation to the typical bond value of 1.530 Å. Comparison with experimentally determined bond lengths of cyclohexene showed reasonable agreement with literature values<ref>V. A. Naumov, V. G. Dashevskii and N. M. Zaripov, J. Struct. Chem., 1971, 11, 736–742.</ref>, highlighting the limitation that treating bonds individually from a valence bond theory perspective does not take into account complex orbital interactions that can affect bond length.

C<sup>3</sup>-C<sup>4</sup> and C<sup>5</sup>-C<sup>6</sup> represent the sp<sup>2</sup>-sp<sup>2</sup> double bonds of butadiene in the reactants, while C<sup>4</sup>-C<sup>5</sup> represents the sp<sup>2</sup>-sp<sup>2</sup> single bond connecting them. Their deviation from typical bond length values can be explained by delocalisation through the overlapping p-orbitals, which lengthens the double bonds (due to loss of electron density in the stabilised bonding orbitals) and shortens the single bond (as it gains partial double bond character). Throughout the reaction, the two double bonds lengthen to form sp<sup>3</sup>-sp<sup>2</sup> single bonds, while the single bond shortens to become a sp<sup>2</sup>-sp<sup>2</sup> double bond in cyclohexene.

Finally C<sup>1</sup>-C<sup>2</sup> represents the ethylene sp<sup>2</sup>-sp<sup>2</sup> double bond in the reactants, which again lengthens to form a sp<sup>3</sup>-sp<sup>3</sup> single bond in the cyclohexene product. Once again, the values obtained all agree strongly with literature values for the cyclohexene product<sup>[10]</sup>.

From the bond length data, the transition state appears to have a structure similar to the reactants. Following on from Hammond's postulate, it can be suggested that this reaction must have an ''early'' transition state, whereby there is little difference in structure and therefore energy between the reactants and transition state, but a large difference between the transition state and products. This suggestion was confirmed by the IRC calculation, which follows the lowest energy pathway to determine the 1D PES, similar to that seen in '''Figure 2'''. The resultant plot, as well as the animated .gif file are shown below in '''Table 4'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 4 - IRC plot and .gif file for the Diels-Alder reaction between Butadiene + Ethylene'''
!IRC Plot
!IRC .gif File
|-
|[[File:BT1215_Butadiene_Ethylene_IRC.png|490x340px]]
|[[File:BT1215_Buteth.gif]]
|}

=== Transition State Vibration Discussion ===
As mentioned before, the Diels-Alder reaction between butadiene and ethylene has been experimentally and theoretically proven through various experimental and theoretical studies, however the '''''concerted''' ''nature of the pathway can also be formed by looking at the vibration which corresponds to the transition state formation. As can be seen below, the vibration shows the key C<sup>1</sup>-C<sup>6</sup> and C<sup>2</sup>-C<sup>3</sup> bonds forming at the same time, hence identifying a synchronous reaction mechanism.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>BT1215_BEDIELSALDER_ORB_COMB_REACT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 17; frank off </script>
<name>VibTSBT1215</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibrate</text>
<target>VibTSBT1215</target>
</jmolbutton>
</jmol>

=== Output Calculation Files ===

SM: [[File:BT1215 CIS BUTADIENE OPT PM6.LOG]]
<br>
IRC: [[File:BT1215 COMB REACT IRC PM6.LOG]]
<br>
PRETS OPT: [[File:BT1215 COMB REACT PM6 PRETS OPT.LOG]]
<br>
TS: [[File:BT1215 BEDIELSALDER ORB COMB REACT TS PM6.LOG]]
<br>
SM: [[File:BT1215 ETHYLENE OPT PM6.LOG]]
<br>
PROD: [[File:BT1215 PROD CYCLOHEXENE OPT PM6.LOG]]
<br>
SINGLE POINT ENERGY REACT: [[File:BT1215 SPE REACT PM6.LOG]]

== Exercise 2: Cyclohexadiene + 1,3-Dioxole - PM6 & B3LYP Level ==

=== Reaction Overview ===
As with Exercise 1, cyclohexadiene and 1,3-dioxole can undergo a [4+2] Diels-Alder cycloaddition reaction, however in this example there are two fundamental points to be aware of. Firstly, by having two disubstituted alkene components, stereoselectivity is introduced whereby the orientation of the alkenes affect the reaction product. The two products formed are denominated endo and exo and are a function of their orientation in the cyclic product. The endo product corresponds to an axially fused ring system (where the extra ring faces downwards), while the exo product represents the equatorial equivalent. For this reaction, the two possible stereoisomers are shown below in '''Scheme 2'''.

[[File:BT1215 Cyclodioxone Reaction Scheme.jpg|centre|thumb|843x418px|'''''Scheme 2 - Reaction scheme showing the stereoselectivity of the Diels-Alder reaction between cyclohexadiene + 1,3-dioxole''''']]

The second key point is that the presence of two electron-donating oxygen atoms adjacent to the dienophile results in an '''''inverse electron demand''''' for the reaction, whereby the electron rich dienophile has a higher energy HOMO and essentially acts as the electron donor. This interacts with the lower energy LUMO of cyclohexadiene to result in an apparent 'reverse' electron flow, and thus generates the HOMO of the transition state. This can be seen qualitatively by comparing the relative reactant MO positions of the normal electron demand reaction above ('''Figure 4''') with those shown below in '''Figure 6 '''and '''Figure 7'''. The comparative energy gap between HOMO-LUMO overlap interactions in both the normal and inverse demand cases was also compared by looking at the computed orbitals in the optimised PM6 structures, and is shown below in '''Table 5'''. As can be seen, the energy gap between the Dienophile HOMO and Diene LUMO is smaller in the Diels-Alder reacton between cyclohexadiene and 1,3-dioxole, leading to the perceived inverse flow. This is confirmed by experimental data with 1,3-dioxole Diels-Alder reactions<ref>M. A. Mckervey, Alicyclic Chemistry, The Chemical Society, 1978.</ref>. The reaction is still thermally allowed following the Woodward-Hoffman rules, since the diene is a (4q+2)<sub>s</sub> component, and there is no (4r)<sub>a</sub> component, thus yielding an odd number which corresponds to a thermal reaction<ref>R. Hoffmann and R. B. Woodward, Acc. Chem. Res., 1968, 1, 17–22.</ref>.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 5 - Comparison of diene and dienophile HOMO-LUMO energy gaps for normal and inverse electron demands'''
!Diels-Alder Reaction
!Diene''' HOMO-Dienophile LUMO Energy gap / Hartrees'''
!Dienophile HOMO-Diene LUMO Energy gap''' / Hartrees'''
!Reaction Type
|-
|Butadiene + Ethylene (PM6)
|'''0.39770'''
|0.39854
|Normal Electron Demand
|-
|Cyclohexadiene + 1,3-Dioxole (PM6)
|0.35354
|'''0.33984'''
|Inverse Electron Demand
|}

It should be noted that the values shown in '''Table 5 '''represent the values obtained from single point energy PM6 calculations, since the B3LYP single point energy optimisations of butadiene + ethylene actually suggest an Inverse Electron Demand reaction. This is likely due to the fact that the butadiene + ethylene case is borderline, making it very difficult to distinguish which pathway the reaction undergoes. In addition, there are several different definitions for normal and inverse electron demand, meaning that while the discussion regarding the HOMO-LUMO gap is still important, it does not always accurately predict the electron demand of the reaction.

Unlike in the previous exercise, the reactants, products, and transition states were all optimised with the more accurate B3LYP method (and 6-31G basis set) after an initial PM6 optimisation, giving a more precise comparison of the orbital interactions in the transition state.

=== Molecular Orbital Discussion ===
The MO diagrams for both the endo and exo transition states are shown below in '''Figure 6''' and '''Figure 7'''. As with the MO diagram in Exercise 1, the occupied orbitals shown for the transition state are significantly destabilised compared to the expected orbitals in the product, since the transition state represents a significantly constrained and therefore high-energy conformation. While the order of the MO interactions is the same in both cases, the relative stability of the orbitals is significantly different for the endo and exo forms. For the frontier HOMO, the endo equivalent is significantly more stable, which can be explained by the involvement of secondary orbital interactions between the two oxygen p-orbitals and the two p-orbitals of the diene which are not directly involved in the diene-dienophile orbital overlap.

[[File:BT1215 cyclodioxone endo MO diagram.jpg|thumb|786x786px|'''''Figure 7 - Frontier MO diagram of the endo stereoisomer in the cyclohexadiene + (1,3)-dioxole Diels-Alder reaction.''''']]
[[File:BT1215 cyclodioxone exo MO diagram.jpg|left|thumb|771x771px|'''''Figure 6 - Frontier MO diagram of the exo stereoisomer in the cyclohexadiene + (1,3)-dioxole Diels-Alder reaction.''''']]

A more thorough discussion of the difference in stabilities is given below in the '''''Energy Discussion''''' section, but secondary orbital interactions can be seen below in the interactive Jmols of the endo orbitals (particularly orbitals 41 and 43). The endo pathway orbitals are shown in '''Table 6''', while those of the exo pathway are given in '''Table 7'''. As before, it is possible to toggle through all of the generated frontier MOs using the drop down box.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 6 - Frontier orbitals in the ENDO Diels-Alder Reaction between cyclohexadiene + 1,3-dioxole'''''
!ENDO Reactant Orbitals
!ENDO Transition State Orbitals
!ENDO Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_SPE_ENDO_OXONE_SM_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCDR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCDR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_OPT_TS_B3LYP_2ND.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCD</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCD</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCD</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCD</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_PROD_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCDP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCDP</target>
</item>
</jmolmenu>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 7 - Frontier orbitals in the EXO Diels-Alder Reaction between cyclohexadiene + 1,3-dioxole'''''
!EXO Reactant Orbitals
!EXO Transition State Orbitals
!EXO Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_SPE_EXO_OXONE_SM_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCDR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCDR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_OPT_TS_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCD</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCD</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCD</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCD</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_PROD_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 14; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCDP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 14; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCDP</target>
</item>
</jmolmenu>
</jmol>
|}

=== Energy Discussion ===
The thermochemical data for the activation and reaction energy of both the endo and exo pathway is given below in '''Table 8''', while the reaction profile is shown below in '''Figure 8'''. As can be seen, the endo reaction represents not only the kinetic product for the reaction (by having a lower activation energy) but also the thermodynamic product, as it has a lower energy than the exo form. The reactant, product, and transition state energies are given in Hartrees in '''Table 9''' for comparison. The reactant energies were summed from separate optimisations to ensure there was no interaction between the two that would affect the computed energy.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 8 - Thermochemical data for both stereochemical routes in the cyclohexadiene + 1,3-dioxole Diels-Alder reaction'''
!Reaction Pathway
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|'''Exo Pathway'''
|0.063853
|167.65
|<nowiki>-0.024302</nowiki>
|<nowiki>-63.81</nowiki>
|-
|'''Endo Pathway'''
|0.060871
|159.82
|<nowiki>-0.025671</nowiki>
|<nowiki>-67.40</nowiki>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 9 - Reactant, transition state, and product energies for the 1,3-dioxole + cyclohexadiene Diels-Alder reaction'''
!Reaction Pathway
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|'''Exo Pathway'''
|<nowiki>-500.393020</nowiki>
|<nowiki>-500.329167</nowiki>
|<nowiki>-500.417322</nowiki>
|-
|'''Endo Pathway'''
|<nowiki>-500.393020</nowiki>
|<nowiki>-500.332149</nowiki>
|<nowiki>-500.418691</nowiki>
|}
[[File:BT1215 cyclodioxone reaction pathway diagram.jpg|centre|thumb|499x499px|'''''Figure 8 - Reaction coordinate of the cyclohexadiene + 1,3-dioxole Diels-Alder reaction showing the activation and reaction energies for both the endo and exo stereoisomers''''']]
Generally, for alkenes containing substituents that are able to form secondary orbital interactions, the endo product is formed under kinetic control due to a lower energy transition state and therefore a lower activation energy. As mentioned before, these secondary orbital interactions consist of the involvement of the oxygen p-orbitals in the 1,3-dioxole ring which form constructive, symmetry allowed overlaps with the cyclohexadiene frontier orbitals. This increase in overlap leads to a greater stabilisation of the HOMO in the product and transition state, thus also lowering the overall energy of both. These interactions are 'secondary' as their contribution to the bonding is not essential for the reaction to occur, however their impact is significant in determining the stereochemistry of the product. The key secondary orbital interaction between oxygen and cyclohexadiene is shown below in '''Figure 9''', while an interactive Jmol of the endo transition state HOMO with a higher isovalue is shown below to highlight the interaction.
[[File:BT1215 Stabilising Orbital Interaction dioxone.jpg|centre|thumb|735x735px|'''''Figure 9 - Stabilising secondary orbital interactions observed in the endo conformer of the 1,3-dioxole + cyclohexadiene Diels-Alder reaction ''''']]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
!ENDO TS HOMO Showing Secondary Orbital Interactions
!EXO TS HOMO (No Secondary Interaction)
|-
|<jmol>
<jmolApplet>
<size>500</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_OPT_TS_B3LYP_2ND.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat "" rotate x -20; frank off</script>
<name>EndoDielsAlderCDO</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDO</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDO</target>
</jmolbutton>
</jmol>
|<jmol>
<jmolApplet>
<size>500</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_OPT_TS_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 20; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat "" rotate x -20; frank off</script>
<name>ExoDielsAlderCDO</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDO</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDO</target>
</jmolbutton>
</jmol>
|}

While secondary orbital interactions are important in determining kinetic control, the endo stereosiomer may not be the thermodynamic product if there is a significant steric clash. In this case, the endo form is actually also thermodynamically more stable than the exo form, due to fewer steric interactions between the bridge of the cyclohexene ring and the -CH<sub>2</sub> group in the 1,3-dioxole ring. A comparison of the steric interactions is shown below in '''Figure 10'''.
[[File:BT1215 Steric Clash Dioxone Diels-Alder.jpg|centre|thumb|649x649px|'''''Figure 10 - Steric clash observed in both stereoisomer products of the Diels-Alder reaction''''']]

=== Output Calculation Files ===

SM: [[File:BT1215 CYCLOHEXADIENE OPT PM6.LOG]]
<br>
SM: [[File:BT1215 CYCLOHEXADIENE OPT B3LYP 2.LOG]]
<br>
SM: [[File:BT1215 DIOXONE OPT PM6.LOG]]
<br>
SM: [[File:BT1215 DIOXONE OPT B3LYP.LOG]]
<br>
ENDO IRC: [[File:BT1215 ENDO OXONE IRC PM6.LOG]]
<br>
ENDO PRETS OPT: [[File:BT1215 ENDO OXONE PREOPT TS PM6.LOG]]
<br>
ENDO TS: [[File:BT1215 ENDO OXONE OPT TS B3LYP 2ND.LOG]]
<br>
ENDO PROD: [[File:BT1215 ENDO OXONE PROD OPT PM6.LOG]]
<br>
ENDO PROD: [[File:BT1215 ENDO OXONE PROD OPT B3LYP.LOG]]
<br>
ENDO SINGLE POINT ENERGY REACT: [[File:BT1215_SPE_ENDO_OXONE_SM.LOG]]
<br>
EXO IRC: [[File:BT1215 EXO OXONE IRC PM6.LOG]]
<br>
EXO PRETS OPT: [[File:BT1215 EXO OXONE PREOPT TS PM6.LOG]]
<br>
EXO TS: [[File:BT1215 EXO OXONE OPT TS B3LYP.LOG]]
<br>
EXO PROD: [[File:BT1215 EXO OXONE PROD OPT PM6.LOG]]
<br>
EXO PROD: [[File:BT1215 EXO OXONE PROD OPT B3LYP.LOG]]
<br>
EXO SINGLE POINT ENERGY REACT: [[File:BT1215 EXO OXONE SM OPT PM6.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic Reactions (Xylylene + SO<sub>2</sub>) - PM6 Level ==

=== Reaction Overview ===
The reaction of xylylene with SO<sub>2</sub> is of particular interest, since the involvement of an electron-rich atom such as sulphur, which can easily become hypervalent, allows for new pericyclic reactions. As before, a [4+2] Diels-Alder cycloaddition an occur between the two exocyclic double bonds and the S=O double bond to give two fused six-membered rings with an either endo or exo stereoselectivity. Alternatively, it is possible for the sulphur atom alone to react with the exocyclic diene to give a 5-membered ring fused to the aromatic phenyl ring, in what is called a cheletropic reaction. The reaction with xylylene also introduces an interesting regioselectivity discussion; as well as the cheletropic reaction, a second endocyclic cis-diene is available to react with the SO<sub>2</sub> to yield alternative products. This pathway is highly disfavoured compared to the exocyclic Diels-Alder, the reasons of which are explained in the '''''Energy Discussion Section'''''. All of the discussed reaction routes are shown below in '''Scheme 3'''

[[File:BT1215 Chele vs Diels Alder React Scheme.jpg|centre|thumb|800x418px|'''''Scheme 3 - Reaction scheme showing all of the Diels-Alder and cheletropic reactions between Xylylene + SO<sub>2</sub>''''']]

=== Energy Discussion ===
As for '''<u>Exercise 2</u>''', the activation and reaction energies for all of the possible routes are given below in '''Table 10''', while a visual representation of the reaction profile can be seen below in '''Figure 11'''. For comparison, the reactant, transition state, and product energies are given in Hartrees below in '''Table 11'''.

Comparing the activation energies, the endo pathway of the exocyclic Diels-Alder reaction appears to be the kinetic product of the reaction, since it has the lowest energy transition state compared to the reactants. The thermodynamic product for the reaction is clearly the '''cheletropic''' product, since it is significantly more stable than any of the Diels-Alder reaction products. This is in agreement with literature results<ref>D. Suárez, T. L. Sordo and J. A. Sordo, J. Org. Chem., 1995, 60, 2848–2852.</ref>, and is likely due to the fact that the cheletropic transition state suffers a higher level of ring strain due to the formation of a 5-membered fused ring, compared to the 6-membered ring formed in the Diels-Alder reactions, which makes the Diels-Alder route kinetically faster. Conversely, the retention of the highly stable S=O bond in the cheletropic product makes this the thermodynamic product. Indeed, as a result of this, the cheletropic product is significantly more accessible experimentally when compared to the reversible Diels-Alder routes. Both the exocyclic Diels-Alder reactions and the cheletropic reaction are all thermodynamically stable compared to the reactants, and can be explained by the formation of the highly stabilised aromatic phenyl ring which lowers the product energy.

In comparison, xylylene is destabilised as it does not possess any aromaticity. The same discussion can be applied to the unfavourable, high-energy endocyclic Diels-Alder reactions; their significantly higher activation barriers and reaction energies compared to the other routes can be explained by the fact there is no aromatic ring in the products, which are also destabilised compared to the reactants due to the creation of a strained bi-fused ring system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 10 - Thermochemical data for all possible reactions between xylylene and SO<sub>2</sub>'''
!Reaction Pathway
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|Cheletropic
|0.040671
|106.78
|<nowiki>-0.058385</nowiki>
|<nowiki>-153.29</nowiki>
|-
|'''Exo'''cyclic '''Exo '''Diels-Alder
|0.033694
|88.46
|<nowiki>-0.036928</nowiki>
|<nowiki>-96.95</nowiki>
|-
|'''Exo'''cyclic '''Endo '''Diels-Alder
|0.032177
|84.48
|<nowiki>-0.036685</nowiki>
|<nowiki>-96.32</nowiki>
|-
|'''Endo'''cyclic '''Exo '''Diels-Alder
|0.046672
|122.54
|0.008922
|23.42
|-
|'''Endo'''cyclic '''Endo '''Diels-Alder
|0.043687
|114.70
|0.007226
|18.97
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 11 - Reactant, transition state, and product energies for all possible reactions between xylylene + SO<sub>2</sub>'''
!Reaction Pathway
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|Cheletropic
|0.058383
|0.099054
|<nowiki>-0.000002</nowiki>
|-
|'''Exo'''cyclic '''Exo '''Diels-Alder
|0.058383
|0.092077
|0.021455
|-
|'''Exo'''cyclic '''Endo '''Diels-Alder
|0.058383
|0.090560
|0.021698
|-
|'''Endo'''cyclic '''Exo '''Diels-Alder
|0.058383
|0.105055
|0.067305
|-
|'''Endo'''cyclic '''Endo '''Diels-Alder
|0.058383
|0.102070
|0.065609
|}
[[File:BT1215 Exercise 3 Reaction Diagram.jpg|centre|thumb|869x869px|'''''Figure 11 - Reaction profile for the key cycloadditions between xylylene + SO<sub>2</sub>''''']]

The .gif files for the IRC calculations of the reaction routes are shown below. Please note that they may not play smoothly until the interactive Jmols above load. A variety of interesting results can be seen from the animations. All of the Diels-Alder reactions occur via an asynchronous bond formation, where the C-O bond forms before the C-S bond. This could be due to the fact that the smaller, more electron dense oxygen atom can get closer to the xylylene ring to form the C-O bond more quickly than the larger, more diffuse sulphur atom. However, this is merely observational and further calculations would be required to confirm this. In contrast, since only the sulphur atom is involved in the cheletropic reaction, both sigma bonds are formed in a synchronous manner. The IRC plots for all of the reactions are shown below, adjacent to the .gif files. It should be noted that for the Exocyclic Exo route the IRC ran from products to reactants, meaning the reactants are on the right side and the products are on the left side. When compared to the other plots the graph should be reversed.

(Be careful here: you can't use GaussView to decide when precisely a "bond" is formed, as it uses a cutoff distance to decide when to draw a bond [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:15, 4 April 2018 (BST))

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Cheletropic IRC Plot
!Cheletropic IRC .gif
|-
|[[File:BT1215_CheletropicIRC_(2).png|490x370px]]
|[[File:BT1215_Cheletropic.gif]]
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Exocyclic Exo IRC Plot
!Exocyclic Exo IRC .gif
!Exocyclic Endo IRC Plot
!Exocyclic Endo IRC .gif
|-
|[[File:BT1215 Exo Exo DA.png|320x330px]]
|[[File:BT1215 Exo Exo.gif]]
|[[File:BT1215 Exo Endo DA png.png|320x330px]]
|[[File:BT1215_Exo_Endo_DA.gif]]
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Endocyclic Exo IRC Plot
!Endocyclic Exo IRC .gif
!Endocyclic Endo IRC Plot
!Endocyclic Endo IRC .gif
|-
|[[File:BT1215 Endo Exo DA 2.png|320x330px]]
|[[File:BT1215_Endo_Exo.gif]]
|[[File:BT1215 Endo Endo DA 2.png|320x330px]]
|[[File:BT1215_Endo_Endo.gif]]
|}

=== Output Calculation Files ===

SM: [[File:BT1215 SO2 SM PM6.LOG]]
<br>
SM: [[File:BT1215 XYLYLENE SM PM6.LOG]]
<br>
CHELO IRC: [[File:BT1215 CHELO XYLYLENE IRC PM6.LOG]]
<br>
CHELO PRETS OPT: [[File:BT1215 CHELO XYLYLENE REDUNDANT OPT.LOG]]
<br>
CHELO TS: [[File:BT1215 CHELO XYLYLENE TS PM6.LOG]]
<br>
CHELO PROD: [[File:BT1215 CHELO XYLYLENE REOPT PM6.LOG]]
<br>
DA EXOCYCLIC ENDO IRC: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE IRC PM6.LOG]]
<br>
DA EXOCYCLIC ENDO PRETS: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE PRETS OPT PM6.LOG]]
<br>
DA EXOCYCLIC ENDO TS: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE TS PM6.LOG]]
<br>
DA EXOCYCLIC ENDO PROD: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE OPT.LOG]]
<br>
DA EXOCYCLIC EXO IRC: [[File:BT1215 DIELS-ALDER XYLYLENE IRC PM6.LOG]]
<br>
DA EXOCYCLIC EXO PRETS: [[File:BT1215 DIELS-ALDER XYLYLENE REDUNDANT OPT.LOG]]
<br>
DA EXOCYCLIC EXO TS: [[File:BT1215 DIELS-ALDER XYLYLENE TS PM6.LOG]]
<br>
DA EXOCYCLIC EXO PROD: [[File:BT1215 DIELS-ALDER XYLYLENE REOPT PM6.LOG]]
<br>
DA ENDOCYCLIC ENDO IRC: [[File:BT1215 HIGH ENERGY IRC.LOG]]
<br>
DA ENDOCYCLIC ENDO PRETS: [[File:BT1215 HIGH ENERGY PREOPT TS PM6 2.LOG]]
<br>
DA ENDOCYCLIC ENDO TS: [[File:BT1215 HIGH ENERGY TS PM6.LOG]]
<br>
DA ENDOCYCLIC ENDO TS: [[File:BT1215 HIGH ENERGY TS CHECK ORB.LOG]]
<br>
DA ENDOCYCLIC ENDO PROD: [[File:BT1215 HIGH ENERGY PRODUCT OPT PM6.LOG]]
<br>
DA ENDOCYCLIC EXO IRC: [[File:BT1215 DA EXO HIGH ENERGY IRC PM6.LOG]]
<br>
DA ENDOCYCLIC EXO PRETS: [[File:BT1215 DA EXO HIGH ENERGY RED OPT PM6.LOG]]
<br>
DA ENDOCYCLIC EXO TS: [[File:BT1215 DA EXO HIGH ENERGY TS PM6.LOG]]
<br>
DA ENDOCYCLIC EXO PROD: [[File:BT1215 DA EXO HIGH ENERGY PROD OPT PM6.LOG]]

== 4π Electrocyclic Reactions: [1,1']-bicyclohexene - PM6 Level ==

=== Reaction Overview ===
The Woodward-Hoffman rules are also essential in predicting the stereochemistry of other pericyclic reactions, including electrocyclic reactions which involve the loss of a π bond and the creation of a σ bond that causes the cyclisation of the molecule. The mechanism for this reaction, shown in '''Scheme 4''', is shown below. For this investigation, [1,1']-bicyclohexene was chosen, with a core diene structure analogous to that of butadiene. This electrocyclic reaction is denoted 4π as 4π electrons are involved in the cyclisation.
<br>
[[File:BT1215 Extension RS 1.jpg|centre|thumb|847x120px|'''''Scheme 4 - Reaction scheme showing the 4π electrocyclic reaction of [1,1']-bicyclohexene''''']]
<br>
The stereoselectivity concerns of this reaction are very important, as shown by the Woodward-Hoffman rules<sup>[13]</sup>, since two possible reactions can occur depending on the conditions that the diene is reacting under. [1,1']-bicyclohexene can cyclise under thermal conditions via a '''''conrotatory''' ''mechanism, shown below in '''Figure 12'''. This is allowed due to the presence of a <sub>π</sub>4<sub>a</sub> orbital component which, when 'pulled together', causes the Hydrogen atoms to rotate in the same direction. An alternative possibility is a '''''disrotatory''''' mechanism with a <sub>π</sub>4<sub>s</sub> orbital component; this is '''thermally disallowed''', but can occur under photochemical conditions to yield a trans-alkene product.
<br>
[[File:BT1215 WH Thermal Vs Photo.jpg|centre|thumb|475x400px|'''''Figure 12 - Symmetry Woodward-Hoffmann rules for both the thermal and photochemical reactions of dienes''''']]
<br>
The full explanation as to whether a reaction is thermally allowed or disallowed can be explained by looking at the frontier orbital overlaps in both a conrotatory and disrotatory mechanism. For simplicity, the orbitals of the analogous butadiene will be used, however the explanation can be directly applied to [1,1']-bicyclohexene. In a conrotatory mechanism, the two terminal symmetry orbitals of butadiene (on the top left of the diagram) shown in '''Figure 12''' can be superimposed using a C2 axis perpendicular to the plane of the screen. For a disrotatory mechanism however, the same orbitals are reflected in a σ symmetry plane that is perpendicular to the screen and runs through the centre of the butadiene. It is important to note that while the symmetry based orbitals often used to describe WH rules cannot be directly compared to the frontier molecular orbitals, the symmetry linking both sets of orbitals remains the same here.

The symmetry of the frontier orbitals of butadiene can then be determined based on these two operators, and a correlation diagram composed to identify which orbitals can overlap in the reaction to make the product. The correlation diagrams for the conrotatory and disrotatory mechanisms are shown below in '''Figure 13'''. As can be seen, the conrotatory mechanism involves the transfer of electrons from the ground state orbitals of the butadiene into the ground state orbitals of the cyclobutene, resulting in a small energy barrier for the reaction. In contrast, the disrotatory mechanism requires the excitation of electrons into an excited state antibonding orbital, giving it a much larger energy barrier and making the reaction thermally disallowed.

'''While this provides an elegant way of explaining the WH rules, it must be stated that it ''cannot'' provide significant insight into the structure of the product orbital, since the reaction proceeds via a 4n Mobius transition state and this allows all of the orbitals to rotate and switch symmetry. The actual frontier orbitals can be seen below in the MO/Energy Discussion'''.
<br>
[[File:BT1215 Extension FO Symmetry.jpg|centre|thumb|1458x415px|'''''Figure 13 - Frontier orbital symmetry of butadiene for conrotatory & disrotatory mechanisms''''']]
<br>

(Good intro, and you have labelled your symmetry axis [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:04, 4 April 2018 (BST))

=== MO/Energy Discussion ===

In this discussion, the thermally allowed pathway will be focused on due to time limitations that meant that the full calculation of the photochemical route could not be performed. All optimisations were performed at the PM6 level, with the key MOs for the reactant, transition state, and product, given below in '''Table 12'''. As can be seen, MO 32 of the product is different to the WH predicted frontier orbital. The expected bonding interaction appears as part of MO 31, along with a more complicated bonding interaction from the alkene of the cyclobutene that appears to be the same symmetry. This is likely a consequence of reacting through a twisted Mobius transition state. It is recommended that further calculations be performed with a more accurate method to confirm the orbital ordering. The rest of the orbitals are as expected in the '''Reaction Overview''' section.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 12 - Frontier orbitals in the 4π electrocyclic reaction of [1,1']-bicyclohexene'''''
!Reactant Orbitals
!Transition State Orbitals
!Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 DIENE SM PM6 OPT 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; mo 32; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 22; mo 32; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 33; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 34; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 35; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 DIENE TS OPT PM6 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 32; mo nodots nomesh fill translucent; mo cutoff 0.04; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneT</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneT</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneT</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 8; mo 32; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 33; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 34; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 35; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneT</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 PRODUCT ALKENE PM6 OPT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 48; mo 31; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 22; mo 31; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 31</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 32; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 33; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 34; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 35; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneP</target>
</item>
</jmolmenu>
</jmol>
|}

The thermochemical data for the reaction is shown below in '''Table 13''', while the energies of the reactant, transition state, and product are given in '''Table 14'''. The computed energies reveal that the starting diene is more stable, and therefore the predominant form. This is likely due to the high levels of ring strain in the cyclobutene ring destabilising the product. Kinetically this reaction is also highly unfavourable, with a much higher activation energy than the previous reaction systems discussed. It is possible that the complexity of the cyclohexene rings means a large amount of bond rearrangement is required in order to form the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 13 - Thermochemical data for the 4π electrocyclic reaction of [1,1']-bicyclohexene'''
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|0.104375
|274.04
|0.028329
|74.3777952
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 14 - Reactant, transition state, and product energies for the electrocyclic reaction of [1,1']-bicyclohexene'''
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|0.199543
|0.303918
|0.227872
|}

An IRC calculation was performed and both the plot and .gif file are shown below. As before, the reaction was computed from products to reactants in the IRC, so the graph should appear reversed. It is also important to note that in the IRC calculation the reactant energy appears to be higher energy than the product, likely due to it converging to a metastable minima where the diene is planar, and not the most stable form of the reactants.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!IRC Plot
!IRC .gif File
|-
|[[File:BT1215 Diene Extension.png|490x375px]]
|[[File:BT1215 Ext Diene.gif]]
|}

Finally, the imaginary vibration corresponding to the transition state can be seen below. As suggested by the vibration and the IRC, the bond formation in the electrocyclic reaction appears to be synchronous, with the hydrogen atoms rotating in a concerted manner.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>BT1215 DIENE TS OPT PM6 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 9; frank off </script>
<name>VibTS2BT1215</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibrate</text>
<target>VibTS2BT1215</target>
</jmolbutton>
</jmol>

=== Output Calculation Files ===

SM: [[File:BT1215 DIENE SM PM6 OPT 2.LOG]]
<br>
IRC: [[File:BT1215 DIENE IRC PM6.LOG]]
<br>
PRETS OPT: [[File:BT1215 DIENE TS PREOPT PM6 2.LOG]]
<br>
TS: [[File:BT1215 DIENE TS OPT PM6 2.LOG]]
<br>
PROD: [[File:BT1215 PRODUCT ALKENE PM6 OPT.LOG]]
<br>

== Conclusion ==
Computational analysis of 4 different pericyclic systems was performed with a large degree of success, both with the Semi-Empirical PM6 and DFT B3LYP methods. In all cases, it was possible to model and correctly predict experimentally determined reaction mechanisms and transition states. The use of Gaussian was also able to provide insight into the change in bond lengths throughout the reaction, the type of transition state, the electron demand of the reaction, and which routes represent the thermodynamic or kinetic product. The computation of molecular orbitals was crucial in justifying the observed stereoselectivities, providing an elegant visual representation of secondary orbital interactions, as well as other factors affecting product formation. Unfortunately, the complexity of the calculations, along with time constraints, meant that the majority of reaction systems could only be optimised using the PM6 method, and so can only yield qualitative results due to the limitations discussed in the introduction. Conclusions for the individual exercises were as follows:

*<u>Exercise 1 - PM6</u> - The Diels-Alder reaction of butadiene + ethylene was modelled and shown to occur via a synchronous 4+2 cycloaddition, with a normal electron demand for the reaction. The transition state was correctly identified and confirmed by the presence of a single imaginary vibration frequency, corresponding to product formation, and an IRC calculation was performed to determine an early transition state. This was also confirmed by modelling the change in bond lengths throughout the course of the reaction, showing a transition state structure close to that of the reactants. Despite the inaccuracies of the PM6 method, bond lengths were in reasonable agreement with the literature.

*<u>Exercise 2 - PM6 & B3LYP</u> - The stereoselectivity of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole was investigated in order to determine whether the endo or exo product represented kinetic and/or thermodynamic control. All structures were optimised first with the PM6 method, before being reoptimised with the B3LYP method in order to give a more accurate depiction of the reaction system and its energies. Relative HOMO-LUMO energy gaps were compared with butadiene + ethylene to determine an inverse electron demand reaction, caused by the electron rich atoms on the dienophile. An MO diagram was constructed, and the kinetic stability of the endo product was explained by the involvement of oxygen p-orbitals in secondary orbital interactions that help to stabilise the transition state. The endo product was also determined to be the thermodynamic product due to the absence of steric clash between the bridged ring and the 1,3-dioxole group.

*<u>Exercise 3 - PM6</u> - The relative stabilities of five different pericyclic routes for the reaction between Xylylene + SO<sub>2</sub> were probed. Optimisations of reactants, products, and transition states were all carried out with the PM6 method. The cheletropic reaction yielded the thermodynamic product via a synchronous bond formation, likely due to the preservation of both S=O bonds. The exocyclic endo Diels-Alder reaction, occurring through asynchronous bond formation, represented kinetic control, due to the fact that the transition state contains a 6-membered fused ring compared to the relatively strained 5-membered cheletropic transition state. An alternative, endocyclic Diels-Alder reaction was investigated and shown to be highly disfavoured due to the fact that no aromatic ring was formed in the product, and the resultant fused ring product had large steric interactions making it thermodynamically unstable compared to the reactants.

*<u>Exercise 4 - PM6</u> - The thermally allowed, conrotatory 4π electrocyclic reaction of [1,1']-bicylcohexene was investigated, with all optimisations taking place at the PM6 level. The reaction was determined to proceed via a 4n Mobius transition state, which could explain discrepancies between the predicted orbital overlap using orbital symmetry and the observed product orbitals. An IRC calculation was performed and showed a concerted bond formation, while the imaginary transition state frequency observed for the transition state also suggested a concerted, conrotatory mechanism. Due to time constraints, the photochemical disrotatory reaction could not be calculated.

Further work could be explored not only in the computation of the photochemical reaction route in Exercise 4, but also by further modelling more obscure pericyclic reaction routes, similar to computational research performed by W. Grimme et al into cheletropic ene reactions<ref>W. Grimme, M. W. Harter, C. A. Sklorz, J. Chem. Soc., Perkin Trans. 2, 1999, 9.</ref>. Alternatively, higher level calculations could be performed to further understand more complex systems, such as ''ab initio'' calculations by F. Monnatt et al into the cheletropic and hetero Diels-Alder additions of SO<sub>2</sub> to (E)-Methoxybutadiene.<ref>F. Monnat, P. Vogel, V. M. Rayón and J. A. Sordo, J. Org. Chem., 2002, 67, 1882–1889.</ref>

== References ==

Rep:Mod:nrwy3ts

2018-04-07T09:42:27Z

Fv611: /* Molecular Orbital Diagram */

= Transition States and Reactivity =

== Introduction ==

The aim of this lab was to investigate a number of Diels-Alder cyclic reactions using the program Gaussian, in order to determine the structure of the transition state formed during these reactions. The transition state in a reaction is the point of highest energy along a reaction coordinate, with a first derivative of zero, and a second negative derivative in the direction of the products, which occurs between the two energies of the reactants and the products, whose firsts derivative are also equal to zero. The enthalpy change of a reaction is determined by calculation of the difference in energy between these two points, and the activation energy corresponds to the difference in energy between the reactant minima and the transition state maxima.

In reality there are many degrees of freedom than seen in the 2D Reaction Coordinate plot, determined by the equation 3N-6, where N is the number of atoms in a molecule. The degrees of freedom can be used to plot a multidimensional Potential Energy Surface, and the reaction coordinate then plotted as a function of the degrees of freedom produced. Depending on the basis set selected, a greater number of basis vectors, such as with 631-G, can be utilised during calculation in order to produce a result with fewer approximations, at the expense of a longer calculation time. The Energy Profile normally corresponds to the minimum energy reaction pathway plotted from a Potential Energy Surface of a reaction, as there is the potential for there to be more than one saddle point on a Potential Energy Surface. In order to determine if the correct energy pathway is calculated using Gaussian, only one negative imaginary frequency should be seen, otherwise there is the possibility that the programme may have plotted another higher energy pathway instead.
[[File:nrwy3ts_Reaction_Coordinate_Diagram.png|x600px|600px]]

''Figure 1 - Reaction Coordinate Diagram''

Location of a transition state using Gaussian can be achieved via 3 different methods, depending on the initial knowledge of the transition state and the accuracy of the calculation required.

=== Method 1 ===
Involves the initial optimisation of the reactants and then placement of the reactants in a geometry similar to that of the transition state (such as 2.2Å being the average between the combined van der Waals radii and a C-C bond length), hence this method is unreliable unless some knowledge of the transition state is known. Although this is the quickest of the methods suggested, it is also the most unreliable, potentially producing multiple transition states, imaginary negative values or fail altogether. This method is best left for smaller systems if completely necessary.

=== Method 2 ===
Requires initial optimisation of the reactants, but during calculation of the transition state, bonds included in the reaction are frozen in place. This allows the system to be as close to the transition state as possible before optimisation, by allowing the unfrozen parts of the system to minimise around the frozen ‘bonds’. This method is more reliable than the previous method and almost as fast, yet still requires some understanding of the transition state before application.

=== Method 3 ===
Requires little knowledge of the transition state, and allows determination of the transition state from either the reactants or the products after optimisation. Using the desired product, the bonds which are formed during the transition state are frozen and placed a sensible distance apart (such as 2.4Å for a S-C bond). The broken bonds are frozen and optimised, then the transition state calculated. Although this is the most reliable of the methods, this method may fail if the transition state closely resembles the structure of the reactants when optimising and changing the structure from the products, as well as requiring multiple additional steps.

All these methods use a combination of both the semi-empirical method PM6 and the DFT method B3LYP, the former of which is quicker and used to optimise the structures initially, before the latter can further optimise the structure produced, giving a more reliable structure via the use of a greater amount of basis vectors.

== Exercise 1 ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job overall.)

The electrocyclic reaction between Ethene and Butadiene to form Cyclohexene was investigated to determine the orbitals involved in the formation of the transition state of the reaction, the energies of the relevant orbitals and the change in the bond lengths between the carbons upon formation of the transition state and products. The carbons are labelled as shown in Figure 2 and the change in bond lengths between the carbons reported in the table below.

=== Reaction Scheme ===

[[File:nrwy3ts_Cyclohexane_Reaction.png|x400px|400px]]

''Figure 2 - Reaction Scheme for the reaction of ethene and butadiene''

=== Molecular Orbital Diagram ===

[[File:nrwy3ts_MO_Diagram.png|x800px|2000px]]

''Figure 3 - Molecular Orbital Diagram for the reaction of ethene and butadiene''

In order for the orbitals to overlap and combine, the orbitals must have the same symmetry to produce a molecular orbital of that same symmetry. Therefore, only symmetric-symmetric and antisymmetric-antisymmetric interactions can occur to produce a non-zero orbital overlap integral and are ‘allowed’, conversely a symmetric-antisymmetric orbital overlap would produce a zero value orbital overlap integral and as such is a ‘forbidden’ reaction. The final produced molecular orbitals are of the same symmetry as the original molecular orbitals, and the energy of the products normally lower than that of the reactants, as discussed earlier. However, as this diagram depicts the formation of the transition state, the molecular orbitals are higher in energy than the final orbitals formed, as shown by the reaction coordinate diagram.

=== HOMOs and LUMOs for Reactants and Transition States ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Ethene HOMO
! style="background: #6ca0dc; color: white;" |Ethene LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_ETHENE.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_ETHENE.LOG</uploadedFileContents></jmolApplet></jmol>
|}

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Butadiene HOMO
! style="background: #6ca0dc; color: white;" |Butadiene LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>BUTADIENE1.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>BUTADIENE1.LOG</uploadedFileContents></jmolApplet></jmol>
|}

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Transition State HOMO -1
! style="background: #6ca0dc; color: white;" |2 - Transition State HOMO
|-
| <jmol><jmolApplet>
<color>white</color>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>TRANSITION_STATE.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>TRANSITION_STATE.LOG</uploadedFileContents></jmolApplet></jmol>
|}

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |3 - Transition State LUMO
! style="background: #6ca0dc; color: white;" |4 - Transition State LUMO +1
|-
| <jmol><jmolApplet>
<color>white</color>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>TRANSITION_STATE.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>TRANSITION_STATE.LOG</uploadedFileContents></jmolApplet></jmol>
|}

{| class="wikitable"
! style="background: #6ca0dc; color: white;" | Bond
! style="background: #6ca0dc; color: white;" | Reactants Bond Length/Å
! style="background: #6ca0dc; color: white;" | Transition State Bond Length/Å
! style="background: #6ca0dc; color: white;" | Product Bond Length/Å
|-
| C1-C2
| 1.35520
| 1.38177
| 1.53773
|-
| C2-C3
| -
| 2.11468
| 1.53582
|-
| C3-C4
| 1.33345
| 1.37979
| 1.49266
|-
| C4-C5
| 1.47077
| 1.41109
| 1.33305
|-
| C5-C6
| 1.33345
| 1.37979
| 1.49266
|-
| C6-C1
| -
| 2.11468
| 1.53582
|}
''Table 1 - Carbon Bond Lengths in the Formation of Cyclohexene''

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You should have explicitly stated that your carbon numbering is the one you use in your reaction scheme.)

From the table above, it can be seen that upon formation of the transition state, bonds C1-C2, C3-C4 and C5-C6 all lengthen as the sp hydridisation increases. Conversely, C4-C5 decreases from 1.47Å to 1.41Å due to the formation of a double bond from the single bond seen in the reactants and the increased s character of the MO. This bond further decreases upon completion of the double bond formation. The initial C6-C1 and C2-C3 'bonds' shorten in length, producing a value of 1.53582Å, incredibly close to the 1.54Å for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond<sup>1</sup>, showing the structure was successfully optimised by Gaussian. Due to the increased s character of the bonds when closer to the sp<sup>2</sup> carbons and C=C bond, there is a slight decrease in bond length from C1-C2 to C2-C3/C6-C1. As expected this increase in s character continues when looking at the bonds around the sp<sup>2</sup> C5 and C4, with the C3-C4/C5-C6 having intermediate values between the 1.54Å for a C-C bond and 1.34Å for an alkene C=C bond. This is consistent with the reported sp<sup>3</sup>-sp<sup>2</sup> value of 1.50Å<sup>1</sup>. The initial transition state produces a bond length of 2.11468Å for C2-C3/C6-C1, which decreases to 1.53582Å upon formation of cyclohexene. The initial bond length of 2.11468Å is comparable to the sum of two carbon van der Waals radii (3.400Å)<sup>2</sup>, and shows a bonding character interaction due to the shorter length observed.

=== Transition State Vibration and IRC ===

<jmol><jmolApplet>
<color>white</color>
<script>frame 17; vibration 1; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_TRANSITION_STATE.LOG</uploadedFileContents></jmolApplet></jmol>
'' Figure 4 - Reaction Path at the Transition State Vibration ''

Figure 4 shows the vibration corresponding to the imaginary frequency produced by the transition state, which represents the reaction path at the transition state. In the IRC, the bonds from the diene and alkene form at the same time, and such is a synchronous, concerted reaction.

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Transition State IRC
|-
| [[File:nrwy3ts_Ex1_Transition_State_IRC.gif]]
|}

==Exercise 2==

The molecular orbital diagrams for the Diels-Alder reaction between 1,3-dioxone and cyclohexadiene were produced to determine the molecular orbitals involved and the overlap of the orbitals in the transition state. Here the production of both the endothermic and exothermic products was investigated, where the approach of the dienophile 1,3-dioxone differs. During formation of the endothermic product, the ring oxygens approach beneath the alkene bonds in cyclohexadiene due to a favourable stabilising interaction. However for the exothermic product, the ring oxygens are positioned away from the alkene bonds. As seen in the previous exercise, only overlap between orbitals of the same symmetry is allowed for a reaction to occur.

=== Reaction Scheme ===

[[File:Reaction_Scheme_Exercise_2.png|x400px|400px]]

''Figure 4 - Reaction Scheme for the Reaction of Cyclohexadiene and 1,3-dioxole''

=== Molecular Orbital Diagram ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Exothermic MO Diagram
! style="background: #6ca0dc; color: white;" |Endothermic MO Diagram
|-
| [[File:nrwy3ts_Exo_MO_Diagram.png|x800px|2000px]]
| [[File:nrwy3ts_Endo_MO_Diagram.png|x800px|2000px]]
|}
''Figure 5 - Molecular Orbital Diagram for the Reaction of Cyclohexadiene and 1,3-dioxole''

A standard Diels-Alder reaction involves the combindation of a diene and a dienophile, where the HOMO of the diene interacts with the LUMO of the diene. However in the reaction investigated here, the electron donating oxygens in the 1,3-dioxone ring increase the energy of the HOMO of the alkene, and thus instead the HOMO of the alkene interacts with the LUMO of the diene in an inverse demand Diels-Alder reaction. Here it can be seen that molecular orbitals 1, 3 and 4 for the endothermic product are higher in energy than the exothermic counterparts, whilst molecular orbital 2 is lower in energy in the endothermic transition state than the exothermic. This effect seen in the endothermic product is due to secondary orbital interactions and is discussed later on, shown in the molecular orbital Jmol images below.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) The endo and exo prefixes are absolutely not related to the thermodynamics of your reaction. This is something you should know in your third year. Additionally you have not dranw the correct endo diagram: you state the numerical values of your MO relative energies, so why wouldn't you order them correctly?)

=== HOMOs and LUMOs for Reactants and Transition States ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1,3-Dioxole HOMO
! style="background: #6ca0dc; color: white;" |1,3-Dioxole LUMO
! style="background: #6ca0dc; color: white;" |Cyclohexadiene HOMO
! style="background: #6ca0dc; color: white;" |Cyclohexadiene LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>DIOXOLE_OPT_MO.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>DIOXOLE_OPT_MO.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>CYCLOHEXADIENE.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>CYCLOHEXADIENE.LOG</uploadedFileContents></jmolApplet></jmol>
|}

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Exo Transition State LUMO +1
! style="background: #6ca0dc; color: white;" |2 - Exo Transition State LUMO
! style="background: #6ca0dc; color: white;" |3 - Exo Transition State HOMO
! style="background: #6ca0dc; color: white;" |4 - Exo Transition State HOMO -1
|-
| <jmol><jmolApplet>
<color>white</color>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_EXO_TS.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_EXO_TS.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_EXO_TS.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_EXO_TS.LOG</uploadedFileContents></jmolApplet></jmol>
|}

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Endo Transition State LUMO +1
! style="background: #6ca0dc; color: white;" |2 - Endo Transition State LUMO
! style="background: #6ca0dc; color: white;" |3 - Endo Transition State HOMO
! style="background: #6ca0dc; color: white;" |4 - Endo Transition State HOMO -1
|-
| <jmol><jmolApplet>
<color>white</color>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_ENDO_TS_631G.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_ENDO_TS_631G.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
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<uploadedFileContents>nrwy3ts_ENDO_TS_631G.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_ENDO_TS_631G.LOG</uploadedFileContents></jmolApplet></jmol>
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=== Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Endo
| -1313771.847
| -1313622.1573
| -1313852.8626
| 149.6897
| -81.01537
|-
| Exo
| -1313771.847
| -1313614.3096
| -1313845.7396
| 157.53763
| -73.8926
|}
'' Table 2 - Activation and Reaction Energies for the Reactions between Cyclohexadiene and 1,3-dioxole ''

From the calculated data in the table above, the exothermic product is shown to have a greater activation energy than the endothermic product. This can be explained by the lack of a non-bonding stabilising interaction between the ring oxygen orbitals overlapping with the alkene bond orbitals during the transition state, meaning the energy of the exothermic transition state is higher than that of the endothermic pathway. This secondary orbital overlap can been seen below (Figure 6). Both reactions are exothermic and thermodynamically favourable enough to overcome the decrease in entropy upon formation of the product. However, the endothermic product is the lower in energy and therefore most stable of the products, which may be due to reduced steric interactions with 1,3-dioxole species avoiding steric clashes with the carbon chain bridging the 2 C=C bonds. This leads to a further favouring of the endothermic product, with both the stabilising oxygen non-bonding interactions and the lack of steric repulsion by bridging carbons, as seen in the data produced.
(It should be noted that upon optimisation of the cyclohexadiene, a negative frequency was observed, corresponding to the stretching of the sp<sup>3</sup> C-H bonds. This resulted in a slightly higher energy in the products than expected.)

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Exo Transition State HOMO
! style="background: #6ca0dc; color: white;" |Endo Transition State HOMO
|-
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'' Figure 6 - Secondary Orbital Effect ''

== Exercise 3 ==

O-Xylylene and sulfur dioxide undergo multiple cycloaddition reactions, which consist of a Diels-Alder and Cheletropic reaction, forming 10 and 9 membered rings respectively with the external cis-butadiene and 6 membered with the internal. During the [4+2] Diels-Alder reactions, the orientation of the SO<sub>2</sub> to the external cis-butadiene during formation of the transition state allows production of an exothermic and endothermic product. The preference of forming either the exothermic or endothermic product via a Diels-Alder reaction, or the cheletropic product, was investigated here by optimisation of each transition state at the PM6 level, and the energies calculated from the data. These pathways were then compared to the [4+2] cycloaddition pathways possible with the internal cis-butadiene.

(You should still count members of a ring by the smallest continuous joined system ie 5 and 6 for both external and internal reaction products [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:03, 4 April 2018 (BST))

=== Reaction Scheme ===

[[File:nrwy3ts_Ex_3_Reaction_Scheme.png|x500px|500px]]

'' Figure 7 - Reaction Scheme for the Reaction of o-Xylylene and Sulfur Dioxide''

=== External Transition State IRCs ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Diels-Alder Exo Transition State IRC
! style="background: #6ca0dc; color: white;" |Diels-Alder Endo Transition State IRC
! style="background: #6ca0dc; color: white;" |Chemetropic Transition State IRC
|-
| [[File:nrwy3ts_DA_EXO_TS_IRC.gif|500px|]]
| [[File:nrwy3ts_DA_ENDO_TS_IRC.gif|500px|]]
| [[File:nrwy3ts_CHELOTROPIC_TS_IRC.gif|500px|]]
|}

(Your exo TS is actually endo as well [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:03, 4 April 2018 (BST))

=== External Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Diels-Alder Endo
| 156.39
| 235.4534
| 56.4044
| 79.0634
| -99.9856
|-
| Diels-Alder Exo
| 156.39
| 235.4612
| 55.7804
| 79.0712
| -100.6096
|-
| Cheletropic
| 156.39
| 257.5612
| 0.013
| 101.1712
| -156.377
|}
'' Table 3 - Activation and Reaction Energies for the External Reactions between o-Xylylene and Sulfur Dioxide ''

From Table 3, it can be seen that the Diels-Alder reactions form a more favourable transition state than the Cheletropic pathway, although the Cheletropic product is lower in energy, at an almost 0 value, corresponding to the thermodynamic product. The increased stability in the product is due to the formation of 2 C-S bonds, and lack of breaking of a S-O bond. Although the C-O bond energy formed during the Diels-Alder reaction is greater than the C-S bonds only formed during the Cheletropic reaction, 358kJ/mol compared to 272kJ/mol<sup>3</sup>, this does not compensate the energy used breaking the S-O bond. The activation energy for the Cheletropic reaction is high due to the formation of a strained 5 membered ring, as opposed to the 6 membered ring formed during the Diels-Alder reaction. All products lead to a decrease in energy due to the produced aromatic molecule, with the Diels-Alder Endo product being the kinetic product due to the smallest activation energy, albeit only by a marginally small amount than the exothermic. The ability for o-Xylylene to form planar aromatic products is the reason for its high reactivity and low stability, at least at the external cis-butadiene site.

=== Reaction Coordinate Diagram ===

[[File:nrwy3ts_Ex_3_Reaction_Coordinate_Diagram.png|x600px|1000px]]

'' Figure 8 - Reaction Coordinate Diagram for the Reaction of o-Xylylene and Sulfur Dioxide''

=== Internal Transition State IRCs ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Exo IRC
! style="background: #6ca0dc; color: white;" |Endo IRC
|-
| [[File:nrwy3ts_Internal_DA_Exo_IRC.gif]]
| [[File:nrwy3ts_Internal_DA_Endo_IRC.gif]]
|}

=== Internal Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Diels-Alder Endo
| 156.39
| 265.382
| 170.5834
| 108.992
| 14.1934
|-
| Diels-Alder Exo
| 156.39
| 273.1404
| 174.9956
| 116.7504
| 18.6056
|}
'' Table 4 - Activation and Reaction Energies for the Internal Reactions between o-Xylylene and Sulfur Dioxide ''

When reacting with the internal cis-butadiene, there is no overall aromatic stabilisation, and the alkene bonds are left as unsubstituted and terminal. Hence in comparison to the external reaction, the internal is far less favoured, as not only is the activation energy higher, but the disturbing of the conjugated pi system leads to a destabilisation of the products in comparison to the reactants. From Table 3, it can be seen that the activation energy upon formation of the transition state with the internal cis-butadiene bond is greater than with the external, with both the endothermic and exothermic transition states. The overall reaction energy is actually positive for this cycloaddition, due to an increase in energy in the products from the reactants. Upon reacting at the internal cis-butadiene, not only is there a lack of aromatic stabilisation in comparison to the external reaction, but the planar conjugated structure is also disturbed.

== Conclusion ==

The reactants, transition states and products were all successfully optimised using Gaussian, with imaginary frequencies only obtained when expected on a transition state. Study into multiple electrocyclic reactions allowed determination of the molecular orbitals involved in the production of the transition state, of the change in bond lengths during a reaction, of the kinetic and thermodynamic products and how effects from non-bonding orbital interactions and aromatic stabilisation may affect the products produced. Use of both 631-G and PM6 allowed practice of situations with different basis sets and methods to produce the desired optimised transition state and products required for energy calculations and discussion, which agreed with the expected trends.

== References ==

1. Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. ISBN 978-3-86025-249-9.

2. S. S. Batsanov, Inorg. Mater., 2001, 37, 871-885.

3. Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds", 1958, 2nd ed., Butterworths, London

Rep:Mod:nrwy3ts

2018-04-07T09:35:03Z

Fv611: /* Exercise 1 */

= Transition States and Reactivity =

== Introduction ==

The aim of this lab was to investigate a number of Diels-Alder cyclic reactions using the program Gaussian, in order to determine the structure of the transition state formed during these reactions. The transition state in a reaction is the point of highest energy along a reaction coordinate, with a first derivative of zero, and a second negative derivative in the direction of the products, which occurs between the two energies of the reactants and the products, whose firsts derivative are also equal to zero. The enthalpy change of a reaction is determined by calculation of the difference in energy between these two points, and the activation energy corresponds to the difference in energy between the reactant minima and the transition state maxima.

In reality there are many degrees of freedom than seen in the 2D Reaction Coordinate plot, determined by the equation 3N-6, where N is the number of atoms in a molecule. The degrees of freedom can be used to plot a multidimensional Potential Energy Surface, and the reaction coordinate then plotted as a function of the degrees of freedom produced. Depending on the basis set selected, a greater number of basis vectors, such as with 631-G, can be utilised during calculation in order to produce a result with fewer approximations, at the expense of a longer calculation time. The Energy Profile normally corresponds to the minimum energy reaction pathway plotted from a Potential Energy Surface of a reaction, as there is the potential for there to be more than one saddle point on a Potential Energy Surface. In order to determine if the correct energy pathway is calculated using Gaussian, only one negative imaginary frequency should be seen, otherwise there is the possibility that the programme may have plotted another higher energy pathway instead.
[[File:nrwy3ts_Reaction_Coordinate_Diagram.png|x600px|600px]]

''Figure 1 - Reaction Coordinate Diagram''

Location of a transition state using Gaussian can be achieved via 3 different methods, depending on the initial knowledge of the transition state and the accuracy of the calculation required.

=== Method 1 ===
Involves the initial optimisation of the reactants and then placement of the reactants in a geometry similar to that of the transition state (such as 2.2Å being the average between the combined van der Waals radii and a C-C bond length), hence this method is unreliable unless some knowledge of the transition state is known. Although this is the quickest of the methods suggested, it is also the most unreliable, potentially producing multiple transition states, imaginary negative values or fail altogether. This method is best left for smaller systems if completely necessary.

=== Method 2 ===
Requires initial optimisation of the reactants, but during calculation of the transition state, bonds included in the reaction are frozen in place. This allows the system to be as close to the transition state as possible before optimisation, by allowing the unfrozen parts of the system to minimise around the frozen ‘bonds’. This method is more reliable than the previous method and almost as fast, yet still requires some understanding of the transition state before application.

=== Method 3 ===
Requires little knowledge of the transition state, and allows determination of the transition state from either the reactants or the products after optimisation. Using the desired product, the bonds which are formed during the transition state are frozen and placed a sensible distance apart (such as 2.4Å for a S-C bond). The broken bonds are frozen and optimised, then the transition state calculated. Although this is the most reliable of the methods, this method may fail if the transition state closely resembles the structure of the reactants when optimising and changing the structure from the products, as well as requiring multiple additional steps.

All these methods use a combination of both the semi-empirical method PM6 and the DFT method B3LYP, the former of which is quicker and used to optimise the structures initially, before the latter can further optimise the structure produced, giving a more reliable structure via the use of a greater amount of basis vectors.

== Exercise 1 ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job overall.)

The electrocyclic reaction between Ethene and Butadiene to form Cyclohexene was investigated to determine the orbitals involved in the formation of the transition state of the reaction, the energies of the relevant orbitals and the change in the bond lengths between the carbons upon formation of the transition state and products. The carbons are labelled as shown in Figure 2 and the change in bond lengths between the carbons reported in the table below.

=== Reaction Scheme ===

[[File:nrwy3ts_Cyclohexane_Reaction.png|x400px|400px]]

''Figure 2 - Reaction Scheme for the reaction of ethene and butadiene''

=== Molecular Orbital Diagram ===

[[File:nrwy3ts_MO_Diagram.png|x800px|2000px]]

''Figure 3 - Molecular Orbital Diagram for the reaction of ethene and butadiene''

In order for the orbitals to overlap and combine, the orbitals must have the same symmetry to produce a molecular orbital of that same symmetry. Therefore, only symmetric-symmetric and antisymmetric-antisymmetric interactions can occur to produce a non-zero orbital overlap integral and are ‘allowed’, conversely a symmetric-antisymmetric orbital overlap would produce a zero value orbital overlap integral and as such is a ‘forbidden’ reaction. The final produced molecular orbitals are of the same symmetry as the original molecular orbitals, and the energy of the products normally lower than that of the reactants, as discussed earlier. However, as this diagram depicts the formation of the transition state, the molecular orbitals are higher in energy than the final orbitals formed, as shown by the reaction coordinate diagram.

=== HOMOs and LUMOs for Reactants and Transition States ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Ethene HOMO
! style="background: #6ca0dc; color: white;" |Ethene LUMO
|-
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<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Butadiene HOMO
! style="background: #6ca0dc; color: white;" |Butadiene LUMO
|-
| <jmol><jmolApplet>
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<uploadedFileContents>BUTADIENE1.LOG</uploadedFileContents></jmolApplet></jmol>
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<uploadedFileContents>BUTADIENE1.LOG</uploadedFileContents></jmolApplet></jmol>
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Transition State HOMO -1
! style="background: #6ca0dc; color: white;" |2 - Transition State HOMO
|-
| <jmol><jmolApplet>
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |3 - Transition State LUMO
! style="background: #6ca0dc; color: white;" |4 - Transition State LUMO +1
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{| class="wikitable"
! style="background: #6ca0dc; color: white;" | Bond
! style="background: #6ca0dc; color: white;" | Reactants Bond Length/Å
! style="background: #6ca0dc; color: white;" | Transition State Bond Length/Å
! style="background: #6ca0dc; color: white;" | Product Bond Length/Å
|-
| C1-C2
| 1.35520
| 1.38177
| 1.53773
|-
| C2-C3
| -
| 2.11468
| 1.53582
|-
| C3-C4
| 1.33345
| 1.37979
| 1.49266
|-
| C4-C5
| 1.47077
| 1.41109
| 1.33305
|-
| C5-C6
| 1.33345
| 1.37979
| 1.49266
|-
| C6-C1
| -
| 2.11468
| 1.53582
|}
''Table 1 - Carbon Bond Lengths in the Formation of Cyclohexene''

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You should have explicitly stated that your carbon numbering is the one you use in your reaction scheme.)

From the table above, it can be seen that upon formation of the transition state, bonds C1-C2, C3-C4 and C5-C6 all lengthen as the sp hydridisation increases. Conversely, C4-C5 decreases from 1.47Å to 1.41Å due to the formation of a double bond from the single bond seen in the reactants and the increased s character of the MO. This bond further decreases upon completion of the double bond formation. The initial C6-C1 and C2-C3 'bonds' shorten in length, producing a value of 1.53582Å, incredibly close to the 1.54Å for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond<sup>1</sup>, showing the structure was successfully optimised by Gaussian. Due to the increased s character of the bonds when closer to the sp<sup>2</sup> carbons and C=C bond, there is a slight decrease in bond length from C1-C2 to C2-C3/C6-C1. As expected this increase in s character continues when looking at the bonds around the sp<sup>2</sup> C5 and C4, with the C3-C4/C5-C6 having intermediate values between the 1.54Å for a C-C bond and 1.34Å for an alkene C=C bond. This is consistent with the reported sp<sup>3</sup>-sp<sup>2</sup> value of 1.50Å<sup>1</sup>. The initial transition state produces a bond length of 2.11468Å for C2-C3/C6-C1, which decreases to 1.53582Å upon formation of cyclohexene. The initial bond length of 2.11468Å is comparable to the sum of two carbon van der Waals radii (3.400Å)<sup>2</sup>, and shows a bonding character interaction due to the shorter length observed.

=== Transition State Vibration and IRC ===

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'' Figure 4 - Reaction Path at the Transition State Vibration ''

Figure 4 shows the vibration corresponding to the imaginary frequency produced by the transition state, which represents the reaction path at the transition state. In the IRC, the bonds from the diene and alkene form at the same time, and such is a synchronous, concerted reaction.

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Transition State IRC
|-
| [[File:nrwy3ts_Ex1_Transition_State_IRC.gif]]
|}

==Exercise 2==

The molecular orbital diagrams for the Diels-Alder reaction between 1,3-dioxone and cyclohexadiene were produced to determine the molecular orbitals involved and the overlap of the orbitals in the transition state. Here the production of both the endothermic and exothermic products was investigated, where the approach of the dienophile 1,3-dioxone differs. During formation of the endothermic product, the ring oxygens approach beneath the alkene bonds in cyclohexadiene due to a favourable stabilising interaction. However for the exothermic product, the ring oxygens are positioned away from the alkene bonds. As seen in the previous exercise, only overlap between orbitals of the same symmetry is allowed for a reaction to occur.

=== Reaction Scheme ===

[[File:Reaction_Scheme_Exercise_2.png|x400px|400px]]

''Figure 4 - Reaction Scheme for the Reaction of Cyclohexadiene and 1,3-dioxole''

=== Molecular Orbital Diagram ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Exothermic MO Diagram
! style="background: #6ca0dc; color: white;" |Endothermic MO Diagram
|-
| [[File:nrwy3ts_Exo_MO_Diagram.png|x800px|2000px]]
| [[File:nrwy3ts_Endo_MO_Diagram.png|x800px|2000px]]
|}
''Figure 5 - Molecular Orbital Diagram for the Reaction of Cyclohexadiene and 1,3-dioxole''

A standard Diels-Alder reaction involves the combindation of a diene and a dienophile, where the HOMO of the diene interacts with the LUMO of the diene. However in the reaction investigated here, the electron donating oxygens in the 1,3-dioxone ring increase the energy of the HOMO of the alkene, and thus instead the HOMO of the alkene interacts with the LUMO of the diene in an inverse demand Diels-Alder reaction. Here it can be seen that molecular orbitals 1, 3 and 4 for the endothermic product are higher in energy than the exothermic counterparts, whilst molecular orbital 2 is lower in energy in the endothermic transition state than the exothermic. This effect seen in the endothermic product is due to secondary orbital interactions and is discussed later on, shown in the molecular orbital Jmol images below.

=== HOMOs and LUMOs for Reactants and Transition States ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1,3-Dioxole HOMO
! style="background: #6ca0dc; color: white;" |1,3-Dioxole LUMO
! style="background: #6ca0dc; color: white;" |Cyclohexadiene HOMO
! style="background: #6ca0dc; color: white;" |Cyclohexadiene LUMO
|-
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Exo Transition State LUMO +1
! style="background: #6ca0dc; color: white;" |2 - Exo Transition State LUMO
! style="background: #6ca0dc; color: white;" |3 - Exo Transition State HOMO
! style="background: #6ca0dc; color: white;" |4 - Exo Transition State HOMO -1
|-
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<uploadedFileContents>nrwy3ts_EXO_TS.LOG</uploadedFileContents></jmolApplet></jmol>
|}

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Endo Transition State LUMO +1
! style="background: #6ca0dc; color: white;" |2 - Endo Transition State LUMO
! style="background: #6ca0dc; color: white;" |3 - Endo Transition State HOMO
! style="background: #6ca0dc; color: white;" |4 - Endo Transition State HOMO -1
|-
| <jmol><jmolApplet>
<color>white</color>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>nrwy3ts_ENDO_TS_631G.LOG</uploadedFileContents></jmolApplet></jmol>
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<uploadedFileContents>nrwy3ts_ENDO_TS_631G.LOG</uploadedFileContents></jmolApplet></jmol>
| <jmol><jmolApplet>
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| <jmol><jmolApplet>
<color>white</color>
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<uploadedFileContents>nrwy3ts_ENDO_TS_631G.LOG</uploadedFileContents></jmolApplet></jmol>
|}

=== Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Endo
| -1313771.847
| -1313622.1573
| -1313852.8626
| 149.6897
| -81.01537
|-
| Exo
| -1313771.847
| -1313614.3096
| -1313845.7396
| 157.53763
| -73.8926
|}
'' Table 2 - Activation and Reaction Energies for the Reactions between Cyclohexadiene and 1,3-dioxole ''

From the calculated data in the table above, the exothermic product is shown to have a greater activation energy than the endothermic product. This can be explained by the lack of a non-bonding stabilising interaction between the ring oxygen orbitals overlapping with the alkene bond orbitals during the transition state, meaning the energy of the exothermic transition state is higher than that of the endothermic pathway. This secondary orbital overlap can been seen below (Figure 6). Both reactions are exothermic and thermodynamically favourable enough to overcome the decrease in entropy upon formation of the product. However, the endothermic product is the lower in energy and therefore most stable of the products, which may be due to reduced steric interactions with 1,3-dioxole species avoiding steric clashes with the carbon chain bridging the 2 C=C bonds. This leads to a further favouring of the endothermic product, with both the stabilising oxygen non-bonding interactions and the lack of steric repulsion by bridging carbons, as seen in the data produced.
(It should be noted that upon optimisation of the cyclohexadiene, a negative frequency was observed, corresponding to the stretching of the sp<sup>3</sup> C-H bonds. This resulted in a slightly higher energy in the products than expected.)

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Exo Transition State HOMO
! style="background: #6ca0dc; color: white;" |Endo Transition State HOMO
|-
| <jmol><jmolApplet>
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<uploadedFileContents>nrwy3ts_ENDO_TS_631G.LOG</uploadedFileContents></jmolApplet></jmol>
|}
'' Figure 6 - Secondary Orbital Effect ''

== Exercise 3 ==

O-Xylylene and sulfur dioxide undergo multiple cycloaddition reactions, which consist of a Diels-Alder and Cheletropic reaction, forming 10 and 9 membered rings respectively with the external cis-butadiene and 6 membered with the internal. During the [4+2] Diels-Alder reactions, the orientation of the SO<sub>2</sub> to the external cis-butadiene during formation of the transition state allows production of an exothermic and endothermic product. The preference of forming either the exothermic or endothermic product via a Diels-Alder reaction, or the cheletropic product, was investigated here by optimisation of each transition state at the PM6 level, and the energies calculated from the data. These pathways were then compared to the [4+2] cycloaddition pathways possible with the internal cis-butadiene.

(You should still count members of a ring by the smallest continuous joined system ie 5 and 6 for both external and internal reaction products [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:03, 4 April 2018 (BST))

=== Reaction Scheme ===

[[File:nrwy3ts_Ex_3_Reaction_Scheme.png|x500px|500px]]

'' Figure 7 - Reaction Scheme for the Reaction of o-Xylylene and Sulfur Dioxide''

=== External Transition State IRCs ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Diels-Alder Exo Transition State IRC
! style="background: #6ca0dc; color: white;" |Diels-Alder Endo Transition State IRC
! style="background: #6ca0dc; color: white;" |Chemetropic Transition State IRC
|-
| [[File:nrwy3ts_DA_EXO_TS_IRC.gif|500px|]]
| [[File:nrwy3ts_DA_ENDO_TS_IRC.gif|500px|]]
| [[File:nrwy3ts_CHELOTROPIC_TS_IRC.gif|500px|]]
|}

(Your exo TS is actually endo as well [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:03, 4 April 2018 (BST))

=== External Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Diels-Alder Endo
| 156.39
| 235.4534
| 56.4044
| 79.0634
| -99.9856
|-
| Diels-Alder Exo
| 156.39
| 235.4612
| 55.7804
| 79.0712
| -100.6096
|-
| Cheletropic
| 156.39
| 257.5612
| 0.013
| 101.1712
| -156.377
|}
'' Table 3 - Activation and Reaction Energies for the External Reactions between o-Xylylene and Sulfur Dioxide ''

From Table 3, it can be seen that the Diels-Alder reactions form a more favourable transition state than the Cheletropic pathway, although the Cheletropic product is lower in energy, at an almost 0 value, corresponding to the thermodynamic product. The increased stability in the product is due to the formation of 2 C-S bonds, and lack of breaking of a S-O bond. Although the C-O bond energy formed during the Diels-Alder reaction is greater than the C-S bonds only formed during the Cheletropic reaction, 358kJ/mol compared to 272kJ/mol<sup>3</sup>, this does not compensate the energy used breaking the S-O bond. The activation energy for the Cheletropic reaction is high due to the formation of a strained 5 membered ring, as opposed to the 6 membered ring formed during the Diels-Alder reaction. All products lead to a decrease in energy due to the produced aromatic molecule, with the Diels-Alder Endo product being the kinetic product due to the smallest activation energy, albeit only by a marginally small amount than the exothermic. The ability for o-Xylylene to form planar aromatic products is the reason for its high reactivity and low stability, at least at the external cis-butadiene site.

=== Reaction Coordinate Diagram ===

[[File:nrwy3ts_Ex_3_Reaction_Coordinate_Diagram.png|x600px|1000px]]

'' Figure 8 - Reaction Coordinate Diagram for the Reaction of o-Xylylene and Sulfur Dioxide''

=== Internal Transition State IRCs ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Exo IRC
! style="background: #6ca0dc; color: white;" |Endo IRC
|-
| [[File:nrwy3ts_Internal_DA_Exo_IRC.gif]]
| [[File:nrwy3ts_Internal_DA_Endo_IRC.gif]]
|}

=== Internal Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Diels-Alder Endo
| 156.39
| 265.382
| 170.5834
| 108.992
| 14.1934
|-
| Diels-Alder Exo
| 156.39
| 273.1404
| 174.9956
| 116.7504
| 18.6056
|}
'' Table 4 - Activation and Reaction Energies for the Internal Reactions between o-Xylylene and Sulfur Dioxide ''

When reacting with the internal cis-butadiene, there is no overall aromatic stabilisation, and the alkene bonds are left as unsubstituted and terminal. Hence in comparison to the external reaction, the internal is far less favoured, as not only is the activation energy higher, but the disturbing of the conjugated pi system leads to a destabilisation of the products in comparison to the reactants. From Table 3, it can be seen that the activation energy upon formation of the transition state with the internal cis-butadiene bond is greater than with the external, with both the endothermic and exothermic transition states. The overall reaction energy is actually positive for this cycloaddition, due to an increase in energy in the products from the reactants. Upon reacting at the internal cis-butadiene, not only is there a lack of aromatic stabilisation in comparison to the external reaction, but the planar conjugated structure is also disturbed.

== Conclusion ==

The reactants, transition states and products were all successfully optimised using Gaussian, with imaginary frequencies only obtained when expected on a transition state. Study into multiple electrocyclic reactions allowed determination of the molecular orbitals involved in the production of the transition state, of the change in bond lengths during a reaction, of the kinetic and thermodynamic products and how effects from non-bonding orbital interactions and aromatic stabilisation may affect the products produced. Use of both 631-G and PM6 allowed practice of situations with different basis sets and methods to produce the desired optimised transition state and products required for energy calculations and discussion, which agreed with the expected trends.

== References ==

1. Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. ISBN 978-3-86025-249-9.

2. S. S. Batsanov, Inorg. Mater., 2001, 37, 871-885.

3. Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds", 1958, 2nd ed., Butterworths, London

Rep:Mod:em2815ts

2018-04-07T09:01:37Z

Fv611: /* Molecular Orbitals */

=Introduction=

===Potential Energy Surfaces===

A potential energy surface (PES) describes the energy of a system in terms of certain parameters, for example nuclear position. For a linear molecule, the potential energy is dependent on 3N-6 degrees of freedom ie normal modes of vibration, where N = the number of atoms.<ref name="one"/> From the PES, a reaction coordinate can be derived; this is a progress variable which describes the reaction. It shows the progression of reactants to products and predicts the exact probability that a certain configuration will reach the product state.

The salient points on a PES are the stationary points, where the gradient, given by the first derivative, is 0. These points correspond to the reactants, products or transition states of the reaction. The curvature of these points, indicated by the second derivative, indicates the type of stationary point and allows the differentiation between the minima and the transition state.

It can be noted that the gradient and curvature of these points correspond to the force and force constant, respectively.

====Reactants and Products====
If the second derivative is > 0 with respect to all 3N-6 degrees of freedom, the stationary point is a minimum. This represents a minimum on the reaction coordinate. There are different types of minima, for example global and relative: the former is the lowest energy minimum which corresponds to the products and the latter can correspond to the reactants.
====Transition State====
If the second derivative is < 0 along the reaction coordinate but > 0 for all other degrees of freedom (in other words, a maximum along the reaction coordinate but a minimum in all other directions), the stationary point corresponds to a transition state. This gives rise to a single negative Hessian eigenvalue and represents a maximum energy point along the reaction coordinate (it is the maximum on the minimum energy path which connects the reactant and product minima).

===Computational Methods===

During this investigation, GaussView was used to locate the transition states of the relevant reactions. Two main computational methods were used, PM6 and B3LYP. PM6 is a fitted semi-empirical method which uses experimental data, ie previously calculated integrals, to solve the Hamiltonian matrix. This method is advantageous since it does not need to calculate all of the integrals in each optimisation; this makes it less expensive and also much faster. The PM6 method is, however, less accurate because it uses many approximations.<ref name="two"/> <ref name="three"/>

B3LYP is a method which uses Density Functional Theory (which uses the electron density) to calculate the terms of the Hamiltonian and the Hartree Fock calculation (which uses electronic position) to find the exchange correlation terms.<ref name="two"/> This method is extremely accurate but it is slower than the PM6 method since it does not use precalculated values. In this investigation, the B3LYP method uses the 6-31G(d) basis set, which is a set of functions which represent atomic orbitals which can be linearly combined to form molecular orbitals.<ref name="four"/> The 6-31G(d) set is high enough such that enough atomic orbitals are used to give an accurate view of the molecular orbitals without costing the computational effort too much. Higher basis sets result in higher computational effort which is expensive and time-consuming; the 6-31G(d) basis set offers a good compromise between accuracy and computational effort.

===Locating the Transition State===

The following methods were used to locate the transition states.

====Method 1====
Method 1 involves the use of the previously PM6 optimised reactants to estimate the transition state structure by altering the distances between the reacting terminii. The estimated structure is then optimised to a transition state at the PM6 or/and B3LYP/6-31G(d) level(s). This method is good because it is the fastest, but it is very unreliable and requires knowledge of the transition state (it will only work if the initial guess of the transition state structure is extremely close to the actual structure).

====Method 2====
Method 2 is similar to method 1 in that it involves the use of previously optimised reactants. The optimised reactants are placed close together and the distances between the reacting atoms are set. These pairs of reacting atoms are then 'frozen' and the frozen structure is optimised to a minimum. The resulting molecule is then optimised to a transition state at the PM6 level and can be further optimised at the B3LYP/6-31G(d) level. This method is much more reliable than method 1.

====Method 3====
Method 3 is slightly different to methods 1 and 2 in that it begins with the product. The product is constructed and optimised to a minimum at the PM6 level. The new bonds which have formed during the reaction are then broken and the distances between the reacting atoms are set. These bonds are then frozen and the structure is optimised to a minimum at the PM6 level. The resulting molecule from this calculation is then optimised to a transition state at the PM6 level and can be optimised further at the B3LYP/6-31G(d) level. Method 3 is the most reliable method since it does not require knowledge of the transition state and it is very easy and more likely to succeed. The only downsides of this method are that it requires more steps and that it may not work with all reactions.

====Checks====
The success of each optimisation was determined by analysing the vibrations/frequency calculations. All molecules which were successfully optimised to a minimum yielded all positive frequencies whereas molecules which were successfully optimised to a transition state resulted in the first normal mode having a negative frequency, indicative of an imaginary number. The transition state has a negative force constant, therefore when substituted into the equation for the simple harmonic oscillator, the output frequency is an imaginary number.

=Part 1: Reaction of 1,3-butadiene with Ethene=

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Great work across the whole exercise. Well done!)

Scheme 1 shows the Diels Alder reaction of ethene and 1,3-butadiene.

[[File:Em2815 e1 scheme.png|thumb|center|Scheme 1 : the reaction of ethene and 1,3-butadiene]]

The reactants were optimised at the PM6 level and the transition state was located using method 3, also at the PM6 level. The success of this reaction was confirmed by the presence of an imaginary frequency at 948.48i cm<sup>-1</sup>. The MOs generated computationally have been correlated with the MOs in Fig 1a (see Table 1).

===Molecular Orbitals===

The molecular orbital diagram for this reaction can be seen in Fig 1a and the molecular orbitals found computationally can be seen below.

[[File:Em2815_exercise1_modiagram.png|480px|thumb|center|Figure 1a: MO diagram for the reaction of ethene and 1,3-butadiene]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 1: shows the important MOs generated computationally for 1,3-butadiene, ethene and the transition state
!Ethene
!1,3-butadiene
!Transition State
|-
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LUMO (corresponds to MO 3)

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LUMO (corresponds to MO 2)

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LUMO +1 (corresponds to MO 8)

|-
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LUMO (corresponds to MO 7)
|-
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HOMO (corresponds to MO 4)

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HOMO (corresponds to MO 1)

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HOMO (corresponds to MO 6)

|-
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HOMO-1 (corresponds to MO 5)

|}

The MO diagram shows that the LUMO of 1,3-butadiene combines with the HOMO of ethene in-phase and out-of-phase to generate the HOMO and LUMO of the transition state, respectively. The HOMO of 1,3-butadiene also combines with the LUMO of ethene in-phase (a stabilising interaction) to generate HOMO-1 and out of phase (a destabilising interaction) to generate LUMO+1.

Evidently, orbitals of the same symmetry combine to form a molecular orbital with a retention of symmetry. Hence, two symmetric orbitals overlap to form an orbital which is symmetric and two antisymmetric orbitals overlap to form an antisymmetric orbital. If the orbitals have the same symmetry, they will overlap spatially and so the overlap integral will be non-zero (thus, the overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions and 0 for antisymmetric-symmetric interactions). This shows that for a reaction to be allowed, there is a requirement for the symmetry to be the same.<ref name="five"/>

In normal electron demand Diels Alder reactions, the HOMO of the diene and the LUMO of the dienophile are closer in energy than the LUMO of the diene and the HOMO of the dienophile.<ref name="six"/> After obtaining the energies of the molecular orbitals by looking at the MO analysis, it was found that this statement is true for this case, hence the reaction between 1,3-butadiene and ethene involves normal electron demand.

===Carbon-Carbon Bond Lengths===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: the carbon-carbon bond lengths in the reactants, transition state and cyclohexadiene product
!'''Bond'''
|'''''Bond Length in Reactants''' '''(Å)'''''
|'''''Bond Length in Transition State (Å)'''''
|'''Bond Length in Product ''(Å)'''''
|-
!1-2
|1.3334
|1.3798
|1.5008
|-
!2-3
|1.4708
|1.4111
|1.3370
|-
!3-4
|1.3334
|1.3798
|1.5009
|-
!4-5
|N/A
|2.1147
|1.5371
|-
!5-6
|1.3273
|1.3818
|1.5346
|-
!6-1
|N/A
|2.1148
|1.5371
|-
|}

The carbon-carbon bond lengths in ethene, 1,3-butadiene, the transition state and the cyclohexene product are shown in Table 2. It can be seen that bonds 1-2 and 3-4 get longer as the reaction proceeds from the reactants to the products; this makes sense since the hybridisation of the carbon atoms is changing from sp<sup>2</sup> to sp<sup>3</sup> as the double bonds change to single bonds. As expected, bond 2-3 gets shorter as the cyclohexene double bond forms (the carbon atoms go from sp<sup>3</sup> to sp<sup>2</sup>). Bonds 4-5 and 6-1 become shorter from the transition state to the product as the reacting terminii approach each other as the bonds form. It can be noted that the distances between the two pairs of reacting atoms in the transition state (4-5 and 6-1) are shorter than 2x the Van der Waals radius of the C atom (1.70 Å), thus confirming the interaction between the reacting terminii and the partial formation of these bonds in the transition state.

The bond lengths obtained computationally are mostly consistent with the typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths of 1.34 and 1.54 Å, respectively.<ref name="seven"/> One deviation, however, is bond 2-3 in the reactant butadiene. This length is slightly shorter than the typical sp<sup>3</sup> C-C bond length due to the delocalised pi system. Another notable deviation involves bonds 1-2 and 3-4 in the product, which are shorter than the expected sp<sup>3</sup> length due to the fact that one carbon atom of each of these bonds is sp<sup>2</sup> hybridised.

===Vibration Analysis===

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<target>ex1_TS</target>
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</jmol>

Fig 1b: the vibration at the transition state of the reaction between 1,3-butadiene and ethene

The vibration which corresponds to the reaction path at the transition state (see Fig 1b) is the vibration with the negative (imaginary) frequency. The animation shows that the reacting terminii of both reactants move towards each other simultaneously as the two new bonds form synchronously (ie, at the same time). This is also confirmed by the IRC, since both bonds form in Step 10 .

===Log Files===

[[Media:Em2815 e1 butadiene minPM6.LOG|LOG file of 1,3-butadiene minimum PM6]]

[[Media:Em2815 e1 ethene minPM6.LOG|LOG file of ethene minimum PM6]]

[[Media:Em2815 e1 cycloadd TS PM6.LOG|LOG file of transition state PM6]]

[[Media:em2815_e1_IRC.LOG|LOG file of IRC PM6]]

[[Media:Em2815_e1_product_min_PM6.LOG|LOG file of product minimum PM6]]

=Part 2: Reaction of Cyclohexadiene and 1,3-dioxole=

Scheme 2 shows the Diels Alder reaction of cyclohexadiene and 1,3-dioxole. This reaction can go via two pathways: exo or endo.

[[File:em2815_e2_scheme_720p.png|380px|thumb|center|Scheme 2: the reaction of cyclohexadiene with 1,3-dioxole to give the exo and endo products]]

The reactants and products were optimised at the B3LYP/6-31G(d) level and the transition state was located using method 3, also at the B3LYP/6-31G(d) level. The success of the endo and exo reactions were confirmed by the presence of the imaginary frequencies at 520.90i and 528.79i cm<sup>-1</sup>, respectively. The MOs generated computationally have been correlated with the MOs in Fig 2 (see Table 3).

===Molecular Orbitals===

The molecular orbital diagram for the exo reaction can be seen in Fig 2 and the molecular orbitals found computationally can be seen below.

[[File:em2815_e2_MO_480p.png|400px|thumb|center|Figure 2: the MO diagram for the exo pathway of the reaction of cyclohexadiene with 1,3-dioxole]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 3: shows the important MOs generated computationally for 1,3-dioxole, cyclohexadiene and the exo and endo transition states
!Cyclohexadiene
!1,3-dioxole
!Endo Transition State
!Exo Transition State
|-
| rowspan="2" |<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 18; mo 24; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e2_endo_cyclohexadiene_min_B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO (corresponds to MO 2)

| rowspan="2" |<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 24; mo 20; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e2_dioxole_min_B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO (corresponds to MO 4)

|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>A2 em2815 e2 endo ts B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO +1 (analogous to MO 8)

|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>E2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO +1 (corresponds to MO 8)

|-
|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>A2 em2815 e2 endo ts B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO (analogous to MO 7)

|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>E2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO (corresponds to MO 7)

|-
| rowspan="2" |<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e2_endo_cyclohexadiene_min_B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
HOMO (corresponds to MO 1)

| rowspan="2" |<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 24; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e2_dioxole_min_B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
HOMO (corresponds to MO 3)

|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>A2 em2815 e2 endo ts B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
HOMO (analogous to MO 6)

|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>E2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
HOMO (corresponds to MO 6)

|-
|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>A2 em2815 e2 endo ts B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
HOMO-1 (analogous to MO 5)

|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>E2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet></jmol>
HOMO-1 (corresponds to MO 5)

|}

The MO diagram shows that the LUMO of cyclohexadiene combines with the HOMO of 1,3-dioxole in-phase and out-of-phase to generate the HOMO and LUMO of the transition state, respectively. The HOMO of cyclohexadiene also combines with the LUMO of 1,3-dioxole in-phase (a stabilising interaction) to generate HOMO-1 and out of phase (a destabilising interaction) to generate LUMO+1.

This MO diagram can be compared to that of the Diels Alder reaction in Part 1. The presence of the electron-donating oxygen atoms in 1,3-dioxole destabilises the HOMO and LUMO of the alkene therefore they are higher in energy compared to the simple ethene molecule. This means that the HOMO of the electron deficient 1,3-dioxole is closer in energy to the LUMO of the electron rich cyclohexadiene, hence these are the orbitals that overlap and interact. Since the HOMO of the alkene (dienophile) and the LUMO of the diene are closer in energy than the LUMO of the alkene and the HOMO of the diene, the reaction goes via inverse electron demand.<ref name="five"/><ref name="six"/>

It is worth noting that the endo pathway would produce transition state molecular orbitals which are lower energy than those depicted for the exo pathway.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You can't compare MO energies on different potential energy surfaces, so your last point should have been discussed in terms of relative energy gaps instead.)

===Thermochemistry===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 4: shows the activation and reaction energies of the endo and exo pathways of the reaction of 1,3-dioxole with cyclohexadiene
!
!Endo
!Exo
|-
!Activation Energy (kJ/mol)
|<nowiki>+157.53</nowiki>
|<nowiki>+165.41</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>-70.89</nowiki>
|<nowiki>-65.64</nowiki>
|}

The 'Thermochemistry Data' from the optimisations were used to calculate the activation and reaction energies of the exo and endo pathways, see Table 4. Since the endo pathway has a smaller activation energy, it is kinetically favoured and leads to the kinetic/endo product, which is faster formed. This is the case because there is less steric clash in the endo transition state. Another possible reason is a stabilising secondary orbital overlap between the pi system of the diene and the pi orbitals of both oxygen atoms in 1,3-dioxole which decreases the energy of the transition state, lowering the activation energy.

The reaction energy for the endo pathway is also more negative than that for the exo pathway, suggesting that the endo product is the more thermodynamically stable (lower energy) product. This is the case because of the same reasons discussed earlier: the secondary orbital interaction is also present in the endo product and there is less steric clash. Hence, the endo product is kinetically and thermodynamically favoured.

The exo pathway has a larger activation energy and a smaller reaction energy than the endo pathway. This shows that the exo product is less thermodynamically stable (higher energy) than the endo product. The aforementioned secondary orbital interaction is not possible in the exo product since the 1,3-dioxole molecule is in the wrong orientation for the pi systems of the oxygen atoms and the diene to overlap. The exo product therefore does not benefit from the additional stabilisation, and this coupled with the fact that there is more steric clash means that the exo product is higher in energy.

===Log Files===

[[Media:Em2815 e2 dioxole min B3LYP.LOG|LOG file of dioxole minimum B3LYP]]

[[Media:Em2815 e2 endo cyclohexadiene min B3LYP.LOG|LOG file of cyclohexadiene minimum B3LYP]]

[[Media:A2 em2815 e2 endo ts B3LYP.LOG|LOG file of endo transition state B3LYP]]

[[Media:E2 EXO TS B3LYP.LOG|LOG file of exo transition state B3LYP]]

[[Media:Em2815 e2 endo product min B3LYP.LOG|LOG file of endo product minimum B3LYP]]

[[Media:Em2815 e2 exo product min B3LYP.LOG|LOG file of exo product minimum B3LYP]]

[[Media:Em2815 e2 endo irc.LOG|LOG file of endo IRC]]

[[Media:Em2815 e2 exo IRC.LOG|LOG file of exo IRC]]

=Part 3: Reaction of o-Xylylene and SO<sub>2</sub>=

Scheme 3 shows the Diels Alder and Cheletropic reactions of o-xylylene and SO<sub>2</sub>.

[[File:em2815_e3_scheme_.png|480px|thumb|center|Scheme 3: the Diels Alder and Cheletropic reactions of o-xylylene with SO<sub>2</sub>]]

The reactants and products were optimised at the PM6 level and the transition state was located using method 3, also at the PM6 level. The success of the endo, exo and cheletropic reactions were confirmed by the presence of the imaginary frequencies at 333.79i, 351.67i and 486.55i cm<sup>-1</sup>, respectively.

===IRC Calculations===

The Intrinsic Reaction Coordinate calculations for the endo, exo and cheletropic reactions can be seen in Figs 3a, 3b and 3c. Evidently, for the Diels Alder reactions, the reacting terminii of both reactants move towards each other at different rates. The C-O and C-S bonds are formed at different rates due to asymmetry, hence the bond formation is asynchronous. For the endo pathway, the C-S bond forms in step 56 whereas the C-O bond forms in step 52 and for the exo pathway, the C-S and C-O bonds form in steps 64 and 60, respectively. This however is not the case for the cheletropic reaction. Since this reaction is symmetric, the reacting terminii move towards each other at the same rate and the C-S bonds are formed synchronously (both C-S bonds form in step 78 of the IRC).

(Don't use the word "rate" here, as their formation is staggered in time. It's very difficult to say when exactly a "bond" is formed. The bonds that GaussView uses are aesthetic (except in molecular mechanical calculations) and are decided when atoms cross a cutoff distance [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:48, 4 April 2018 (BST))

[[File:em2815_e3_endo_IRC.gif|450px|thumb|center|Figure 3a : IRC for the Endo Diels-Alder Reaction of o-xylylene and SO<sub>2</sub>]]
[[File:em2815_e3_exo_IRC.gif|450px|thumb|center|Figure 3b : IRC for the Exo Diels-Alder Reaction of o-xylylene and SO<sub>2</sub>]]
[[File:em2815_e3_cheletropic_IRC.gif|450px|thumb|center|Figure 3c : IRC for the Cheletropic Reaction of o-xylylene and SO<sub>2</sub>]]

====o-Xylylene Stability====
The IRCs for the reactions show that the two double bonds in the 6 membered ring of xylylene break and a delocalised ring structure forms. This shows that xylylene is extremely reactive since there is a very large driving force for aromatisation.

===Thermochemistry===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 5: shows the activation and reaction energies of the endo, exo and cheletropic pathways of the reaction of o-xylylene with SO<sub>2</sub>
!
!Endo
!Exo
!Cheletropic
|-
!Activation Energy (kJ/mol)
|<nowiki>+82.72</nowiki>
|<nowiki>+86.72</nowiki>
|<nowiki>+105.08</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>-98.04</nowiki>
|<nowiki>-98.71</nowiki>
|<nowiki>-155.01</nowiki>
|}

The 'Thermochemistry Data' were used to calculate the activation and reaction energies of each of the three pathways, see Table 5. The endo pathway has the smallest activation energy, therefore it is kinetically favoured (thus the endo product is the kinetic product). The endo transition state could be lower in energy because there is reduced steric clash. It may also be stabilised by a secondary orbital overlap between the pi systems of the xylylene and the oxygen atoms from SO<sub>2</sub>. Since these factors stabilise the transition state, they result in a lower activation barrier.

The exo transition state has more steric clash and does not benefit from the secondary orbital overlap therefore it is higher in energy. Furthermore, the cheletropic transition state consists of a highly strained 5 membered ring. This is much higher in energy than the 6 membered ring in the exo and endo transition states (6 membered rings are essentially strain-free), therefore the cheletropic transition state is much less stable, resulting in the largest activation barrier.

The cheletropic reaction has the most negative reaction energy, indicating that the cheletropic product is the most energetically stable and therefore the thermodynamic product. This is the case because the S=O bonds are extremely strong and high energy therefore they stabilise the product.

The values for activation energy and reaction energy were used to generate the reaction profile shown in Fig 4.

[[File:Em2815_reactionprofileyay.png|550px|thumb|center|Figure 4: the reaction profile for the Diels Alder and Cheletropic pathways of the reaction of o-xylylene with SO<sub>2</sub>]]

===Alternative Diels-Alder Pathway===

So far, the reaction at the terminal diene has been discussed. There is also an alternative reaction pathway involving the second cis-butadiene fragment which is in the 6 membered ring of o-xylylene. See Scheme 4.

[[File:em2815_e3_altscheme_720p.png|480px|thumb|center|Scheme 4: the alternative reaction pathway involving the cis-butadiene fragment in the o-xylylene ring]]

The IRC calculations and thermodynamic data for the exo and endo pathways involving this cis-butadiene fragment can be seen below in Figs 5a & 5b and Table 6. The activation energies for both pathways are extremely high, indicating that reactions at this site are very kinetically unfavourable. The reaction energies are also positive, indicating that both the exo and endo products are relatively high in energy compared to the products of terminal diene pathway discussed earlier. Since both products are less stable, there is a lower driving force for the xylylene compound to react at this site. The positive reaction energy also indicates that the reactions are endothermic and hence thermodynamically unfavourable.

[[File:em2815_e3_ringendo_IRC.gif|450px|thumb|center|Figure 5a : IRC for the endo Diels-Alder reaction of o-xylylene and SO<sub>2</sub> at the alternative site]]
[[File:em2815_e3_ringexo_IRC.gif|450px|thumb|center|Figure 5b : IRC for the exo Diels-Alder reaction of o-xylylene and SO<sub>2</sub> at the alternative site]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 6: shows the activation and reaction energies of the endo and exo pathways of the reaction of o-xylylene with SO<sub>2</sub> at the alternative site
!
!Endo
!Exo
|-
!Activation Energy (kJ/mol)
|<nowiki>+112.94</nowiki>
|<nowiki>+120.78</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>+17.22</nowiki>
|<nowiki>+21.67</nowiki>
|}

The kinetic and thermodynamic unfavourability of these pathways can be explained by the fact that these reactions do not achieve aromatisation of the xylylene ring in the product. The conjugation is also lost in this pathway, therefore the reactants are much less stable and are disfavoured. Aromatisation and conjugation can however be achieved and maintained in the reaction occurring at the terminal diene, therefore this is the kinetically and thermodynamically favourable site of the reaction.

===Log Files===

[[Media:Em2815_SO2_REACTANT_MINIMUM_PM6.LOG|LOG file of SO<sub>2</sub> Reactant Minimum PM6 ]]

[[Media:Em2815_e3_XYLYLENE_REACTANT_MINIMUM_PM6.LOG|LOG file of o-Xylylene Reactant Minimum PM6 ]]

[[Media:Em2815_e3_ENDO_TS_PM6.LOG‎|LOG file of endo transition state PM6 ]]

[[Media:Em2815_e3_ENDO_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of endo product minimum PM6 ]]

[[Media:Em2815_e3_Exo_TS_PM6.LOG‎|LOG file of exo transition state PM6 ]]

[[Media:Em2815_e3_Exo_Product_Minimum_PM6.LOG‎|LOG file of exo product minimum PM6 ]]

[[Media:Em2815_e3_CHELETROPIC_TS_PM6.LOG‎|LOG file of cheletropic transition state PM6 ]]

[[Media:E3_CHELETROPIC_MINIMUM_PROD_PM6.LOG|LOG file of cheletropic product minimum PM6 ]]

[[Media:Em2815 e3 ENDO IRC PM6.LOG|LOG file of endo pathway IRC]]

[[Media:Em2815 e3 EXO IRC PM6.LOG|LOG file of exo pathway IRC]]

[[Media:Em2815 e3 CHELETROPIC IRC PM6.LOG|LOG file of cheletropic pathway IRC ]]

Alternative Pathway

[[Media:Em2815_e3_ENDO_RING_TS_PM6.LOG‎|LOG file of endo transition state (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_ENDO_RING_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of endo product minimum(reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_EXO_RING_TS_PM6.LOG‎|LOG file of exo transition state (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_EXO_RING_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of exo product minimum (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815 e3 ENDO RING IRC PM6.LOG|LOG file of endo pathway (reacting in the xylylene ring) IRC]]

[[Media:Em2815 e3 EXO RING IRC PM6.LOG|LOG file of exo pathway (reacting in the xylylene ring) IRC]]

=Conclusion=

This investigation used the PM6 and B3LYP/6-31G(d) computational methods to locate the transition states of various cycloaddition reactions. Method 3 proved to be the most efficient and reliable method which lead to successful calculations. It was found that the type of reactants affected the type of reaction occurring; from part 1 to part 2, the addition of the heteroatoms in the alkene resulted in an inverse electron demand reaction, affecting the ordering of the orbitals involved in the reaction.

For part 2, the competition of different reacting pathways was investigated. The exo and endo pathways of the Diels Alder reaction of cyclohexadiene with 1,3-dioxole were observed and it was found that the endo pathway has a lower activation barrier than the exo pathway therefore the endo product is kinetically favoured. This product was also found to be more stable than the exo product, hence it is thermodynamically favoured too. It has been suggested that the kinetic and thermodynamic favouring of the endo product is due to the reduced steric clash and the secondary orbital overlap between the pi orbitals of the oxygen atoms and the pi system of the diene, which is only possible in the endo configuration.

In part 3, the competition of three different reacting pathways was investigated. SO<sub>2</sub> can react with o-xylylene in a Diels Alder fashion, with one S atom and one O atom as part of a 6 membered ring, or in a cheletropic fashion, with just the S atom as part of a 5 membered ring. It was found that the endo product is kinetically favoured for this reaction since it has the smallest activation energy, however the thermodynamically favoured product is the cheletropic molecule. Although the cheletropic transiton state is disfavoured in terms of kinetics (due to the strained 5 membered ring), it is the most thermodynamically stable due to its strong and unreactive S=O bonds.

=References=

<references>
<ref name="one">
P. Atkin, J. Paula, ''Physical chemistry'', 8th edn, 2006.
</ref>

<ref name="two">
X. Qu, D. Latino and J. Aires-De-sousa, ''J. Cheminform''., 2013, '''5''', 1.
</ref>

<ref name="three">
E. Lewars, ''Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics'', 1st edn, 2011.
</ref>

<ref name="four">
F. Jensen, ''Wiley Interdiscip. Rev. Comput. Mol. Sci.'', 2013, '''3''', 273–295.
</ref>

<ref name="five">
R. Hoffmann and R. B. Woodward, ''Acc. Chem. Res.'', 1968, '''1''', 17–22.
</ref>

<ref name="six">
D. Boger, ''Progress in Heterocyclic Chemistry'', 1st edn, 1989.
</ref>

<ref name="seven">
H. J. Bernstein, ''Trans. Faraday Soc.'', 1961, '''57''', 1649–1656.
</ref>

Rep:Mod:em2815ts

2018-04-07T08:57:26Z

Fv611: /* Part 1: Reaction of 1,3-butadiene with Ethene */

=Introduction=

===Potential Energy Surfaces===

A potential energy surface (PES) describes the energy of a system in terms of certain parameters, for example nuclear position. For a linear molecule, the potential energy is dependent on 3N-6 degrees of freedom ie normal modes of vibration, where N = the number of atoms.<ref name="one"/> From the PES, a reaction coordinate can be derived; this is a progress variable which describes the reaction. It shows the progression of reactants to products and predicts the exact probability that a certain configuration will reach the product state.

The salient points on a PES are the stationary points, where the gradient, given by the first derivative, is 0. These points correspond to the reactants, products or transition states of the reaction. The curvature of these points, indicated by the second derivative, indicates the type of stationary point and allows the differentiation between the minima and the transition state.

It can be noted that the gradient and curvature of these points correspond to the force and force constant, respectively.

====Reactants and Products====
If the second derivative is > 0 with respect to all 3N-6 degrees of freedom, the stationary point is a minimum. This represents a minimum on the reaction coordinate. There are different types of minima, for example global and relative: the former is the lowest energy minimum which corresponds to the products and the latter can correspond to the reactants.
====Transition State====
If the second derivative is < 0 along the reaction coordinate but > 0 for all other degrees of freedom (in other words, a maximum along the reaction coordinate but a minimum in all other directions), the stationary point corresponds to a transition state. This gives rise to a single negative Hessian eigenvalue and represents a maximum energy point along the reaction coordinate (it is the maximum on the minimum energy path which connects the reactant and product minima).

===Computational Methods===

During this investigation, GaussView was used to locate the transition states of the relevant reactions. Two main computational methods were used, PM6 and B3LYP. PM6 is a fitted semi-empirical method which uses experimental data, ie previously calculated integrals, to solve the Hamiltonian matrix. This method is advantageous since it does not need to calculate all of the integrals in each optimisation; this makes it less expensive and also much faster. The PM6 method is, however, less accurate because it uses many approximations.<ref name="two"/> <ref name="three"/>

B3LYP is a method which uses Density Functional Theory (which uses the electron density) to calculate the terms of the Hamiltonian and the Hartree Fock calculation (which uses electronic position) to find the exchange correlation terms.<ref name="two"/> This method is extremely accurate but it is slower than the PM6 method since it does not use precalculated values. In this investigation, the B3LYP method uses the 6-31G(d) basis set, which is a set of functions which represent atomic orbitals which can be linearly combined to form molecular orbitals.<ref name="four"/> The 6-31G(d) set is high enough such that enough atomic orbitals are used to give an accurate view of the molecular orbitals without costing the computational effort too much. Higher basis sets result in higher computational effort which is expensive and time-consuming; the 6-31G(d) basis set offers a good compromise between accuracy and computational effort.

===Locating the Transition State===

The following methods were used to locate the transition states.

====Method 1====
Method 1 involves the use of the previously PM6 optimised reactants to estimate the transition state structure by altering the distances between the reacting terminii. The estimated structure is then optimised to a transition state at the PM6 or/and B3LYP/6-31G(d) level(s). This method is good because it is the fastest, but it is very unreliable and requires knowledge of the transition state (it will only work if the initial guess of the transition state structure is extremely close to the actual structure).

====Method 2====
Method 2 is similar to method 1 in that it involves the use of previously optimised reactants. The optimised reactants are placed close together and the distances between the reacting atoms are set. These pairs of reacting atoms are then 'frozen' and the frozen structure is optimised to a minimum. The resulting molecule is then optimised to a transition state at the PM6 level and can be further optimised at the B3LYP/6-31G(d) level. This method is much more reliable than method 1.

====Method 3====
Method 3 is slightly different to methods 1 and 2 in that it begins with the product. The product is constructed and optimised to a minimum at the PM6 level. The new bonds which have formed during the reaction are then broken and the distances between the reacting atoms are set. These bonds are then frozen and the structure is optimised to a minimum at the PM6 level. The resulting molecule from this calculation is then optimised to a transition state at the PM6 level and can be optimised further at the B3LYP/6-31G(d) level. Method 3 is the most reliable method since it does not require knowledge of the transition state and it is very easy and more likely to succeed. The only downsides of this method are that it requires more steps and that it may not work with all reactions.

====Checks====
The success of each optimisation was determined by analysing the vibrations/frequency calculations. All molecules which were successfully optimised to a minimum yielded all positive frequencies whereas molecules which were successfully optimised to a transition state resulted in the first normal mode having a negative frequency, indicative of an imaginary number. The transition state has a negative force constant, therefore when substituted into the equation for the simple harmonic oscillator, the output frequency is an imaginary number.

=Part 1: Reaction of 1,3-butadiene with Ethene=

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Great work across the whole exercise. Well done!)

Scheme 1 shows the Diels Alder reaction of ethene and 1,3-butadiene.

[[File:Em2815 e1 scheme.png|thumb|center|Scheme 1 : the reaction of ethene and 1,3-butadiene]]

The reactants were optimised at the PM6 level and the transition state was located using method 3, also at the PM6 level. The success of this reaction was confirmed by the presence of an imaginary frequency at 948.48i cm<sup>-1</sup>. The MOs generated computationally have been correlated with the MOs in Fig 1a (see Table 1).

===Molecular Orbitals===

The molecular orbital diagram for this reaction can be seen in Fig 1a and the molecular orbitals found computationally can be seen below.

[[File:Em2815_exercise1_modiagram.png|480px|thumb|center|Figure 1a: MO diagram for the reaction of ethene and 1,3-butadiene]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 1: shows the important MOs generated computationally for 1,3-butadiene, ethene and the transition state
!Ethene
!1,3-butadiene
!Transition State
|-
| rowspan="2" |<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e1_ethene_minPM6.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO (corresponds to MO 3)

| rowspan="2" |<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e1_butadiene_minPM6.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO (corresponds to MO 2)

|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e1_cycloadd_TS_PM6.LOG</uploadedFileContents>
</jmolApplet></jmol>
LUMO +1 (corresponds to MO 8)

|-
|<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e1_cycloadd_TS_PM6.LOG</uploadedFileContents>
</jmolApplet></jmol>

LUMO (corresponds to MO 7)
|-
| rowspan="2" |<jmol><jmolApplet>
<color>#F9F9F9</color>
<size>150</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>em2815_e1_ethene_minPM6.LOG</uploadedFileContents>
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HOMO (corresponds to MO 4)

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HOMO (corresponds to MO 1)

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HOMO (corresponds to MO 6)

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HOMO-1 (corresponds to MO 5)

|}

The MO diagram shows that the LUMO of 1,3-butadiene combines with the HOMO of ethene in-phase and out-of-phase to generate the HOMO and LUMO of the transition state, respectively. The HOMO of 1,3-butadiene also combines with the LUMO of ethene in-phase (a stabilising interaction) to generate HOMO-1 and out of phase (a destabilising interaction) to generate LUMO+1.

Evidently, orbitals of the same symmetry combine to form a molecular orbital with a retention of symmetry. Hence, two symmetric orbitals overlap to form an orbital which is symmetric and two antisymmetric orbitals overlap to form an antisymmetric orbital. If the orbitals have the same symmetry, they will overlap spatially and so the overlap integral will be non-zero (thus, the overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions and 0 for antisymmetric-symmetric interactions). This shows that for a reaction to be allowed, there is a requirement for the symmetry to be the same.<ref name="five"/>

In normal electron demand Diels Alder reactions, the HOMO of the diene and the LUMO of the dienophile are closer in energy than the LUMO of the diene and the HOMO of the dienophile.<ref name="six"/> After obtaining the energies of the molecular orbitals by looking at the MO analysis, it was found that this statement is true for this case, hence the reaction between 1,3-butadiene and ethene involves normal electron demand.

===Carbon-Carbon Bond Lengths===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: the carbon-carbon bond lengths in the reactants, transition state and cyclohexadiene product
!'''Bond'''
|'''''Bond Length in Reactants''' '''(Å)'''''
|'''''Bond Length in Transition State (Å)'''''
|'''Bond Length in Product ''(Å)'''''
|-
!1-2
|1.3334
|1.3798
|1.5008
|-
!2-3
|1.4708
|1.4111
|1.3370
|-
!3-4
|1.3334
|1.3798
|1.5009
|-
!4-5
|N/A
|2.1147
|1.5371
|-
!5-6
|1.3273
|1.3818
|1.5346
|-
!6-1
|N/A
|2.1148
|1.5371
|-
|}

The carbon-carbon bond lengths in ethene, 1,3-butadiene, the transition state and the cyclohexene product are shown in Table 2. It can be seen that bonds 1-2 and 3-4 get longer as the reaction proceeds from the reactants to the products; this makes sense since the hybridisation of the carbon atoms is changing from sp<sup>2</sup> to sp<sup>3</sup> as the double bonds change to single bonds. As expected, bond 2-3 gets shorter as the cyclohexene double bond forms (the carbon atoms go from sp<sup>3</sup> to sp<sup>2</sup>). Bonds 4-5 and 6-1 become shorter from the transition state to the product as the reacting terminii approach each other as the bonds form. It can be noted that the distances between the two pairs of reacting atoms in the transition state (4-5 and 6-1) are shorter than 2x the Van der Waals radius of the C atom (1.70 Å), thus confirming the interaction between the reacting terminii and the partial formation of these bonds in the transition state.

The bond lengths obtained computationally are mostly consistent with the typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths of 1.34 and 1.54 Å, respectively.<ref name="seven"/> One deviation, however, is bond 2-3 in the reactant butadiene. This length is slightly shorter than the typical sp<sup>3</sup> C-C bond length due to the delocalised pi system. Another notable deviation involves bonds 1-2 and 3-4 in the product, which are shorter than the expected sp<sup>3</sup> length due to the fact that one carbon atom of each of these bonds is sp<sup>2</sup> hybridised.

===Vibration Analysis===

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Fig 1b: the vibration at the transition state of the reaction between 1,3-butadiene and ethene

The vibration which corresponds to the reaction path at the transition state (see Fig 1b) is the vibration with the negative (imaginary) frequency. The animation shows that the reacting terminii of both reactants move towards each other simultaneously as the two new bonds form synchronously (ie, at the same time). This is also confirmed by the IRC, since both bonds form in Step 10 .

===Log Files===

[[Media:Em2815 e1 butadiene minPM6.LOG|LOG file of 1,3-butadiene minimum PM6]]

[[Media:Em2815 e1 ethene minPM6.LOG|LOG file of ethene minimum PM6]]

[[Media:Em2815 e1 cycloadd TS PM6.LOG|LOG file of transition state PM6]]

[[Media:em2815_e1_IRC.LOG|LOG file of IRC PM6]]

[[Media:Em2815_e1_product_min_PM6.LOG|LOG file of product minimum PM6]]

=Part 2: Reaction of Cyclohexadiene and 1,3-dioxole=

Scheme 2 shows the Diels Alder reaction of cyclohexadiene and 1,3-dioxole. This reaction can go via two pathways: exo or endo.

[[File:em2815_e2_scheme_720p.png|380px|thumb|center|Scheme 2: the reaction of cyclohexadiene with 1,3-dioxole to give the exo and endo products]]

The reactants and products were optimised at the B3LYP/6-31G(d) level and the transition state was located using method 3, also at the B3LYP/6-31G(d) level. The success of the endo and exo reactions were confirmed by the presence of the imaginary frequencies at 520.90i and 528.79i cm<sup>-1</sup>, respectively. The MOs generated computationally have been correlated with the MOs in Fig 2 (see Table 3).

===Molecular Orbitals===

The molecular orbital diagram for the exo reaction can be seen in Fig 2 and the molecular orbitals found computationally can be seen below.

[[File:em2815_e2_MO_480p.png|400px|thumb|center|Figure 2: the MO diagram for the exo pathway of the reaction of cyclohexadiene with 1,3-dioxole]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 3: shows the important MOs generated computationally for 1,3-dioxole, cyclohexadiene and the exo and endo transition states
!Cyclohexadiene
!1,3-dioxole
!Endo Transition State
!Exo Transition State
|-
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LUMO (corresponds to MO 2)

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LUMO (corresponds to MO 4)

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LUMO +1 (analogous to MO 8)

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LUMO +1 (corresponds to MO 8)

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LUMO (analogous to MO 7)

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LUMO (corresponds to MO 7)

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HOMO (corresponds to MO 1)

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HOMO (corresponds to MO 3)

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HOMO (analogous to MO 6)

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HOMO (corresponds to MO 6)

|-
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HOMO-1 (analogous to MO 5)

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HOMO-1 (corresponds to MO 5)

|}

The MO diagram shows that the LUMO of cyclohexadiene combines with the HOMO of 1,3-dioxole in-phase and out-of-phase to generate the HOMO and LUMO of the transition state, respectively. The HOMO of cyclohexadiene also combines with the LUMO of 1,3-dioxole in-phase (a stabilising interaction) to generate HOMO-1 and out of phase (a destabilising interaction) to generate LUMO+1.

This MO diagram can be compared to that of the Diels Alder reaction in Part 1. The presence of the electron-donating oxygen atoms in 1,3-dioxole destabilises the HOMO and LUMO of the alkene therefore they are higher in energy compared to the simple ethene molecule. This means that the HOMO of the electron deficient 1,3-dioxole is closer in energy to the LUMO of the electron rich cyclohexadiene, hence these are the orbitals that overlap and interact. Since the HOMO of the alkene (dienophile) and the LUMO of the diene are closer in energy than the LUMO of the alkene and the HOMO of the diene, the reaction goes via inverse electron demand.<ref name="five"/><ref name="six"/>

It is worth noting that the endo pathway would produce transition state molecular orbitals which are lower energy than those depicted for the exo pathway.

===Thermochemistry===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 4: shows the activation and reaction energies of the endo and exo pathways of the reaction of 1,3-dioxole with cyclohexadiene
!
!Endo
!Exo
|-
!Activation Energy (kJ/mol)
|<nowiki>+157.53</nowiki>
|<nowiki>+165.41</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>-70.89</nowiki>
|<nowiki>-65.64</nowiki>
|}

The 'Thermochemistry Data' from the optimisations were used to calculate the activation and reaction energies of the exo and endo pathways, see Table 4. Since the endo pathway has a smaller activation energy, it is kinetically favoured and leads to the kinetic/endo product, which is faster formed. This is the case because there is less steric clash in the endo transition state. Another possible reason is a stabilising secondary orbital overlap between the pi system of the diene and the pi orbitals of both oxygen atoms in 1,3-dioxole which decreases the energy of the transition state, lowering the activation energy.

The reaction energy for the endo pathway is also more negative than that for the exo pathway, suggesting that the endo product is the more thermodynamically stable (lower energy) product. This is the case because of the same reasons discussed earlier: the secondary orbital interaction is also present in the endo product and there is less steric clash. Hence, the endo product is kinetically and thermodynamically favoured.

The exo pathway has a larger activation energy and a smaller reaction energy than the endo pathway. This shows that the exo product is less thermodynamically stable (higher energy) than the endo product. The aforementioned secondary orbital interaction is not possible in the exo product since the 1,3-dioxole molecule is in the wrong orientation for the pi systems of the oxygen atoms and the diene to overlap. The exo product therefore does not benefit from the additional stabilisation, and this coupled with the fact that there is more steric clash means that the exo product is higher in energy.

===Log Files===

[[Media:Em2815 e2 dioxole min B3LYP.LOG|LOG file of dioxole minimum B3LYP]]

[[Media:Em2815 e2 endo cyclohexadiene min B3LYP.LOG|LOG file of cyclohexadiene minimum B3LYP]]

[[Media:A2 em2815 e2 endo ts B3LYP.LOG|LOG file of endo transition state B3LYP]]

[[Media:E2 EXO TS B3LYP.LOG|LOG file of exo transition state B3LYP]]

[[Media:Em2815 e2 endo product min B3LYP.LOG|LOG file of endo product minimum B3LYP]]

[[Media:Em2815 e2 exo product min B3LYP.LOG|LOG file of exo product minimum B3LYP]]

[[Media:Em2815 e2 endo irc.LOG|LOG file of endo IRC]]

[[Media:Em2815 e2 exo IRC.LOG|LOG file of exo IRC]]

=Part 3: Reaction of o-Xylylene and SO<sub>2</sub>=

Scheme 3 shows the Diels Alder and Cheletropic reactions of o-xylylene and SO<sub>2</sub>.

[[File:em2815_e3_scheme_.png|480px|thumb|center|Scheme 3: the Diels Alder and Cheletropic reactions of o-xylylene with SO<sub>2</sub>]]

The reactants and products were optimised at the PM6 level and the transition state was located using method 3, also at the PM6 level. The success of the endo, exo and cheletropic reactions were confirmed by the presence of the imaginary frequencies at 333.79i, 351.67i and 486.55i cm<sup>-1</sup>, respectively.

===IRC Calculations===

The Intrinsic Reaction Coordinate calculations for the endo, exo and cheletropic reactions can be seen in Figs 3a, 3b and 3c. Evidently, for the Diels Alder reactions, the reacting terminii of both reactants move towards each other at different rates. The C-O and C-S bonds are formed at different rates due to asymmetry, hence the bond formation is asynchronous. For the endo pathway, the C-S bond forms in step 56 whereas the C-O bond forms in step 52 and for the exo pathway, the C-S and C-O bonds form in steps 64 and 60, respectively. This however is not the case for the cheletropic reaction. Since this reaction is symmetric, the reacting terminii move towards each other at the same rate and the C-S bonds are formed synchronously (both C-S bonds form in step 78 of the IRC).

(Don't use the word "rate" here, as their formation is staggered in time. It's very difficult to say when exactly a "bond" is formed. The bonds that GaussView uses are aesthetic (except in molecular mechanical calculations) and are decided when atoms cross a cutoff distance [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:48, 4 April 2018 (BST))

[[File:em2815_e3_endo_IRC.gif|450px|thumb|center|Figure 3a : IRC for the Endo Diels-Alder Reaction of o-xylylene and SO<sub>2</sub>]]
[[File:em2815_e3_exo_IRC.gif|450px|thumb|center|Figure 3b : IRC for the Exo Diels-Alder Reaction of o-xylylene and SO<sub>2</sub>]]
[[File:em2815_e3_cheletropic_IRC.gif|450px|thumb|center|Figure 3c : IRC for the Cheletropic Reaction of o-xylylene and SO<sub>2</sub>]]

====o-Xylylene Stability====
The IRCs for the reactions show that the two double bonds in the 6 membered ring of xylylene break and a delocalised ring structure forms. This shows that xylylene is extremely reactive since there is a very large driving force for aromatisation.

===Thermochemistry===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 5: shows the activation and reaction energies of the endo, exo and cheletropic pathways of the reaction of o-xylylene with SO<sub>2</sub>
!
!Endo
!Exo
!Cheletropic
|-
!Activation Energy (kJ/mol)
|<nowiki>+82.72</nowiki>
|<nowiki>+86.72</nowiki>
|<nowiki>+105.08</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>-98.04</nowiki>
|<nowiki>-98.71</nowiki>
|<nowiki>-155.01</nowiki>
|}

The 'Thermochemistry Data' were used to calculate the activation and reaction energies of each of the three pathways, see Table 5. The endo pathway has the smallest activation energy, therefore it is kinetically favoured (thus the endo product is the kinetic product). The endo transition state could be lower in energy because there is reduced steric clash. It may also be stabilised by a secondary orbital overlap between the pi systems of the xylylene and the oxygen atoms from SO<sub>2</sub>. Since these factors stabilise the transition state, they result in a lower activation barrier.

The exo transition state has more steric clash and does not benefit from the secondary orbital overlap therefore it is higher in energy. Furthermore, the cheletropic transition state consists of a highly strained 5 membered ring. This is much higher in energy than the 6 membered ring in the exo and endo transition states (6 membered rings are essentially strain-free), therefore the cheletropic transition state is much less stable, resulting in the largest activation barrier.

The cheletropic reaction has the most negative reaction energy, indicating that the cheletropic product is the most energetically stable and therefore the thermodynamic product. This is the case because the S=O bonds are extremely strong and high energy therefore they stabilise the product.

The values for activation energy and reaction energy were used to generate the reaction profile shown in Fig 4.

[[File:Em2815_reactionprofileyay.png|550px|thumb|center|Figure 4: the reaction profile for the Diels Alder and Cheletropic pathways of the reaction of o-xylylene with SO<sub>2</sub>]]

===Alternative Diels-Alder Pathway===

So far, the reaction at the terminal diene has been discussed. There is also an alternative reaction pathway involving the second cis-butadiene fragment which is in the 6 membered ring of o-xylylene. See Scheme 4.

[[File:em2815_e3_altscheme_720p.png|480px|thumb|center|Scheme 4: the alternative reaction pathway involving the cis-butadiene fragment in the o-xylylene ring]]

The IRC calculations and thermodynamic data for the exo and endo pathways involving this cis-butadiene fragment can be seen below in Figs 5a & 5b and Table 6. The activation energies for both pathways are extremely high, indicating that reactions at this site are very kinetically unfavourable. The reaction energies are also positive, indicating that both the exo and endo products are relatively high in energy compared to the products of terminal diene pathway discussed earlier. Since both products are less stable, there is a lower driving force for the xylylene compound to react at this site. The positive reaction energy also indicates that the reactions are endothermic and hence thermodynamically unfavourable.

[[File:em2815_e3_ringendo_IRC.gif|450px|thumb|center|Figure 5a : IRC for the endo Diels-Alder reaction of o-xylylene and SO<sub>2</sub> at the alternative site]]
[[File:em2815_e3_ringexo_IRC.gif|450px|thumb|center|Figure 5b : IRC for the exo Diels-Alder reaction of o-xylylene and SO<sub>2</sub> at the alternative site]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 6: shows the activation and reaction energies of the endo and exo pathways of the reaction of o-xylylene with SO<sub>2</sub> at the alternative site
!
!Endo
!Exo
|-
!Activation Energy (kJ/mol)
|<nowiki>+112.94</nowiki>
|<nowiki>+120.78</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>+17.22</nowiki>
|<nowiki>+21.67</nowiki>
|}

The kinetic and thermodynamic unfavourability of these pathways can be explained by the fact that these reactions do not achieve aromatisation of the xylylene ring in the product. The conjugation is also lost in this pathway, therefore the reactants are much less stable and are disfavoured. Aromatisation and conjugation can however be achieved and maintained in the reaction occurring at the terminal diene, therefore this is the kinetically and thermodynamically favourable site of the reaction.

===Log Files===

[[Media:Em2815_SO2_REACTANT_MINIMUM_PM6.LOG|LOG file of SO<sub>2</sub> Reactant Minimum PM6 ]]

[[Media:Em2815_e3_XYLYLENE_REACTANT_MINIMUM_PM6.LOG|LOG file of o-Xylylene Reactant Minimum PM6 ]]

[[Media:Em2815_e3_ENDO_TS_PM6.LOG‎|LOG file of endo transition state PM6 ]]

[[Media:Em2815_e3_ENDO_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of endo product minimum PM6 ]]

[[Media:Em2815_e3_Exo_TS_PM6.LOG‎|LOG file of exo transition state PM6 ]]

[[Media:Em2815_e3_Exo_Product_Minimum_PM6.LOG‎|LOG file of exo product minimum PM6 ]]

[[Media:Em2815_e3_CHELETROPIC_TS_PM6.LOG‎|LOG file of cheletropic transition state PM6 ]]

[[Media:E3_CHELETROPIC_MINIMUM_PROD_PM6.LOG|LOG file of cheletropic product minimum PM6 ]]

[[Media:Em2815 e3 ENDO IRC PM6.LOG|LOG file of endo pathway IRC]]

[[Media:Em2815 e3 EXO IRC PM6.LOG|LOG file of exo pathway IRC]]

[[Media:Em2815 e3 CHELETROPIC IRC PM6.LOG|LOG file of cheletropic pathway IRC ]]

Alternative Pathway

[[Media:Em2815_e3_ENDO_RING_TS_PM6.LOG‎|LOG file of endo transition state (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_ENDO_RING_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of endo product minimum(reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_EXO_RING_TS_PM6.LOG‎|LOG file of exo transition state (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_EXO_RING_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of exo product minimum (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815 e3 ENDO RING IRC PM6.LOG|LOG file of endo pathway (reacting in the xylylene ring) IRC]]

[[Media:Em2815 e3 EXO RING IRC PM6.LOG|LOG file of exo pathway (reacting in the xylylene ring) IRC]]

=Conclusion=

This investigation used the PM6 and B3LYP/6-31G(d) computational methods to locate the transition states of various cycloaddition reactions. Method 3 proved to be the most efficient and reliable method which lead to successful calculations. It was found that the type of reactants affected the type of reaction occurring; from part 1 to part 2, the addition of the heteroatoms in the alkene resulted in an inverse electron demand reaction, affecting the ordering of the orbitals involved in the reaction.

For part 2, the competition of different reacting pathways was investigated. The exo and endo pathways of the Diels Alder reaction of cyclohexadiene with 1,3-dioxole were observed and it was found that the endo pathway has a lower activation barrier than the exo pathway therefore the endo product is kinetically favoured. This product was also found to be more stable than the exo product, hence it is thermodynamically favoured too. It has been suggested that the kinetic and thermodynamic favouring of the endo product is due to the reduced steric clash and the secondary orbital overlap between the pi orbitals of the oxygen atoms and the pi system of the diene, which is only possible in the endo configuration.

In part 3, the competition of three different reacting pathways was investigated. SO<sub>2</sub> can react with o-xylylene in a Diels Alder fashion, with one S atom and one O atom as part of a 6 membered ring, or in a cheletropic fashion, with just the S atom as part of a 5 membered ring. It was found that the endo product is kinetically favoured for this reaction since it has the smallest activation energy, however the thermodynamically favoured product is the cheletropic molecule. Although the cheletropic transiton state is disfavoured in terms of kinetics (due to the strained 5 membered ring), it is the most thermodynamically stable due to its strong and unreactive S=O bonds.

=References=

<references>
<ref name="one">
P. Atkin, J. Paula, ''Physical chemistry'', 8th edn, 2006.
</ref>

<ref name="two">
X. Qu, D. Latino and J. Aires-De-sousa, ''J. Cheminform''., 2013, '''5''', 1.
</ref>

<ref name="three">
E. Lewars, ''Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics'', 1st edn, 2011.
</ref>

<ref name="four">
F. Jensen, ''Wiley Interdiscip. Rev. Comput. Mol. Sci.'', 2013, '''3''', 273–295.
</ref>

<ref name="five">
R. Hoffmann and R. B. Woodward, ''Acc. Chem. Res.'', 1968, '''1''', 17–22.
</ref>

<ref name="six">
D. Boger, ''Progress in Heterocyclic Chemistry'', 1st edn, 1989.
</ref>

<ref name="seven">
H. J. Bernstein, ''Trans. Faraday Soc.'', 1961, '''57''', 1649–1656.
</ref>

Rep:Mod:smw415TS

2018-03-28T10:31:08Z

Fv611: /* [4+2] Cycloaddition of ethene and butadiene */

== '''Transition States via Computational Methods''' ==

== Introduction ==

This study was carried out to analyse Molecular orbitals, reaction kinetics and thermodynamics of different pericyclic reactions

A potential energy surface is plot or a mathematical function that represents the potential energy of a chemical system as a function of multiple reaction coordinates. The number of dimensions of such surface is given by 3N-6 where N is the number of atoms considered in the molecular system. The first derivative relates to the force acting on atoms whereas the second derivative which determines the curvature relates to the force constant, k. The value of k obtained can be used to calculate the vibrational frequency of each 3N-6 mode.

A minimum point, with a positive second derivative, along the reaction coordinate represents a stable species which could be either a reactant, product or an intermediate of the reaction. A transition state (TS) is related to a maximum point (negative second derivative) along a reaction coordinate. A TS is a first order saddle point on a potential energy surface and always has one dimension of the negative curvature. This could be obtained by diagonalising the force constant and by evaluating the Eigen values.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:26, 23 March 2018 (UTC) Some confusion here. You diaginalise the Hessian matrix which is the gives you the force constants which are the eigen values and the eigen vectors which are the normal modes which are linear combinations of he degrees of freedom.

In this exercise, two different optimisation methods were used; the semi-empirical route with PM6 and the density functional theory (DFT), B3LYP. These methods are based on the Hartree-Fock model which calculates electron-electron interactions by the assumption that any electron in the chemical system experiences an average field from other electrons. The PM6 method is faster as it uses pre-calculated empirical data to determine the electron density. The B3LYP uses the basis set 6-31(G) which includes the atomic orbitals that make up the molecular orbitals using the theory of Linear Combination of Atomic Orbitals (LCAO). These methods can solve the time-independant Schrödinger equation along the reaction coordinate in order to calculate the energy of the system at each point as well as the first and second derivatives of the energy. These produces optimised geometries which is either a stable species in the reacion (a minimum point with a positive second derivative) or a transition state.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:28, 23 March 2018 (UTC) Some confusion here. PM6 is based on the HF hamiltonian but B3LYP is a DFT hamitonian which works with e- density and has a term which uses the HF energy (exchange correlation).

The Gaussian software was used to find the TS of the reaction given below and three different methods were used. The guess TS of could be optimised directly however previous knowledge of the TS was required and this method is the most unreliable even though it is the fastest. Another method employed involved generating the guess TS and then freezing the reacting atoms which also required previous knowledge of the TS however it was more reliable and at the same time it was considered a relatively faster method. The final method started from either the reactants and product, then altering bond lengths and again freezing atoms. This was considered the most reliable method and it did not require any knowledge of the TS but the disadvantages were that it required additional steps and if the minimum point does not resemble the TS geometry, the method would not work.

== [4+2] Cycloaddition of ethene and butadiene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) The log files are missing but the MO diagram is good. Your bond length analysis is missing a discussion on the most important bonds (the one being formed at the transition state), which length you have not reported.)

For this Diels Alder reaction (Figure 1), the reactants were separately optimised to a minimum, the structures placed in correct geometry and the distance between reacting atoms were frozen at 2.2 Â. This structure was optimised to a minimum and then to the TS. The product was separately optimised at PM6 level.

[[File:Reaction_Scheme.cdx|thumb|center|Figure 1: Reaction Scheme|600px]]

=== MO Diagram of the Transition State ===

[[File:MOD.jpg|thumb|center|Figure 2: Molecular Orbital Diagram of Transition State|1200px]]

The MO diagram illustrates how the MOs of the reactants, ethylene and butadiene, combine at the transition state. The IRC calculation for the optimised TS and the log file initial frame corresponding to the reactants, was run to make the relative energies of reactants and the optimised TS comparable.
As shown in the MO diagram, the MOs of TS is quite high in energy compared to the reactant species since the TS represents the highest energy point in the reaction coordinate. Therefore the theoretical activated species should be destabilised compared to the reactants.

=== HOMO and LUMO of reactants and optmised TS ===

The following table shows the HOMO and LUMO of ethylene and butadiene (optimised to a minimum with PM6) as well as the four MOs of the transition state resulting from the linear combination of frontier MOs of the reactants. The HOMO-1 (MO16) and LUMO+1 (MO19) result from the constructive (in-phase) and destructive (out-of-phase) interference respectively, between the HOMO of butadiene and the LUMO of ethylene. The HOMO (MO17) and LUMO (MO18) results from the constructive and destructive interference respectively, between HOMO of ethylene and LUMO of butadiene.
The resulting MOs of the optimised TS agrees with the MO diagram drawn above and as well as the principle of conservation of orbital symmetry. The presence of MOs resulting from symmetric-symmetric or asymmetric-asymmetric interactions and the absence of symmetric-asymmetric interactions could be explained using the overlap integral. The overlap between orbitals of different symmetry results in an equal amounts of in-phase and out-of-phase interactions, producing an overall overlap integral of zero. The overlap of orbitals of same symmetry results in either a net in-phase (Positive) or out-of-phase (negative) overlap, therefore the overlap integral is not zero. The HOMO (butadiene) and LUMO (ethylene) are asymmetric, therefore they linearly combine to produce MO16 and MO19 whereas both LUMO (Butadiene) and HOMO (ethylene) are symmetric and combine to produce MO17 and MO18 of the optimised TS.

{| class="wikitable" border="1"
|+ MOs of Optimised reactants, TS and Product
! Name !! MO Image
|-
| HOMO (Ethylene) || [[File:EthyleneHOMO.jpg|150px]]
|-
| LUMO (Ethylene) || [[File:EthyleneLUMO.jpg|150px]]
|-
| HOMO (Butadiene) || [[File:ButadieneHOMO.jpg|150px]]
|-
| LUMO (Butadiene) || [[File:ButadieneLUMO.jpg|150px]]
|-
| HOMO (TS) || [[File:HOMO.jpg|150px]]
|-
| HOMO-1 (TS) || [[File:HOMO-1.jpg|150px]]
|-
| LUMO (TS) || [[File:LUMO.jpg|150px]]
|-
| LUMO+1 (TS) || [[File:LUMO+1.jpg|150px]]
|}

=== C-C Bond Lengths of optimised reactants, TS and product ===

The following table shows the bond lengths calculated for the above mentioned species.

{| class="wikitable" border="1"
|+ C-C Bond lengths/ Å
! Optimised Structure !! C=C (Ethylene) !! C=C (Terminal Butadiene) !! C=C (Butadiene centre) !! C-C (Newly Formed)
|-
| Reactants || 1.33 || 1.34 || 1.47 || -
|-
| TS || 1.39 || 1.38 || 1.41 || -
|-
| Product || 1.53 || 1.50 || 1.34 || 1.54
|}

In Diels Alder reactions, the hybridisation of the reacting species changes. The typical C-C bond lengths of different levels of carbon hybridisation are given below,

C(sp<sup>3</sup>)-C(sp<sup>3</sup>) = 1.54 Å

C(sp<sup>2</sup>)-C(sp<sup>2</sup>) = 1.34 Å

C(sp<sup>3</sup>)-C(sp<sup>2</sup>) = 1.50 Å

C atom (Van der Waal radius) = 1.70 Å

The C-C bond lengths of the optimised produce and reactants agrees with the values given above. The carbons of ethylene (dienophile) undergoes a change in hybridisation from sp<sup>3</sup> to sp<sup>2</sup> which can be confirmed by the length of the same bond being 1.38 Å at the optimised TS which is between 1.54 (sp<sup>3</sup>-(sp<sup>3</sup>) and 1.34 (sp<sup>2</sup>-(sp<sup>2</sup>). The same explanation could be used to describe the changes in the bond length of terminal C-C bonds of butadiene. The distance between interacting atoms in the TS is lower than 1.70 Å (C-Van der Waal radius) which confirms the interaction between the reacting atoms at the TS. The central C-C bond of butadiene changes from sp<sup>3</sup> to sp<sup>2</sup> in cyclohexene. This is confirmed by the intermediate bond length of 1.41 Å in the TS. All the bond lengths in the TS consists of values which are in between the values of the corresponding bond lengths of reactants and product.

=== Vibration at the reaction path of Transition State ===

[[File:TS Animation165465.gif|thumb|centre|Figure 4: Transition State Vibration|450px]]

The above vibration relates to a negative frequency value of -949.30 cm<sup>-1</sup>. The frequency is negative because the force constant is negative at the TS as the energy is maximum, which produces a negative value for the second derivative which is related to the force constant. The above animation both bonds form at the same time which means this reaction is synchronous and thereby it is concerted.

=== LOG files ===

[[Media:BUTADIENEOPT.log| Optimised Butadiene]]

[[Media:OPTIMISED ETHYLENE.txt| Optimised ethylene]]

[[Media:Optimised TS.log| Optimised TS]]

[[Media:PRODUCT OPT1.LOG| Optimised Cyclohexene]]

== [4+2] Cycloaddition of 1,3-Dioxole and Cyclohexadiene ==

[[File:ReactionbloodyScheme.jpg|thumb|centre|Figure 5: Reaction Scheme|600px]]

The endo and exo reaction pathways of this Diels Alder reaction was investigated. The product structures were built and optimised to a minimum. The two C-C bonds which formed during reaction were broken and frozen at 2.2 Å to produce guess endo and exo TS structures. These were then minimised and then optimised at B3LYP to produce the final optimised TS structures. Then IRC calculations were performed at PM6 level.

=== Molecular Orbital Diagrams for Endo and Exo TS ===

[[File:Endo TS MO Diagram.jpg|thumb|left|Figure 6: Molecular Orbital Diagram of Endo Transition State|600px]]
[[File:Exo TS MO Diagram.jpg|thumb|right|Figure 7: Molecular Orbital Diagram of Exo Transition State|600px]]

The MO diagrams are broadly similar to the MO diagram in the previous exercise where the TS MOs are higher in energy compared to reactants.In a normal electron demand process the diene HOMO is higher in energy than the dienophile HOMO, and the diene HOMO-dienophile LUMO energy gap is smaller compared to the converse dienophile HOMO-diene LUMO energy gap. However, in this reaction the HOMO of the 1,3-dioxole (dienophile) is higher in energy than the cyclohexa-1,3-diene (diene) HOMO, and this means that the reaction is an inverse electron demand Diels-Alder. This is because the dienophile is relatively electron rich as the lone pairs of electrons on oxygen can donate electron density to the C=C π-bond, thereby raising the energy of MOs above the diene. This reaction obeys the principle of conservation of orbital symmetry as well.

It is observed that the energy levels of endo and exo TS are different. The HOMO (MO41) is lower in energy in the endo TS compared to the exo TS. This is due to the secondary orbital interactions between oxygen p-orbitals and the MOs of the diene component(see below). This in turn lowers the energy of TS and the activation energy barrier of the reaction.

{| class="wikitable" border="1"
|+ Reactants
! MO !! 1,3-Dioxole !! Cyclohexadiene
|-
| HOMO || [[File:Dioxole HOMO.jpg|150px]] || [[File:Cyclohexadiene HOMO123456.jpg|150px]]
|-
| LUMO || [[File:Dioxole LUMO.jpg|150px]] || [[File:Cyclohexadiene LUMO123456789.jpg|150px]]
|}

{| class="wikitable" border="1"
|+ Transition State MOs
! TS !! HOMO-1 !! HOMO !! LUMO !! LUMO+1
|-
| Endo || [[File:Endo TS HOMO-1 bkjdshfkjsdh.jpg|150px]] || [[File:Endo TS HOMO bkjdshfkjsdh.jpg|150px]] || [[File:Endo TS LUMO bkjdshfkjsdh.jpg|150px]] || [[File:Endo TS LUMO+1 bkjdshfkjsdh.jpg|150px]]
|-
| Exo || [[File:Exo TS HOMO-1 gfjhsgfksk.jpg|150px]] || [[File:Exo TS HOMO gfjhsgfksk.jpg|150px]] || [[File:Exo TS LUMO djhfkjsahdgfkdjs.jpg|150px]] || [[File:Exo TS LUMO+1 djhfkjsahdgfkdjs.jpg|150px]]
|}

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:30, 23 March 2018 (UTC) How do you know the electron demand of the reaction. have you investigated it properly?

=== Thermochemistry ===

{| class="wikitable" border="1"
|+ Electronic + Thermal Free energies
! Molecule !! Sum of electronic and thermal Free energies/ (Hartee/particle)
|-
| 1,3-Dioxole || -267.074708
|-
| Cyclohexadiene || -233.336102
|-
| Endo-TS || -500.350529
|-
| Exo-TS || -500.347583
|-
| Endo-Product || -500.436132
|-
| Exo-Product || -500.434786
|}

{| class="wikitable" border="1"
|+ Reaction Barrier and Energies
! Reaction Pathway !! Reaction Barrier/(kJ/mol) !! Reaction Energy/(kJ/mol)
|-
| Exo || 166.002501 || -62.9489928
|-
| Endo || 158.267778 || -66.48291606
|}

The thermochemistry section from the log output file contained values of the sum of electronic and thermal free energies which were used to calculate the reaction barriers and reaction energies. The values of the reaction barrier for the endo-pathway is lower than for the exo-pathway. This is due to the lower energy endo-TS which consists of stabilising secondary orbital interactions which do not exist in the exo-TS. The endo-product is comparatively lower in energy, thermodynamic product, which is shown by the more negative reaction energy. This could be explained by the presence of extra steric hindrance in the exo-product (see figure X below) and this raises the energy of the exo-product and lowers the reaction energy. Therefore it can be concluded that the endo reaction pathway provides both the kinetic and thermodynamic product. The steric repulsion between substituents in exo-pathway could increase the energy of the exo-TS as well which subsequently raises the reaction barrier energy.

[[File:Endo Product145414541.jpg|thumb|left|Figure 8: Endo Product which forms stabilising secondary orbital interactions|450px]]
[[File:Exo Product778778.jpg|thumb|left|Figure 9: Exo Product with steric repulsion|450px]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:32, 23 March 2018 (UTC) Good section, slightly brief but you have some good figures. Your energies are slightly out. I suspect your reactants are not fully optimized. you could have gone into more detail in areas such as the electron demand.

=== LOG Files ===

[[Media:ENDO PRODUCT OPTfhgdhdhd.LOG| Optimised Endo-Product]]

[[Media:EXO PRODUCT OPThdhdfhdhds.LOG| Optimised Exo-Product]]

[[Media:DIOXOLE OPT1fdgdsgdf.LOG| Optimised 1,3-Dioxole]]

[[Media:CYCLOHEXADIENE OPTfgsaaaasgf.LOG| Optimised Cyclohexadiene]]

[[Media:ENDO TS OPT B3LYP.LOG| Optimised Endo-TS]]

[[Media:EXO TS OPT B3LYP.LOG| Optimised Exo-TS]]

== Diels Alder vs Cheletropic reactions ==

[[File:Reaction Scheme123456789.jpg|thumb|centre|Figure 10: Reaction Scheme|450px]]

In this exercise, the possible TS produced from different reaction pathways were optimised at PM6 level. The products from each reaction were minimised and the bonds at reacting atoms were broken and frozen. Then the structures were optimised to produce an accurate TS. The LOG output files from the final optimised TS were used for the IRC calculations and to determine the free energy values for the reactants, product and TS to subsequently calculate the reaction barriers and energies for each possible pathway.

=== Thermochemistry ===

[[File:Energy Profile of different pathways.jpg|thumb|center|Figure 11: Energy Profile|900px]]

Again, the above reaction profile illustrates that the endo-product is the kinetic product due to the lowest reaction barrier. The stabilising secondary orbital interactions in the endo-TS, as seen in the previous exercise, results in a lower activation energy for the reaction. The endo-pathway has a higher reaction energy than the exo-pathway which concludes that the endo-product is more thermodynamically favoured. The cheletropic reaction pathway consists of both the largest reaction barrier and the reaction energy which means that this is the least kinetically favoured and the most thermodynamically favoured pathway. The cheletropic-product does not form from the breaking of a relatively strong S=O bonds compared to exo/endo products. The presence of two strong S=O bonds in the final product raises the reaction energy of the cheletropic-pathway. This reaction also involves the initial formation of a five-membered ring which raises the ring strain in the system compared to the chair like six-membered ring in Diels Alder chemistry. This results in an increase in reaction barrier energy and the energy of the cheletropic-TS, making it the least kinetically favourable pathway.

(You should show evidence for effects such as secondary orbital overlap [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:48, 16 March 2018 (UTC))

{| class="wikitable" border="1"
|+ Electronic + Thermal Free energies
! Molecule !! Sum of electronic and thermal Free energies/ (Hartee/particle)
|-
| Sulfur dioxide || -0.118614
|-
| o-xylylene || 0.178073
|-
| Endo-TS || 0.090562
|-
| Exo-TS || 0.092078
|-
| Cheletropic-TS || 0.098102
|-
| Endo-Product || 0.021698
|-
| Exo-Product || 0.021454
|-
| Cheletropic-Product || 0.000005
|}

{| class="wikitable" border="1"
|+ Reaction Barrier and Energies
! Reaction Pathway !! Reaction Barrier/(kJ/mol) !! Reaction Energy/(kJ/mol)
|-
| Exo || 85.641191 || -99.7821351
|-
| Endo || 81.6609327 || -99.14151305
|-
| Cheletropic || 101.457204 || -156.0964889
|}

The aromatisation of the xylylene to benzene is a major thermodynamic driving force of the reaction. This occurs in both Diels Alder chemistry and cheletropic reactions. The following animations illustrates that ortho-xylylene is highly unstable and readily converted to the aromatic product.

[[File:Endo IRC.gif|thumb|center|Figure 12: Endo-Reaction Pathway|550px]]

(It's pretty hard to tell that this is endo from this angle [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:48, 16 March 2018 (UTC))

[[File:Exo IRCsfrqewtrwe.gif|thumb|center|Figure 13: Exo-Reaction Pathway|550px]]

[[File:Cheletropic IRC.gif|thumb|center|Figure 14: Cheletropic-Reaction Pathway|550px]]

=== Reaction with alternate Butadiene component on xylylene ===

[[File:ReactionScheme15151515.jpg|thumb|centre|Figure 15: Reaction Scheme|450px]]

There is a second cis-diene unit found on xylylene which could possible undergo an alternative Diels Alder reaction with sulfur dioxide to produce exo/endo products as shown above. The same procedure was used to produce the optimised TS and the energy analysis is summarised in the tables given below.

{| class="wikitable" border="1"
|+ Electronic + Thermal Free energies
! Molecule !! Sum of electronic and thermal Free energies/ (Hartee/particle)
|-
| Sulfur dioxide || -0.118614
|-
| o-xylylene || 0.178073
|-
| Endo-TS || 0.095656
|-
| Exo-TS || 0.093577
|-
| Endo-Product || 0.065609
|-
| Exo-Product || 0.067306
|}

{| class="wikitable" border="1"
|+ Reaction Barrier and Energies
! Reaction Pathway !! Reaction Barrier/(kJ/mol) !! Reaction Energy/(kJ/mol)
|-
| Exo || 89.5768158 || 20.6023001
|-
| Endo || 95.0352307 || 16.146826
|}

Using the data obtained, it can be concluded that this alternate Diels-Alder pathway is both kinetically and thermodynamically unfavourable. This has a larger reaction barrier for both endo/exo TS due to the high approach trajectory for sulfur dioxide towards the sterically hindered cis-diene component within the xylylene ring compared to the exocyclic reaction pathway. The reaction energies for this pathway are both positive as it does not involve the aromatisation of the xylylene ring, raising the energy of the final product.

=== LOG Files ===

[[Media:CHELETROPIC PRODUCT MIN PM6.LOG| Optimised Cheletropic-Product]]

[[Media:ENDO Product OPT PM6.LOG| Optimised Endo-Product]]

[[Media:EXO PRODUCT OPT PM6.LOG| Optimised Exo-Product]]

[[Media:CHELETROPIC TS MIN PM6.LOG| Optimised Cheletropic-TS]]

[[Media:ENDO TS OPT PM6 1.LOG| Optimised Endo-TS]]

[[Media:EXO TS PM6 OPT 2.LOG| Optimised Exo-TS]]

[[Media:SO2 OPT PM6.LOG| Sulfur dioxide]]

[[Media:XYLYLENE OPT PM6.LOG| o-xylylene]]

[[Media:ENDO PRODUCT MIN.LOG| Alternative Endo-Product]]

[[Media:EXO PRODUCT MIN.LOG| Alternative Exo-Product]]

[[Media:ENDO TS OPT PM6 1.LOG| Alternative Endo-TS]]

[[Media:EXO TS PM6 OPT 3454.LOG| Alternative Exo-TS]]

== Conclusion ==

This study involved the use of Gaussian Software to locate the TS of three different pericyclic reactions. This information was in turn used to calculate reaction energies and reaction barrier energies.

The first reaction was a [4+2] cycloaddition between betadiene and ethene and the MOs that were involved in the reaction between the two species were investigated along with the TS. The second reaction was another [4+2] cycloaddition between 1,3-dioxole and cyclohexadiene which consisted of an inverse electron demand compared to general Diels-Alder reactions. The two different reaction pathways, exo and endo were studied and the location of the TS and the final products indicated that the endo-pathway produced both the kinetic and thermodynamic product. The final study involved the comparison between the cheletropic and Diels-Alder reaction pathways for the same reactants, Sulfur dioxide and ortho-xylylene. It was concluded that the Diels-Alder reactions for both endo and exo pathways produced the kinetic product via the lower energy TS whereas the cheletropic reaction generated the thermodynamic product with the lowest energy final product.

The experiment could be improved with the use of B3LYP method for all three reactions with better accuracy.

Rep:Mod:hnt14Y3

2018-03-28T10:24:59Z

Fv611: /* Question 2ː Reaction of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

In this project, a series of pericyclic reactions were explored. Diels-Alder cycloaddition, chelotropic and electrocyclic reactions were all studied. A Diels-Alder cycloaddition between a diene and a dienophile can be normal or inverse demand. A normal demand reaction occurs when the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of a transition state or product are formed from the diene HOMO and the dienophile LUMO. Inverse demand occurs as a result of interaction between the diene LUMO and dienophile HOMO. Both inverse and normal demand Diels-Alder cycloaddition were under investigation.

The reactants, products and transition states were built in GaussView and optimised using the semi-empirical PM6 method and Density Functional Theory (DFT) B3LYP method. This allowed the MOs (molecular orbitals) of each to be visualised and their relative energy levels to be determined. The MOs are built by linearly combining basis sets. Hence, this is a quantum mechanical approach to generating MOs. The PM6 optimisation is faster and thus offers an initial optimisation which can be more accurately optimised using the more complex B3LYP where necessary.

A potential energy surface (PES) shows how the potential energy of a system changes along numerous reaction coordinates. Along a particular coordinate, the transition state is a maximum, where the gradient is zero. Transition states occur at maxima because they are high in energy and unstable. However, the transition state is also a minimum in all other directions, thus making it a saddle point. The reactants and products along a reaction coordinate will be minima, also with a zero gradient. As the first derivative is zero in both cases, a second derivative (the curvature) is determined to distinguish between maxima and minima. The second derivative will have a negative value for a maximum and a positive value for a minimum. Thus, when trying to locate a transition state in GaussView by running a frequency calculation, a single negative frequency value will be an indication that a transition state has been found.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:19, 23 March 2018 (UTC) Your discussion of the levels of theory is quite brief and more detail/ equations could have happened here. And remember to say that when on the PES you should be in 3N-6 coords.

== Question 1ː Reaction of Butadiene with Ethylene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very good job across the whole section. Well done.)

[[File:SchemeImage.PNG|400px|thumb|right|none|Figure 1-Reaction Scheme for [4+2] cycloaddition between butadiene and ethylene]]
[[File:MODiagramImageUPDATED.PNG|400px|thumb|right|none|Figure 2-MO diagram for the transition state of the [4+2] cycloaddition between butadiene and ethylene]]

Figure 1 shows the reaction scheme for the cycloaddition between butadiene and ethylene. In Figure 2, an MO diagram is constructed based on the interacting orbitals in the transition state of the Diels-Alder cycloaddition. These were determined by observing the relevant orbitals of the transition state formed from the HOMO and LUMO of each of the reactants in GaussView. The orbitals drawn in the MO diagram in Figure 2 correlate with those extracted from GaussView, which are shown in Table 1. It can be concluded from the resulting MOs in the transition state that only orbitals of the same symmetry are allowed to interact. Thus, there is a symmetry requirement for two interacting orbitals. In the case of orbitals with different symmetry, the interaction is forbidden and the orbital overlap integral will be zero. For orbitals of the same symmetry, the interaction is allowed and the overlap integral is non-zero. The results are summarised in Table 2.

{| class="wikitable" border="1"
|+ Table 1- Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <jmol>
<jmolApplet>
<title>Ethylene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_OPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Ethylene LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_OPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 36; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_BUTADIENEOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 36; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_BUTADIENEOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" border="1"
|+ Table 2-Allowed and Forbidden Interactions
! !! Allowed !! Forbidden !! Orbital Overlap Integral
|-
| Symmetric-Symmetric || X || || Non-zero
|-
| Asymmetric-Asymmetric || X || || Non-zero
|-
| Symmetric-Asymmetric || || X || Zero
|}

In the reaction, the distances between atoms vary depending on whether a bond is being made or broken. Where a bond is being broken, its length will increase in the transition state until the bond eventually breaks. In the case of a bond being made, the distance between the atoms decreases as the bond forms. Where a bond is going from a single bond to a double bond, the bond length shortens and vice versa. The typical bond length for a single sp<sup>3</sup>-sp<sup>3</sup> C-C bond is 1.54 Å <ref name="Bond lengths"/> and 1.34 Å <ref name="Bond lengths"/> for a double sp<sup>3</sup>-sp<sup>2</sup> bond. In the transition state, the two bonds being formed are between C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub>. Both have a length of 2.11 Å between the carbon atoms in the transition state. This is considerably less than twice the Van der Waals radius of the carbon atom which is 3.4 Å. Hence, it can be concluded that there is an interaction between C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub> in the transition state. In the product, bonds are formed at these sites that have a length of 1.54 Å, as expected for carbon-carbon single bonds.
The overall change in bond lengths can be seen in Table 3.

{| class="wikitable" border="1"
|+ Table 3-Bond lengths (Å) in reactants, transition states and products
! !! Butadiene !! Ethylene !! Transition State !! Product !! Change in bond
|-
| C<sub>1</sub>-C<sub>2</sub> || 1.3335 || - || 1.3798 || 1.4926 || Longer
|-
| C<sub>2</sub>-C<sub>3</sub> || 1.4708 || - || 1.4111 || 1.3331 || Shorter
|-
| C<sub>3</sub>-C<sub>4</sub> || 1.3334 || - || 1.3798 || 1.4926 || Longer
|-
| C<sub>4</sub>-C<sub>5</sub> || - || - || 2.1146 || 1.5358 || -
|-
| C<sub>5</sub>-C<sub>6</sub> || - || 1.3273 || 1.3818 || 1.5376 || Longer
|-
| C<sub>1</sub>-C<sub>6</sub> || - || - || 2.1149 || 1.5358 || -
|}

The vibration shown below corresponds to the vibration along the reaction path that occurs at the transition state of the reaction. As the two new bonds at C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub> form at the same time, the reaction is concerted and the formation of the two bonds is synchronous.

<jmol>
<jmolApplet>
<title> Figure 3-Vibration Mode at the Transition State</title>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 1;rotate x -20; </script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Files for the optimised reactants at PM6 levelː [[Media:HNT14_OPTMINPM6.LOG|Ethylene Optimisation]], [[Media:HNT14_BUTADIENEOPTMINPM6.LOG|Butadiene Optimisation]]

Files for the optimised transition state and the IRC at PM6 level: [[Media:HNT14_TSPM6.LOG|TS Optimisation]],[[Media:HNT14 IRC.LOG|IRC]]

File for the optimised product at PM6 levelː [[Media:HNT14 PRODUCTOPTPM6.LOG|Product Optimisation]]

== Question 2ː Reaction of Cyclohexadiene and 1,3-Dioxole ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) The MO diagram is good, but you should have discussed the differences between the endo and exo conformations in terms of relative TS MO energies.)

[[File:ReactionSchemeImage2.PNG|400px|thumb|right|none|Figure 4-Reaction Scheme for [4+2] cycloaddition between cyclohexadiene and 1,3-dioxole]]

[[File:MODIAGRAMENDOEXO.PNG|400px|thumb|right|none|Figure 5-Exo and Endo MO Diagrams for [4+2] cycloaddition between cyclohexadiene and 1,3-dioxole Transition States]]

The MO's of both the exo and endo transition states can be seen in Figure 5. The relative energy levels were determined using the B3LYP optimisations of the reactants and transition states in GaussView. The orbitals in Table 4 correlate with the energy levels and MOs in figure 5.

This reaction is an inverse demand Diels-Alder reaction because the HOMOs and LUMOs of both the exo and endo transition states occur as a result of the interaction between the diene (cyclohexadiene) LUMO and the dienophile (1,3-dioxole) HOMO.

{| class="wikitable" border="1"
|+ Table 4-Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>Exo TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Exo TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Exo TS LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> ||<jmol>
<jmolApplet>
<title>Exo TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>Endo TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Endo TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <jmol>
<jmolApplet>
<title>Endo TS LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>Endo TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Cyclohexadiene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 CYCLOHEXADIENEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Cyclohexadiene LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 CYCLOHEXADIENEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>1,3-Dioxole HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 OPTMINDIOXOLEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>1,3-Dioxole LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 OPTMINDIOXOLEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" border="1"
|+ Table 5- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 166.30 || -65.15
|-
| Endo || 158.51 || -68.75
|}

The endo adduct has a lower reaction barrier (due to the endo ts being of lower energy) than the exo adduct, indicating the endo product will be the kinetically favourable product (faster formation). Furthermore, the endo adduct also has a lower reaction energy than the exo adduct, meaning the endo product is also the thermodynamically favourable product. The energies can be seen in Table 5.

The lower energy of the endo ts is due to the secondary orbital interactions arising from orbital overlap between the O p orbital and the diene pi system. TS Stabilisation is hence a result of conjugation. This can only be achieved in the endo conformation, where the orbitals are in the correct orientation for overlap, as opposed to the orbitals in the exo adduct. This is in accordance with the endo rule.

The energies in Table 5 were calculated using the free energies of the reactants, products and transition states of the endo and exo adducts, which can be found in the log files below extracted from GaussView.

Files for the optimised reactants at B3LYP levelː [[Media:HNT14 CYCLOHEXADIENEB3LYP.LOG |Cyclohexadiene Optimisation]], [[Media:HNT14 OPTMINDIOXOLEB3LYP.LOG |1,3-Dioxole Optimisation]]

Files for the optimised transition states at B3LYP levelː[[Media:HNT14 EXOTSB3LYP.LOG |Exo TS Optimisation]], [[Media:HNT14 ENDOTSB3LYPH.LOG |Endo TS Optimisation]]

Files for the IRCs of the optimised transition states at PM6 levelː [[Media:HNT14 IRCEXOTSPM6I.LOG |Exo IRC]], [[Media:HNT14 IRCENDOTSPM6I.LOG |Endo IRC]]

Files for the optimised products at B3LYP levelː [[Media:HNT14 PRODUCTEXOB3LYPXXY.LOG |Exo Product Optimisation]], [[Media:HNT14 PRODUCTENDOB3LYPXX.LOG |Endo Product Optimisation]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:22, 23 March 2018 (UTC) You got your energies correct, and have made some very brief conclusions, but in general there is not enough detail in this section. There are a few things you didnt do, such as properly investigating the electron demand of the reaction.

== Question 3ː Diels-Alder vs Chelotropic ==

[[File:Q3imagereactionscheme4.PNG|400px|thumb|right|none|Figure 6-Reaction Scheme for Diels-Alder and chelotropic pathways for the reaction between Xylylene and SO<sub>2</sub>]]

The reaction scheme in Figure 6 shows both the Diels-Alder and chelotropic reaction pathways at one of the dienes in xylylene. The Diels-Alder reaction can result in both an endo and exo product.

[[File:Hnt14 ALTexoGIFXXX.gif|400px|thumb|none|Figure 7-Exo adduct IRC]]

[[File:Hnt14 altendoXXYGIF.gif|400px|thumb|none|Figure 8-Endo adduct IRC]]

[[File:Hnt14 chelotropicGIFXXX.gif|400px|thumb|none|Figure 9-Chelotropic adduct IRC]]

The IRCs of the exo, endo and chelotropic reactions can be seen in Figures 7, 8 and 9 respectively. These allow the reaction coordinates to be visualised. Xylylene is highly unstable because the ring prefers to be aromatic to lower the molecule's energy. Formation of the products would result in the formation of a benzenoid ring. This 'aromatisation' makes these reactions favourable and results in overall stabilisation. This can be observed in the IRCs, where the bond lengths in the six-membered ring become equal throughout the reaction, indicating the ring is aromatic.

{| class="wikitable" border="1"
|+ Table 5- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 87.19 || -98.23
|-
| Endo || 83.22 || -97.58
|-
| Chelotropic || 105.53 || -154.56
|}

In Table 5, the reaction barriers and energies are calculated for each of endo, exo and chelotropic adducts as before. As can be seen, the exo adduct has a lower reaction energy, making the exo product the more thermodynamically favourable product (compared to the endo product). This is because steric strain is minimised in the exo conformation. On the other hand,the endo adduct affords the lowest reaction barrier due to secondary orbital interactions, making the endo product the fastest forming (kinetically favourable) product. However, the exo and endo energies are only marginally different. In contrast, The chelotropic adduct has a much higher reaction barrier, meaning its formation is considerably slower than both the exo and endo products. The exo and endo adducts form stable six-membered ring transition states (resulting in faster formation), whereas the chelotropic transition state contains a 5-membered ring, making it sterically unfavourable due to ring strain. However, the chelotropic adduct has the lowest reaction energy by far, making it the most thermodynamically favourable product. The driving force is the formation of the double S=O bond compared with the much weaker single S-O bonds. This results in increased stabilisation and thus lower energy (thermodynamically stable) products. The relative reaction profiles for each of the two Diels-Alder reactions and the chelotropic reaction can be seen in figure 10.

[[File:ReactionprofileEX3.PNG|400px|thumb|right|none|Figure 10-Reaction profiles for endo, exo and chelotropic reactions]]

Files for the optimsed reactions at PM6 levelː [[Media:HNT14 XYLYLENEOPTMINPM6.LOG |Xylylene optimisation]], [[Media:HNT14 SO2OPTMINPM6.LOG |SO<sub>2</sub> optimisation]]

File for the optimised transition states at PM6 levelː [[Media:HNT14 EXODIELSALDERT1EXOTS2PM6.LOG |Exo TS optimisation]], [[Media:HNT14 DIELSALDERENDOTSPM6FINALPM6.LOG |Endo TS optimisation]], [[Media:HNT14 chelotropicTSPM6.LOG |Chelotropic TS optimisation]]

Files for IRCs at PM6 levelː [[Media:HNT14 IRCEXODIELSALDERPM6.LOG |Exo TS IRC]], [[Media:HNT14 IRCDIELSALDERENDOPM6.LOG |Endo TS IRC]], [[Media:HNT14 IRCCHELOTROPICPM6.LOG |Chelotropic TS IRC]]

Files for the optimised products at PM6 levelː [[Media:HNT14 EXODIELSALDERPRODUCTPM6.LOG |Exo product optimisation]], [[Media:HNT14 PRODUCTENDODIELSALDEROPTMINPM6.LOG |Exo product optimisation]], [[Media:HNT14 PRODUCTCHELOTROPICOPTMINPM6.LOG |Chelotropic product optimisation]]

=== Reaction at Cyclic Diene ===

Both the Diels-Alder and chelotropic reactions can occur at the cyclic diene as well. This will also result in exo, endo and chelotropic products. The reaction barriers and energies are reported in Table 6.

{| class="wikitable" border="1"
|+ Table 6- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 121.27 || 22.15
|-
| Endo || 113.42 || 17.70
|-
| Chelotropic || 142.14 || 48.74
|}

As can be observed, the reaction barriers for all three adducts are very high, meaning reaction at the cyclic diene is kinetically unfavourable. Furthermore, the reaction energies of all three adducts are very high, probably due to the non-aromatic product formation. Hence reaction at this diene is also thermodynamically unfavourable.

Files for the optimised transition states at PM6 levelː[[Media:HNT14 ALTEXOTSPM6.LOG |Alternative exo TS optimisation]], [[Media:HNT14 ALTENDOTSPM6.LOG |Alternative endo TS optimisation]],
[[Media:HNT14 ALTTYPE2TSPM6.LOG |Alternative chelotropic TS optimisation]]

Files for the IRCs at PM6 levelː [[Media:HNT14 IRCALTEXOTSPM6HNZT.LOG |Alternative exo IRC]], [[Media:HNT14 IRCALTENDOTSPM6.LOG |Alternative endo IRC]], [[Media:HNT14 IRCALTTYPE2TSPM6.LOG |Alternative chelotropic IRC]]

Files for the optimised products at PM6 levelː [[Media:HNT14 PRODUCTALTEXOOPTMINPM6.LOG |Alternative exo product optimisation]], [[Media:HNT14 ALTENDOPRODUCTOPTMINPM6.LOG |Alternative endo product optimisation]], [[Media:HNT14 PRODUCTALTTYPE2OPTMINPM6.LOG |Alternative chelotropic product optimisation]]

== Future Work ==

[[File:Futureworkscheme.PNG|500px|thumb|right|none|Figure 11-Reaction Scheme for electrocylic reaction]]

[[File:Disrotationhnt14.PNG|500px|thumb|right|none|Figure 12-Electrocyclic reaction by disrotation]]

The scheme shown in Figure 11 represents an electrocyclic reaction occuring by disrotation. The bond formation is suprafacial, as seen in Figure 12.
The LUMO of the reactant and the HOMO of the transition state that are visualised with Gaussview are consistent with those in figure 12, confirming that the reaction proceeds by disrotation. The visualised MOs are observed in Table 7.

{| class="wikitable" border="1"
|+ Table 7- Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>Reactant LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 FUTUREREACTANTOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 94; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 FUTURETSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(This reaction is conrotation under thermal conditions, which it will be under PM6. Confirm this by visualising the IRC [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:46, 16 March 2018 (UTC))

File for optimised reactant at PM6 levelː [[Media:HNT14 FUTUREREACTANTOPTMINPM6.LOG |Reactant optimisation]]

File for optimised TS at PM6 levelː [[Media:HNT14 FUTURETSPM6.LOG |TS optimisation]]

File for IRC at PM6 levelː [[Media:HNT14 IRCFUTURETSPM6.LOG |IRC]]

File for optimised product at PM6 levelː [[Media:HNT14 FUTUREPRODUCTOPTMINPM6.LOG |Product optimisation]]

== Conclusion ==

Gaussview was used to visualise a series of pericyclic reactionsː Diels-Alder, chelotropic and electrocyclic reactions. With Gaussian, molecules and transition states for a large range of reactions can be optimised. Furthermore, MOs and reaction coordinates can be visualised and free energies extracted which can then be used for finding reaction barriers and energies. In this project, this data was extracted for well known reactions. However, the same software and methods can be used for reactions of which the outcome is less well known. This means computational methods can be used to predict the outcome and likelihood of a reaction, giving quantitative results on how a reaction may proceed. Hence, invaluable information can be extracted using these techniques, highlighting the importance of computational chemistry.

== References ==

<references>
<ref name="Bond lengths">Zavitsas, A. (2003). The Relation between Bond Lengths and Dissociation Energies of Carbon−Carbon Bonds. The Journal of Physical Chemistry A, 107(6), pp.897-898. </ref>

Rep:Mod:hnt14Y3

2018-03-28T10:19:50Z

Fv611: /* Question 1ː Reaction of Butadiene with Ethylene */

== Introduction ==

In this project, a series of pericyclic reactions were explored. Diels-Alder cycloaddition, chelotropic and electrocyclic reactions were all studied. A Diels-Alder cycloaddition between a diene and a dienophile can be normal or inverse demand. A normal demand reaction occurs when the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of a transition state or product are formed from the diene HOMO and the dienophile LUMO. Inverse demand occurs as a result of interaction between the diene LUMO and dienophile HOMO. Both inverse and normal demand Diels-Alder cycloaddition were under investigation.

The reactants, products and transition states were built in GaussView and optimised using the semi-empirical PM6 method and Density Functional Theory (DFT) B3LYP method. This allowed the MOs (molecular orbitals) of each to be visualised and their relative energy levels to be determined. The MOs are built by linearly combining basis sets. Hence, this is a quantum mechanical approach to generating MOs. The PM6 optimisation is faster and thus offers an initial optimisation which can be more accurately optimised using the more complex B3LYP where necessary.

A potential energy surface (PES) shows how the potential energy of a system changes along numerous reaction coordinates. Along a particular coordinate, the transition state is a maximum, where the gradient is zero. Transition states occur at maxima because they are high in energy and unstable. However, the transition state is also a minimum in all other directions, thus making it a saddle point. The reactants and products along a reaction coordinate will be minima, also with a zero gradient. As the first derivative is zero in both cases, a second derivative (the curvature) is determined to distinguish between maxima and minima. The second derivative will have a negative value for a maximum and a positive value for a minimum. Thus, when trying to locate a transition state in GaussView by running a frequency calculation, a single negative frequency value will be an indication that a transition state has been found.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:19, 23 March 2018 (UTC) Your discussion of the levels of theory is quite brief and more detail/ equations could have happened here. And remember to say that when on the PES you should be in 3N-6 coords.

== Question 1ː Reaction of Butadiene with Ethylene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very good job across the whole section. Well done.)

[[File:SchemeImage.PNG|400px|thumb|right|none|Figure 1-Reaction Scheme for [4+2] cycloaddition between butadiene and ethylene]]
[[File:MODiagramImageUPDATED.PNG|400px|thumb|right|none|Figure 2-MO diagram for the transition state of the [4+2] cycloaddition between butadiene and ethylene]]

Figure 1 shows the reaction scheme for the cycloaddition between butadiene and ethylene. In Figure 2, an MO diagram is constructed based on the interacting orbitals in the transition state of the Diels-Alder cycloaddition. These were determined by observing the relevant orbitals of the transition state formed from the HOMO and LUMO of each of the reactants in GaussView. The orbitals drawn in the MO diagram in Figure 2 correlate with those extracted from GaussView, which are shown in Table 1. It can be concluded from the resulting MOs in the transition state that only orbitals of the same symmetry are allowed to interact. Thus, there is a symmetry requirement for two interacting orbitals. In the case of orbitals with different symmetry, the interaction is forbidden and the orbital overlap integral will be zero. For orbitals of the same symmetry, the interaction is allowed and the overlap integral is non-zero. The results are summarised in Table 2.

{| class="wikitable" border="1"
|+ Table 1- Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS HOMO</title>
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<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS LUMO</title>
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<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <jmol>
<jmolApplet>
<title>Ethylene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_OPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Ethylene LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_OPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 36; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_BUTADIENEOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
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<script>frame 36; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_BUTADIENEOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" border="1"
|+ Table 2-Allowed and Forbidden Interactions
! !! Allowed !! Forbidden !! Orbital Overlap Integral
|-
| Symmetric-Symmetric || X || || Non-zero
|-
| Asymmetric-Asymmetric || X || || Non-zero
|-
| Symmetric-Asymmetric || || X || Zero
|}

In the reaction, the distances between atoms vary depending on whether a bond is being made or broken. Where a bond is being broken, its length will increase in the transition state until the bond eventually breaks. In the case of a bond being made, the distance between the atoms decreases as the bond forms. Where a bond is going from a single bond to a double bond, the bond length shortens and vice versa. The typical bond length for a single sp<sup>3</sup>-sp<sup>3</sup> C-C bond is 1.54 Å <ref name="Bond lengths"/> and 1.34 Å <ref name="Bond lengths"/> for a double sp<sup>3</sup>-sp<sup>2</sup> bond. In the transition state, the two bonds being formed are between C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub>. Both have a length of 2.11 Å between the carbon atoms in the transition state. This is considerably less than twice the Van der Waals radius of the carbon atom which is 3.4 Å. Hence, it can be concluded that there is an interaction between C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub> in the transition state. In the product, bonds are formed at these sites that have a length of 1.54 Å, as expected for carbon-carbon single bonds.
The overall change in bond lengths can be seen in Table 3.

{| class="wikitable" border="1"
|+ Table 3-Bond lengths (Å) in reactants, transition states and products
! !! Butadiene !! Ethylene !! Transition State !! Product !! Change in bond
|-
| C<sub>1</sub>-C<sub>2</sub> || 1.3335 || - || 1.3798 || 1.4926 || Longer
|-
| C<sub>2</sub>-C<sub>3</sub> || 1.4708 || - || 1.4111 || 1.3331 || Shorter
|-
| C<sub>3</sub>-C<sub>4</sub> || 1.3334 || - || 1.3798 || 1.4926 || Longer
|-
| C<sub>4</sub>-C<sub>5</sub> || - || - || 2.1146 || 1.5358 || -
|-
| C<sub>5</sub>-C<sub>6</sub> || - || 1.3273 || 1.3818 || 1.5376 || Longer
|-
| C<sub>1</sub>-C<sub>6</sub> || - || - || 2.1149 || 1.5358 || -
|}

The vibration shown below corresponds to the vibration along the reaction path that occurs at the transition state of the reaction. As the two new bonds at C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub> form at the same time, the reaction is concerted and the formation of the two bonds is synchronous.

<jmol>
<jmolApplet>
<title> Figure 3-Vibration Mode at the Transition State</title>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 1;rotate x -20; </script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Files for the optimised reactants at PM6 levelː [[Media:HNT14_OPTMINPM6.LOG|Ethylene Optimisation]], [[Media:HNT14_BUTADIENEOPTMINPM6.LOG|Butadiene Optimisation]]

Files for the optimised transition state and the IRC at PM6 level: [[Media:HNT14_TSPM6.LOG|TS Optimisation]],[[Media:HNT14 IRC.LOG|IRC]]

File for the optimised product at PM6 levelː [[Media:HNT14 PRODUCTOPTPM6.LOG|Product Optimisation]]

== Question 2ː Reaction of Cyclohexadiene and 1,3-Dioxole ==

[[File:ReactionSchemeImage2.PNG|400px|thumb|right|none|Figure 4-Reaction Scheme for [4+2] cycloaddition between cyclohexadiene and 1,3-dioxole]]

[[File:MODIAGRAMENDOEXO.PNG|400px|thumb|right|none|Figure 5-Exo and Endo MO Diagrams for [4+2] cycloaddition between cyclohexadiene and 1,3-dioxole Transition States]]

The MO's of both the exo and endo transition states can be seen in Figure 5. The relative energy levels were determined using the B3LYP optimisations of the reactants and transition states in GaussView. The orbitals in Table 4 correlate with the energy levels and MOs in figure 5.

This reaction is an inverse demand Diels-Alder reaction because the HOMOs and LUMOs of both the exo and endo transition states occur as a result of the interaction between the diene (cyclohexadiene) LUMO and the dienophile (1,3-dioxole) HOMO.

{| class="wikitable" border="1"
|+ Table 4-Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>Exo TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Exo TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Exo TS LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> ||<jmol>
<jmolApplet>
<title>Exo TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>Endo TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Endo TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <jmol>
<jmolApplet>
<title>Endo TS LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>Endo TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Cyclohexadiene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 CYCLOHEXADIENEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Cyclohexadiene LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 CYCLOHEXADIENEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>1,3-Dioxole HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 OPTMINDIOXOLEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>1,3-Dioxole LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 OPTMINDIOXOLEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" border="1"
|+ Table 5- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 166.30 || -65.15
|-
| Endo || 158.51 || -68.75
|}

The endo adduct has a lower reaction barrier (due to the endo ts being of lower energy) than the exo adduct, indicating the endo product will be the kinetically favourable product (faster formation). Furthermore, the endo adduct also has a lower reaction energy than the exo adduct, meaning the endo product is also the thermodynamically favourable product. The energies can be seen in Table 5.

The lower energy of the endo ts is due to the secondary orbital interactions arising from orbital overlap between the O p orbital and the diene pi system. TS Stabilisation is hence a result of conjugation. This can only be achieved in the endo conformation, where the orbitals are in the correct orientation for overlap, as opposed to the orbitals in the exo adduct. This is in accordance with the endo rule.

The energies in Table 5 were calculated using the free energies of the reactants, products and transition states of the endo and exo adducts, which can be found in the log files below extracted from GaussView.

Files for the optimised reactants at B3LYP levelː [[Media:HNT14 CYCLOHEXADIENEB3LYP.LOG |Cyclohexadiene Optimisation]], [[Media:HNT14 OPTMINDIOXOLEB3LYP.LOG |1,3-Dioxole Optimisation]]

Files for the optimised transition states at B3LYP levelː[[Media:HNT14 EXOTSB3LYP.LOG |Exo TS Optimisation]], [[Media:HNT14 ENDOTSB3LYPH.LOG |Endo TS Optimisation]]

Files for the IRCs of the optimised transition states at PM6 levelː [[Media:HNT14 IRCEXOTSPM6I.LOG |Exo IRC]], [[Media:HNT14 IRCENDOTSPM6I.LOG |Endo IRC]]

Files for the optimised products at B3LYP levelː [[Media:HNT14 PRODUCTEXOB3LYPXXY.LOG |Exo Product Optimisation]], [[Media:HNT14 PRODUCTENDOB3LYPXX.LOG |Endo Product Optimisation]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:22, 23 March 2018 (UTC) You got your energies correct, and have made some very brief conclusions, but in general there is not enough detail in this section. There are a few things you didnt do, such as properly investigating the electron demand of the reaction.

== Question 3ː Diels-Alder vs Chelotropic ==

[[File:Q3imagereactionscheme4.PNG|400px|thumb|right|none|Figure 6-Reaction Scheme for Diels-Alder and chelotropic pathways for the reaction between Xylylene and SO<sub>2</sub>]]

The reaction scheme in Figure 6 shows both the Diels-Alder and chelotropic reaction pathways at one of the dienes in xylylene. The Diels-Alder reaction can result in both an endo and exo product.

[[File:Hnt14 ALTexoGIFXXX.gif|400px|thumb|none|Figure 7-Exo adduct IRC]]

[[File:Hnt14 altendoXXYGIF.gif|400px|thumb|none|Figure 8-Endo adduct IRC]]

[[File:Hnt14 chelotropicGIFXXX.gif|400px|thumb|none|Figure 9-Chelotropic adduct IRC]]

The IRCs of the exo, endo and chelotropic reactions can be seen in Figures 7, 8 and 9 respectively. These allow the reaction coordinates to be visualised. Xylylene is highly unstable because the ring prefers to be aromatic to lower the molecule's energy. Formation of the products would result in the formation of a benzenoid ring. This 'aromatisation' makes these reactions favourable and results in overall stabilisation. This can be observed in the IRCs, where the bond lengths in the six-membered ring become equal throughout the reaction, indicating the ring is aromatic.

{| class="wikitable" border="1"
|+ Table 5- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 87.19 || -98.23
|-
| Endo || 83.22 || -97.58
|-
| Chelotropic || 105.53 || -154.56
|}

In Table 5, the reaction barriers and energies are calculated for each of endo, exo and chelotropic adducts as before. As can be seen, the exo adduct has a lower reaction energy, making the exo product the more thermodynamically favourable product (compared to the endo product). This is because steric strain is minimised in the exo conformation. On the other hand,the endo adduct affords the lowest reaction barrier due to secondary orbital interactions, making the endo product the fastest forming (kinetically favourable) product. However, the exo and endo energies are only marginally different. In contrast, The chelotropic adduct has a much higher reaction barrier, meaning its formation is considerably slower than both the exo and endo products. The exo and endo adducts form stable six-membered ring transition states (resulting in faster formation), whereas the chelotropic transition state contains a 5-membered ring, making it sterically unfavourable due to ring strain. However, the chelotropic adduct has the lowest reaction energy by far, making it the most thermodynamically favourable product. The driving force is the formation of the double S=O bond compared with the much weaker single S-O bonds. This results in increased stabilisation and thus lower energy (thermodynamically stable) products. The relative reaction profiles for each of the two Diels-Alder reactions and the chelotropic reaction can be seen in figure 10.

[[File:ReactionprofileEX3.PNG|400px|thumb|right|none|Figure 10-Reaction profiles for endo, exo and chelotropic reactions]]

Files for the optimsed reactions at PM6 levelː [[Media:HNT14 XYLYLENEOPTMINPM6.LOG |Xylylene optimisation]], [[Media:HNT14 SO2OPTMINPM6.LOG |SO<sub>2</sub> optimisation]]

File for the optimised transition states at PM6 levelː [[Media:HNT14 EXODIELSALDERT1EXOTS2PM6.LOG |Exo TS optimisation]], [[Media:HNT14 DIELSALDERENDOTSPM6FINALPM6.LOG |Endo TS optimisation]], [[Media:HNT14 chelotropicTSPM6.LOG |Chelotropic TS optimisation]]

Files for IRCs at PM6 levelː [[Media:HNT14 IRCEXODIELSALDERPM6.LOG |Exo TS IRC]], [[Media:HNT14 IRCDIELSALDERENDOPM6.LOG |Endo TS IRC]], [[Media:HNT14 IRCCHELOTROPICPM6.LOG |Chelotropic TS IRC]]

Files for the optimised products at PM6 levelː [[Media:HNT14 EXODIELSALDERPRODUCTPM6.LOG |Exo product optimisation]], [[Media:HNT14 PRODUCTENDODIELSALDEROPTMINPM6.LOG |Exo product optimisation]], [[Media:HNT14 PRODUCTCHELOTROPICOPTMINPM6.LOG |Chelotropic product optimisation]]

=== Reaction at Cyclic Diene ===

Both the Diels-Alder and chelotropic reactions can occur at the cyclic diene as well. This will also result in exo, endo and chelotropic products. The reaction barriers and energies are reported in Table 6.

{| class="wikitable" border="1"
|+ Table 6- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 121.27 || 22.15
|-
| Endo || 113.42 || 17.70
|-
| Chelotropic || 142.14 || 48.74
|}

As can be observed, the reaction barriers for all three adducts are very high, meaning reaction at the cyclic diene is kinetically unfavourable. Furthermore, the reaction energies of all three adducts are very high, probably due to the non-aromatic product formation. Hence reaction at this diene is also thermodynamically unfavourable.

Files for the optimised transition states at PM6 levelː[[Media:HNT14 ALTEXOTSPM6.LOG |Alternative exo TS optimisation]], [[Media:HNT14 ALTENDOTSPM6.LOG |Alternative endo TS optimisation]],
[[Media:HNT14 ALTTYPE2TSPM6.LOG |Alternative chelotropic TS optimisation]]

Files for the IRCs at PM6 levelː [[Media:HNT14 IRCALTEXOTSPM6HNZT.LOG |Alternative exo IRC]], [[Media:HNT14 IRCALTENDOTSPM6.LOG |Alternative endo IRC]], [[Media:HNT14 IRCALTTYPE2TSPM6.LOG |Alternative chelotropic IRC]]

Files for the optimised products at PM6 levelː [[Media:HNT14 PRODUCTALTEXOOPTMINPM6.LOG |Alternative exo product optimisation]], [[Media:HNT14 ALTENDOPRODUCTOPTMINPM6.LOG |Alternative endo product optimisation]], [[Media:HNT14 PRODUCTALTTYPE2OPTMINPM6.LOG |Alternative chelotropic product optimisation]]

== Future Work ==

[[File:Futureworkscheme.PNG|500px|thumb|right|none|Figure 11-Reaction Scheme for electrocylic reaction]]

[[File:Disrotationhnt14.PNG|500px|thumb|right|none|Figure 12-Electrocyclic reaction by disrotation]]

The scheme shown in Figure 11 represents an electrocyclic reaction occuring by disrotation. The bond formation is suprafacial, as seen in Figure 12.
The LUMO of the reactant and the HOMO of the transition state that are visualised with Gaussview are consistent with those in figure 12, confirming that the reaction proceeds by disrotation. The visualised MOs are observed in Table 7.

{| class="wikitable" border="1"
|+ Table 7- Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>Reactant LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 FUTUREREACTANTOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 94; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 FUTURETSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(This reaction is conrotation under thermal conditions, which it will be under PM6. Confirm this by visualising the IRC [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:46, 16 March 2018 (UTC))

File for optimised reactant at PM6 levelː [[Media:HNT14 FUTUREREACTANTOPTMINPM6.LOG |Reactant optimisation]]

File for optimised TS at PM6 levelː [[Media:HNT14 FUTURETSPM6.LOG |TS optimisation]]

File for IRC at PM6 levelː [[Media:HNT14 IRCFUTURETSPM6.LOG |IRC]]

File for optimised product at PM6 levelː [[Media:HNT14 FUTUREPRODUCTOPTMINPM6.LOG |Product optimisation]]

== Conclusion ==

Gaussview was used to visualise a series of pericyclic reactionsː Diels-Alder, chelotropic and electrocyclic reactions. With Gaussian, molecules and transition states for a large range of reactions can be optimised. Furthermore, MOs and reaction coordinates can be visualised and free energies extracted which can then be used for finding reaction barriers and energies. In this project, this data was extracted for well known reactions. However, the same software and methods can be used for reactions of which the outcome is less well known. This means computational methods can be used to predict the outcome and likelihood of a reaction, giving quantitative results on how a reaction may proceed. Hence, invaluable information can be extracted using these techniques, highlighting the importance of computational chemistry.

== References ==

<references>
<ref name="Bond lengths">Zavitsas, A. (2003). The Relation between Bond Lengths and Dissociation Energies of Carbon−Carbon Bonds. The Journal of Physical Chemistry A, 107(6), pp.897-898. </ref>

Rep:FD915 TRANSITION

2018-03-28T10:11:48Z

Fv611: /* Log files */

= Transition Structure and Reactivity =

Felix de Courcy-Ireland
01062960
Transition States and Reactivity Computational Lab

==Introduction ==

Stationary points on potential energy surfaces (or ‘hypersurfaces’) are defined by a value of zero for the first derivative at that point<sup>(1)</sup>. However, it is through the use of second derivatives that the distinction can be made between the various types of stationary points, including reactants, transition states, intermediates and products<sup>(1)</sup>.

Products, reactants and intermediates are all minima on a potential energy surface. They are characterised by the fact that all paths through these points have a positive second derivative<sup>(1)</sup>.

Transition states are characterised by having a single normal coordinate for which the second derivative is negative, with all other paths through the transition state giving a positive second derivative at this point<sup>(1)</sup>. They are known as ‘saddle-points’. If a point on a potential energy surface is a maximum in more than one normal coordinate, it is diagnostic that there is a lower energy path for the reaction to proceed in the vicinity of this point<sup>(1)</sup>.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:09, 23 March 2018 (UTC) This is a good explanation. But remember that you are working in 3N-6 coordinates.

The calculations carried out were effectively an interrogation of the potential energy surface of a simple reaction. The aims of the calculations were to locate the stationary points of the potential energy surfaces. This was done through using the Gaussian software, which traced paths across the potential energy surface, iteratively calculating the second derivative of each point on the path until a point with a zero first derivative was reached.

In this laboratory, a successfully located transition state was denoted by there being a single negative frequency in the frequency calculation, which when animated, showed the desired reaction coordinate for the reaction.

In the relatively simple reactions investigated, where the reactants pass through only one transition state, it is simple to calculate important quantities such as the activation energy and the reaction energy, from knowledge of the free energies of the reactants, products and transition states.

In this laboratory, two computational methods were used; the semi-empirical PM6 method and the DFT method B3LYP/6-31(d).

The semi-empirical PM6 is a less accurate method but not as computationally expensive. Therefore, it proved useful in optimising structures, be they reactants, products or transition states, in preparation for the use of the more accurate and expensive B3LYP method.
B3LYP/6-31(d) is based in density functional theory (DFT)<sup>(1)</sup>. DFT finds approximate solutions to unsolvable many-electron wave functions by analysis of functionals of the one electron density, ρ(r), of the molecule<sup>(1)</sup>.

In some instances, use of chemical intuition in the location of transition states was most useful. There were cases where it proved fruitful to optimise a product or reactant(s) at the PM6 level, and then freeze the atoms immediately involved in the transition and further minimise the molecule around this frozen ‘transition state’ at the B3LYP level. A final calculation to find the transition state of at the B3LYP level was often more successful when using this ‘bond freezing’ technique.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:09, 23 March 2018 (UTC) OK intro, you could have gone into more detail in part and added some equations/ diagrams

==Exercise 1 ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Excellent work throughout the whole section - well done!)

=== Reaction Scheme ===

[[File:Reaction_scheme.png|550px|center]]

=== Log Files ===

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Butadiene + Ethene
! colspan = "2" style="background: #0D4F8B; color: white;" | Log Files - Butadiene + Ethene
|-
| Minimisation of butadiene (PM6)
| [[Media:CIS_BUTADIENE_ATTEMPT3.LOG| Minimisation of butadiene (PM6)]]
|-
| Minimisation of ethene (PM6)
| [[Media:ETHENE_MINIMISATION_ATTEMPT1.LOG|Minimisation of ethene (PM6)]]
|-
| Minimisation of cyclohexene (PM6)
| [[Media:CYCLOHEXENE_OPTIMISATION_ATTEMPT4.LOG|Minimisation of cyclohexene (PM6)]]
|-
| Transition State (PM6)
| [[Media:BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG|Transition State (PM6)]]
|-
| IRC (PM6)
| [[Media:IRC_FROM_CYCLOHEXENE_ATTEMPT1_BOTH_WAYS.LOG|IRC (PM6)]]
|}

=== MO diagram ===

[[File:Ex1_MO_diagram.png|500px|center| MO diagram for reaction of butadiene and ethene]]

The above molecular orbital diagram shows the interaction between the HOMOs and LUMOs of the ethene and butadiene. Each MO is assigned a symmetry value (assignments were based on the phasing of orbitals) - from these assignments it can be seen that only orbitals of like symmetry interact. The orbital overlap integral is zero for the case of a symmetric-(anti-symmetric) interaction and non-zero for either a symmetric-symmetric or (anti-symmetric)-(anti-symmetric) interaction. The orbital energies are relative to one another rather than being absolute. An attempt has been made to draw the MOs of the transition state - the calculated MOs can be found in the table below.

=== Jmols of the HOMOs and LUMOS of Butadiene and Ethene ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 1 showing the HOMO and LUMO of ethene with relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Ethene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<title>Ethene HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_MINIMISATION_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.39228 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<title>Ethene LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_MINIMISATION_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.04256 E<sub>h</sub>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 2 showing the HOMO and LUMO of butadiene, with relative energies in Hartrees.
! colspan = "3" style="background: #0D4F8B; color: white;" | Butadiene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS_BUTADIENE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.35899 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS_BUTADIENE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01943 E<sub>h</sub>
|}

=== Jmols of the MOs in the Transition State ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 3 showing the four MOs produced from the interaction of the ethene and butadiene MOs with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 16
| <jmol>
<jmolApplet>
<title> MO 16 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.32754 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 17
| <jmol>
<jmolApplet>
<title> MO 17 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.32532 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 18
| <jmol>
<jmolApplet>
<title> MO 18 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.03</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01732 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 19
| <jmol>
<jmolApplet>
<title> MO 19 </title>
<color>white</color>
<size>300</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.03 </script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.03066 E<sub>h</sub>
|}

=== C-C Bond Lengths of Reactants, Transition State and Products ===

[[File:Reaction_scheme.png|550px|center]]

Reaction Scheme repeated for clarity when analysing the bond lengths below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 4 showing bond distances in the reactants.
! colspan = "2" style="background: #0D4F8B; color: white;" | Reactants
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.33344
|-
| C2-C3
| 1.47077
|-
| C3-C4
| 1.33344
|-
| C5-C6
| 1.32731
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 5 showing bond distances in the transition state
! colspan = "2" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.37978
|-
| C2-C3
| 1.41104
|-
| C3-C4
| 1.37981
|-
| C4-C5
| 2.11452
|-
| C5-C6
| 1.38177
|-
| C6-C1
| 2.11469
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 6 showing bond distances in the product
! colspan = "2" style="background: #0D4F8B; color: white;" | Cyclohexene
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.49118
|-
| C2-C3
| 1.36309
|-
| C3-C4
| 1.49118
|-
| C4-C5
| 1.58345
|-
| C5-C6
| 1.56027
|-
| C6-C1
| 1.58345
|}

==== Discussion of carbon-carbon (C-C) bond lengths ====

The C-C single bond length of typical n-hydrocarbon is 1.533 Å, and the bond length of a typical C-C double bond is 1.33 Å<sup>(2)</sup>. These lengths will be used as a point of comparison in the following discussion.

The two pairs of carbon atoms which make up the two alkene bonds in the butadiene (C1-C2 and C3-C4) lengthen from a separation of 1.33 Å to a separation of 1.49 Å. This can be rationalised by observing that these two double bonds in the butadiene reactant will be present in the cyclohexene product as single bonds in the cyclohexene ring.

The internal C-C bond in butadiene (C2-C3) shortens from a distance of 1.47 Å to a distance of 1.36 Å. Again, although this bond is shorter than a typical C-C single bond due to the conjugation of the butadiene, it shortens to a distance more typical of a C-C double bond which it adopts in the cyclohexene product.

The ethene C-C double bond lengthens from 1.327 Å to 1.560 Å. This is due to the carbons moving from the sp<sup>2</sup> hybridised environment of the ethene molecule to the sp<sup>3</sup> hybridised environment of the cyclohexene ring.

The two new C-C bonds which are formed upon the Diels-Alder [4+2] cycloaddition between the butadiene and ethene have a value of 2.115 Å in the transition state, which shortens to a value of 1.583 Å in the cyclohexene product. This change in bond distance shows a shortening of bond lengths from an effectively infinite value in the reactants, through to a bond distance of 1.583 Å in the cyclohexene product.

Van der Waals radius of a carbon atom is 1.7 Å <sup>(3)</sup>, and this can be used in discussion of the partially formed bond between the ethene and butadiene in the transition state.

The length of the partly formed C-C bonds between butadiene and ethene is 2.115 Å. This is less than two times the van der Waals radius of carbon. Therefore, although there is not formally a bond formed between the atoms, the atoms are close enough to interact through van der Waals forces.

==== Vibration corresponding to the transition state ====

<jmol>
<jmolApplet>
<title> Reaction Path Vibration </title>
<color>white</color>
<size>500</size>
<script>frame 15; vibration 2;rotate x -20;</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Jmol above shows the vibration that corresponds to the reaction path at the transition state. It shows that the formation of the two bonds is synchronous - both bonds form simultaneously<sup>(4)</sup>.

==Exercise 2 ==

=== Reaction Scheme ===

[[File:Ex2_reaction_scheme.png|500px|center]]

=== Log files ===

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - 1,3-Dioxole + Cyclohexadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Log Files - 1,3-Dioxole + Cyclohexadiene
|-
| Minimised Cyclohexadiene (B3LYP/6-31G(d))
| [[Media:CYCLOHEXADIENE_REPEAT_AGAIN_B3LYP_MINIMISATION.LOG|Minimised Cyclohexadiene (B3LYP/6-31G(d))]]
|-
| Minimised 1,3-Dioxole (B3LYP/6-31G(d))
| [[Media:13DIOXOLE_PROPER_MINIMISATION_B3LYP_ATTEMPT3.LOG|Minimised 1,3-Dioxole (B3LYP/6-31G(d))]]
|-
| Minimised exo-product (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_MINIMISATION.LOG|Minimised exo-product (B3LYP/6-31G(d))]]
|-
| Minimised endo-product (B3LYP/6-31G(d))
| [[Media:ENDO_FULL_MOLECULE_INITIAL_MINIMISATION_B3LYP.LOG|Minimised endo-product (B3LYP/6-31G(d))]]
|-
| Minimised exo-transition state (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG|Minimised exo-transition state (B3LYP/6-31G(d))]]
|-
| Minimised endo-transition state (B3LYP/6-31G(d))
| [[Media:ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG|Minimised endo-transition state (B3LYP/6-31G(d))]]
|-
| IRC on Exo Transition State (PM6)
| [[Media:EXO_FULL_MOLECULE_IRC_ATTEMPT1.LOG|IRC on Exo Transition State (PM6)]]
|-
| IRC on Endo Transition State (PM6)
| [[Media:ENDO_MOLECULE_PM6_IRC_ATTEMPT1.LOG|IRC on Endo Transition State (PM6)]]
|-
| Single Point Energy on Exo Transition State (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_SINGLEPOINTENERGY.LOG|Single Point Energy on Exo Transition State (B3LYP/6-31G(d))]]
|-
| Single Point Energy on Endo Transition State (B3LYP/6-31G(d))
| [[Media:ENDO_MOLECULE_B3LYP_SINGLEPOINTENERGY.LOG|Single Point Energy on Endo Transition State (B3LYP/6-31G(d))]]
|}

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very nice MO diagrams here too. )

=== Jmols and Molecular Orbital Diagram for the Endo Reaction of Cyclohexadiene and 1,3-Dioxole ===

[[File:Ex2_MO_diagram_endo.png|500px|right| MO diagram for reaction with endo arrangement between 1,3-dioxole and cyclohexadiene]]

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Table 7 showing the MOs of the endo transition state with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 40 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 40 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19648 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 41 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 41 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19052 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 42 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 42 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.00462 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 43 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 43 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01543 E<sub>h</sub>
|}

Above is the new MO diagram from the endo reaction of cyclohexadiene and 1,3-dioxole. The endo reaction involves the two oxygen atoms of the 1,3-dioxole tucking under the cyclohexadiene. This leads to a stabilising secondary orbital interaction which shall be discussed later. The MO's produced by the interaction of the cyclohexadiene and 1,3-dioxole orbitals are shown in Table 7.

=== Jmols and Molecular Orbital Diagram for the Exo Reaction of Cyclohexadiene and 1,3-Dioxole ===

[[File:Ex2_MO_diagram_exo.png|500px|right| MO diagram for reaction with exo arrangement between 1,3-dioxole and cyclohexadiene]]

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Table 8 showing the MOs of the exo transition state with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 40 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 40 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19801 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 41 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 41 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.18560 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 42 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 42 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.00699 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 43 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 43 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01019 E<sub>h</sub>
|}

Above is the MO diagram from the exo transition state, with the MOs produced from interaction of the reactant HOMOs and LUMOs shown in Table 8. It should be noted that, similarly to the previous Diels-Alder reaction of butadiene and ethene, that only orbitals of like symmetry interact to give MOs in the transition state.

=== Inverse and Normal Electron Demand Diels-Alder Reactions ===

The reaction between 1,3-dioxole and cyclohexadiene is an inverse electron demand Diels-Alder reaction. Inverse electron demand Diels-Alder reactions are characterised by there being a smaller energy gap between the HOMO of the dienophile (1,3-dioxole) and the LUMO of the diene (cyclohexadiene) than the energy gap between the HOMO of the diene and the LUMO of the dienophile<sup>(5)</sup>.

[[File:Inverse_normal_DA.png|400px|center|Figure highlighting the relative energy differences that lead to definition of normal and inverse electron demand Diels-Alder reactions.]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:12, 23 March 2018 (UTC) This is correct however you have just stated it with no values. You have even done a single point energy calculation too! Why not use the numbers for the MOs that you have calculated to prove your hypothesis.

=== Thermochemistry ===

If the formation of more than one product is possible from a given set of reactants, knowledge of reaction energies and activation energies can lead to assignment of the kinetic and thermodynamic products. The kinetically favourable product is that from the reaction which has the lowest energy barrier to conversion between reactants and products. The thermodynamically favourable product is the lower energy product relative to the reactant(s).

In the case that there are two possible products of a reaction, as is the situation in this Diels-Alder reaction between 1,3-dioxole and cyclohexadiene, it is not necessary for one product to be the thermodynamic product and the other product to be the kinetic product. It may be the case that one of the products is both the thermodynamic and kinetic product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Energies Endo Reaction
|-
! style="background: #0D4F8B; color: white;" | Molecule
! style="background: #0D4F8B; color: white;" | Gibbs Free Energy (kJ/mol)
|-
| 1,3dioxole
| -701,188.414
|-
| cyclohexadiene
| -612,592.877
|-
| 1,3dioxole and cyclohexadiene
| -1,313,781.291
|-
| Endo Transition State
| -1,313,621.479
|-
| Endo Product
| -1,313,848.695
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Endo Reaction Parameters
|-
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
| 159.811
|-
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
| -67.404
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Energies Exo Reaction
|-
! style="background: #0D4F8B; color: white;" | Molecule
! style="background: #0D4F8B; color: white;" | Gibbs Free Energy (kJ/mol)
|-
| 1,3dioxole
| -701,188.414
|-
| cyclohexadiene
| -612,592.877
|-
| 1,3dioxole and cyclohexadiene
| -1,313,781.291
|-
| Exo Transition State
| -1,313,613.639
|-
| Exo Product
| -1,313,845.098
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Exo Reaction Parameters
|-
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
| 167.651
|-
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
| -63.807
|}

As shown in the above tables, the reaction barrier for the exo reaction is higher at a value of 167.651 kJ/mol, due to the transition state through which the reaction proceeds being of higher energy. Therefore, due to the lower reaction barrier of 159.811 kJ/mol, the endo product is kinetic product.

The endo product proceeds through a lower energy transition state due to the secondary orbital interactions between the oxygen p orbitals and the p orbitals of the internal carbons of the cis-butadiene fragment<sup>(5)</sup>.

The Jmol of the HOMO of the endo transition state is repeated here, where it can be seen that there is a stabilising interaction between the orbitals which lie on the oxygens of 1,3-dioxole and the two carbons which eventually form the double bond in the product, for the portion of the orbital located in these areas is the same phase.

<jmol>
<jmolApplet>
<title> MO 41 - Endo Transition State </title>
<color>white</color>
<size>350</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The endo product is again the thermodynamic product, as the energy of the endo product (-67.404 kJ/mol) is lower than that of the exo product (-63.807) - although the difference in energy is less in the products than in the reactants. This reason for the greater stabilisation of the endo product is possibly due to this same orbital interaction between the p orbitals on the oxygens with the alkene pi system. The fact that the difference in energy between the products is less than the difference in energy of the transition states is a consequence of this orbital interaction being poorer in the products.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:14, 23 March 2018 (UTC) This is a good section. You have got the correct energies and come to the correct conclusions. However there are part where you could have gone into more detail. Such as the thermo and kinetic theory, or the electron demand.

==Exercise 3 ==

[[File:Ex3_reaction_scheme.png|500px|center]]

=== Log Files ===

==== Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Dioxide + Exo-Cyclic Butadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment
|-
| Xylylene Minimisation (PM6)
|[[File:XYLYLENE_MINIMISATION_PM6.LOG| Xylylene Minimisation (PM6)]]
|-
| Sulfur Dioxide Minimisation (PM6)
| [[File:SULFUR_DIOXIDE.LOG| Sulfur Dioxide Minimisation (PM6)]]
|-
| Cheletropic Transition State (PM6)]
| [[File:CHELETROPIC_PM6_PRODUCT_TRANSITIONSTATE_NOTFROZEN.LOG| Cheletropic Transition State (PM6)]]
|-
| Cheletropic Product (PM6)]
| [[File:CHELETROPIC_PRODUCT_INITIAL_MINIMISATION_2.LOG| Cheletropic Product (PM6)]]
|-
| Endo (Xylylene-SO2) Transition State (PM6)
| [[File:DA_ENDO_PM6_TRANSITIONSTATE_ATTEMPT1.LOG| Endo (Xylylene-SO2) Transition State (PM6)]]
|-
| Endo (Xylylene-SO2) Product (PM6)]
| [[File:DA_ENDO_PM6_PRODUCT_ATTEMPT1_NOTFROZEN_MINIMISATION.LOG| Endo (Xylylene-SO2) Product (PM6)]]
|-
| Exo (Xylylene-SO2) Transition State (PM6)]
| [[File:DA_EXO_PM6_TRANSITIONSTATE_SECOND.LOG| Exo (Xylylene-SO2) Transition State (PM6)]]
|-
| Cheletropic IRC (PM6)]
| [[File:CHELETROPIC_PM6_IRC_ATTEMPT1.LOG | Cheletropic IRC (PM6)]]
|-
| Endo (Xylylene-SO2) IRC (PM6)
| [[File:DA_ENDO_PM6_IRC_ATTEMPT1.LOG| Endo (Xylylene-SO2) IRC (PM6)]]
|-
| Exo (Xylylene-SO2) IRC (PM6)]
| [[File:DA_EXO_PM6_IRC_ATTEMPT1.LOG| Exo (Xylylene-SO2) IRC (PM6)]]
|}

==== Reaction of Sulfur with Alternate, Endo-Cyclic Cis-Butadiene Fragment of Xylylene ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Dioxide + Endo-Cyclic Butadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment
|-
| Endo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]
|[[File:ENDO EXTRA NEW TRANSITIONSTATE ATTEMPT2.LOG| Endo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Endo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:ENDO_EXTRA_NEW_MINIMISATION_ATTEMPT1.LOG| Endo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Exo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:EXO_EXTRA_TRANSITIONSTATE_ATTEMPT1.LOG| Exo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Exo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:EXO_EXTRA_MINIMISATION_ATTEMPT1.LOG| Exo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Cheletropic Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:CHELETROPIC_EXTRA_TRANSITIONSTATE_NOTFROZEN_ATTEMPT2.LOG| Cheletropic Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Cheletropic Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:CHELETROPIC_PRODUC_MINIMISATION_HOPEFULLY_ATTEMPT2.LOG| Cheletropic Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|}

=== GIFs of IRC for Reaction of Sulfur Dioxide and Xylylene ===

It can be seen in all of the GIFs of the reactions below that the 6-membered ring of the highly unstable xylylene molecule becomes aromatic on reaction with sulfur dioxide.

==== GIF for Endo Reaction ====

[[File:Endo_IRC_GIF.gif]]

==== GIF for Exo Reaction ====

[[File:Exo_IRC_GIF.gif]]

This reaction goes from products to reactants.

==== GIF for Cheletropic Reaction ====

[[File:Cheletropic_IRC_GIF.gif]]

=== Thermochemistry ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "3" style="background: #0D4F8B; color: white;" | Reaction Parameters For Reaction of Sulfur Dioxide With Xylylene
|-
! style="background: #0D4F8B; color: white;" | Reaction Type
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
|-
| style="background: #0D4F8B; color: white;" | Endo
| 81.724
| -99.050
|-
| style="background: #0D4F8B; color: white;" | Exo
| 85.709
| -99.714
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| 104.049
| -156.041
|}

The data above shows that the kinetic product is the endo product, due to it having the lowest reaction barrier of 111.946 kJ/mol. This is probably a consequence of the secondary orbitals interactions that were previously discussed, between the second sulfur oxygen and the carbon p orbitals that eventually form the alkene. The cheletropic reaction has the highest reaction barrier of 140.666 kJ/mol. This is potentially due to the 5-membered transition states that forms being of higher energy than that of the 6-membered transition states that form in the endo and exo forms of the reaction.

(The barriers in this text refer to the alternate reactions [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:32, 16 March 2018 (UTC))

The thermodynamic product is also that from the endo reaction, due to it having the lowest energy (-156.041 kJ/mol). This is best explained in terms of bond enthalpies. In the endo and exo reactions, a sulfur-oxygen bond is broken and a carbon-oxygen and sulfur-carbon bond are formed, whereas in the cheletropic reaction, no bonds are broken, and two bonds are formed.

Although the cheletropic reaction proceeds through a higher energy transition states, the formation of two bonds with the loss of none leads to a lower energy product.

=== Reaction Profile for the Reaction of Sulfur Dioxide and the Exo-Cyclic Cis-Butadiene Fragment of Xylylene ===

[[File:Reaction_Profile_for_Exercise_3.png|500px|center]]

=== Further Comment ===

==== Discussion of Stability of Xylylene ====

Xylylene is an 8 electron system, and therefore anti-aromatic (Huckel's 4n rule, with n=2)<sup>(5)</sup>. These systems are often bent to avoid planarity of the p orbitals of the molecule, however xylylene is somewhat constrained to a planar configuration due to the sp<sup>2</sup>) nature of the 6 ring carbons. This makes for a very strained molecule with a high relative energy of 467.460 kJ/mol.

=== Reaction at the Endo-Cyclic, Cis-Butadiene Fragment ===

[[File:Ex3 reaction scheme extension.png|500px|center]]

Reaction scheme above shows the same reactions are possible at the endo-cyclic cis-butadiene fragment of xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "3" style="background: #0D4F8B; color: white;" | Reaction Parameters For Reaction at the Alternate Cis-Butadiene Site of Xylylene
|-
! style="background: #0D4F8B; color: white;" | Reaction Type
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
|-
| style="background: #0D4F8B; color: white;" | Endo
| 111.946
| 16.197
|-
| style="background: #0D4F8B; color: white;" | Exo
| 119.783
| 20.668
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| 140.666
| 47.238
|}

The values for activation energy (reaction barrier) and reaction energy above show these reactions are far less favoured. All the reactions are endothermic, and also have larger reactions barriers than the reactions at the original cis-butadiene fragment.

The reason for the positive values for the reaction energy is due to the fact that there is no gain of aromaticity in these reactions, like there was previously.

The reason for the higher activation barrier is potentially a consequence of the endo-cyclic cis-butadiene fragment being harder to access, therefore the molecules need to adopt higher energy conformations in the transition states to yield the products

== Further Work ==

=== Ring Opening of the Dimethyl Ester Cyclobutene ===

[[File:Cyclobutene.png|500px|center]]

==== Log Files ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Ring Opening of the Dimethyl Ester Cyclobutene
! colspan = "2" style="background: #0D4F8B; color: white;" | Ring Opening of the Dimethyl Ester Cyclobutene
|-
| Dimethyl Ester of Cyclobutene
| [[Media:CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG|Dimethyl Ester of Cyclobutene]]
|-
| Transition State
| [[Media:FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG|Transition State]]
|-
| Diene Product
| [[Media:DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG|Diene Product]]
|-
| IRC Calculation
| [[Media:BIS_CYCLOHEXENE_IRC_ATTEMPT1.LOG| IRC Calculations]]
|}

==== Jmols of MOs ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Jmols of MOs for Ring Opening of the Dimethyl Ester Cyclobutene
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
|-
| Reactant (ring closed)
| <jmol>
<jmolApplet>
<title> Reactant HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Reactant LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Transition State
| <jmol>
<jmolApplet>
<title> Transition State HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Transition State LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product (ring open)
| <jmol>
<jmolApplet>
<title> Product HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Product LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Disrotatory or Conrotatory? ====

Due to running out of time, I have not been able to put the correct MO for the transition state into the table above (I am doing something wrong, but I am sure that the marker will be able to work out what it is I have done). However, the reaction proceeds in a conrotatory fashion, as expected due to it being a 4n cyclisation under thermal conditions<sup>(5)</sup>.

(So what's happened is that you're showing the MOs of the initial geometries of the calculations eg product frame should be 64 not 2. Yes this reaction is conrotatory as you're on the ground state [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:41, 16 March 2018 (UTC))

=== Cyclisation of [1,1']bicyclohexyl-1,1'-diene ===

[[File:Diene_one.png|500px|center]]

==== Log Files ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Cyclisation of [1,1']bicyclohexyl-1,1'-diene
! colspan = "2" style="background: #0D4F8B; color: white;" | Cyclisation of [1,1']bicyclohexyl-1,1'-diene
|-
| [1,1']bicyclohexyl-1,1'-diene
| [[Media:REACTANT_EXTENSION_MINIMISATION.LOG|[1,1']bicyclohexyl-1,1'-diene]]
|-
| Transition State
| [[Media:PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG|Transition State]]
|-
| Cyclised Product
| [[Media:PRODUCT_INITIAL_MINIMISATION.LOG|Cyclised Product]]
|-
| IRC Calculation
| [[Media:FRESHCYCLOBUTENE_PM6_IRC_ATTEMPT1.LOG|IRC Calculation]]
|}

==== Jmols of MOs ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Jmols of MOs for Cyclisation of [1,1']bicyclohexyl-1,1'-diene
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
|-
| Reactant (ring open)
| <jmol>
<jmolApplet>
<title> Reactant HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REACTANT_EXTENSION_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Reactant LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REACTANT_EXTENSION_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Transition State
| <jmol>
<jmolApplet>
<title> Transition State HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Transition State LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product (ring closed)
| <jmol>
<jmolApplet>
<title> Product HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_INITIAL_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Product LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_INITIAL_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(The same problem as before, but perhaps worse here. You've started with geometries that have a plane of symmetry, which in this case have favoured MOs with the same symmetry (just happen to correspond to the orbitals that would be populated under photochemical conditions). If you use the correct frame you'll see that it is all conrotation. Also observing the IRC should show the same result. Perhaps important to know is PM6 is a ground state, single-reference method [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:41, 16 March 2018 (UTC))

==== Disrotatory or Conrotatory? ====

As can be seen from the MOs of the transition state structures for the cyclisation of this [1,1']bicyclohexyl-1,1'-diene, the cyclisation proceeds in a disrotatory fashion, with either end of the butadiene fragment twisting in the opposite direction. This is anticipated due to it being a 4n cyclisation performed under photochemical conditions<sup>(5)</sup>.

==Conclusion==

A computational analysis of three different reactions of increasingly complexity were studied. Through the introduction to Gaussian, two computational methods were used (PM6 and B3LYP/6-31(d)) to optimise both the reactants and products of a reaction. From these initial minimisations, and using chemical intuition, the transition states for these reactions were located.

From using the relative energies of the transition states, reactants and products, thermodynamic properties of the systems were calculated (the activation energy (reaction barrier) and reaction energy). These values were used in discussion of the thermodynamic and kinetic products of the reaction.

Further work was carried out on two electrocyclic reactions, however the student ran out of time to conduct a full analysis of these reactions, for said was enjoying carrying out the calculations too much.

The tutorial and further reading provided facilitated an introduction to potential energy surfaces and the underlying quantum mechanics of the Gaussian code. A computational chemist must marry a working knowledge of the computational methods (and underlying approximations) with the savoir-faire of an experimental chemist.

==References==
{{Reflist}}

1. W. J. Ot, Computational quantum chemistry, 1990, vol. 207.

2. L. S. Bartell, J. Am. Chem. Soc., 1959, 81, 3497–3498.

3. A. Bondi, J. Phys. Chem., 1964, 68, 441–451.

4. B. R. Beno, K. N. Houk and D. A. Singleton, J. Am. Chem. Soc., 1996, 118, 9984–9985.

5. J.Clayden, Organic Chemistry, OUP, Oxford, 2001

6. E. Białkowska-Jaworska, M. Jaworski and Z. Kisiel, J. Mol. Struct., 1995, 350, 247–254.

Rep:FD915 TRANSITION

2018-03-28T10:03:24Z

Fv611: /* Exercise 1 */

= Transition Structure and Reactivity =

Felix de Courcy-Ireland
01062960
Transition States and Reactivity Computational Lab

==Introduction ==

Stationary points on potential energy surfaces (or ‘hypersurfaces’) are defined by a value of zero for the first derivative at that point<sup>(1)</sup>. However, it is through the use of second derivatives that the distinction can be made between the various types of stationary points, including reactants, transition states, intermediates and products<sup>(1)</sup>.

Products, reactants and intermediates are all minima on a potential energy surface. They are characterised by the fact that all paths through these points have a positive second derivative<sup>(1)</sup>.

Transition states are characterised by having a single normal coordinate for which the second derivative is negative, with all other paths through the transition state giving a positive second derivative at this point<sup>(1)</sup>. They are known as ‘saddle-points’. If a point on a potential energy surface is a maximum in more than one normal coordinate, it is diagnostic that there is a lower energy path for the reaction to proceed in the vicinity of this point<sup>(1)</sup>.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:09, 23 March 2018 (UTC) This is a good explanation. But remember that you are working in 3N-6 coordinates.

The calculations carried out were effectively an interrogation of the potential energy surface of a simple reaction. The aims of the calculations were to locate the stationary points of the potential energy surfaces. This was done through using the Gaussian software, which traced paths across the potential energy surface, iteratively calculating the second derivative of each point on the path until a point with a zero first derivative was reached.

In this laboratory, a successfully located transition state was denoted by there being a single negative frequency in the frequency calculation, which when animated, showed the desired reaction coordinate for the reaction.

In the relatively simple reactions investigated, where the reactants pass through only one transition state, it is simple to calculate important quantities such as the activation energy and the reaction energy, from knowledge of the free energies of the reactants, products and transition states.

In this laboratory, two computational methods were used; the semi-empirical PM6 method and the DFT method B3LYP/6-31(d).

The semi-empirical PM6 is a less accurate method but not as computationally expensive. Therefore, it proved useful in optimising structures, be they reactants, products or transition states, in preparation for the use of the more accurate and expensive B3LYP method.
B3LYP/6-31(d) is based in density functional theory (DFT)<sup>(1)</sup>. DFT finds approximate solutions to unsolvable many-electron wave functions by analysis of functionals of the one electron density, ρ(r), of the molecule<sup>(1)</sup>.

In some instances, use of chemical intuition in the location of transition states was most useful. There were cases where it proved fruitful to optimise a product or reactant(s) at the PM6 level, and then freeze the atoms immediately involved in the transition and further minimise the molecule around this frozen ‘transition state’ at the B3LYP level. A final calculation to find the transition state of at the B3LYP level was often more successful when using this ‘bond freezing’ technique.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:09, 23 March 2018 (UTC) OK intro, you could have gone into more detail in part and added some equations/ diagrams

==Exercise 1 ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Excellent work throughout the whole section - well done!)

=== Reaction Scheme ===

[[File:Reaction_scheme.png|550px|center]]

=== Log Files ===

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Butadiene + Ethene
! colspan = "2" style="background: #0D4F8B; color: white;" | Log Files - Butadiene + Ethene
|-
| Minimisation of butadiene (PM6)
| [[Media:CIS_BUTADIENE_ATTEMPT3.LOG| Minimisation of butadiene (PM6)]]
|-
| Minimisation of ethene (PM6)
| [[Media:ETHENE_MINIMISATION_ATTEMPT1.LOG|Minimisation of ethene (PM6)]]
|-
| Minimisation of cyclohexene (PM6)
| [[Media:CYCLOHEXENE_OPTIMISATION_ATTEMPT4.LOG|Minimisation of cyclohexene (PM6)]]
|-
| Transition State (PM6)
| [[Media:BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG|Transition State (PM6)]]
|-
| IRC (PM6)
| [[Media:IRC_FROM_CYCLOHEXENE_ATTEMPT1_BOTH_WAYS.LOG|IRC (PM6)]]
|}

=== MO diagram ===

[[File:Ex1_MO_diagram.png|500px|center| MO diagram for reaction of butadiene and ethene]]

The above molecular orbital diagram shows the interaction between the HOMOs and LUMOs of the ethene and butadiene. Each MO is assigned a symmetry value (assignments were based on the phasing of orbitals) - from these assignments it can be seen that only orbitals of like symmetry interact. The orbital overlap integral is zero for the case of a symmetric-(anti-symmetric) interaction and non-zero for either a symmetric-symmetric or (anti-symmetric)-(anti-symmetric) interaction. The orbital energies are relative to one another rather than being absolute. An attempt has been made to draw the MOs of the transition state - the calculated MOs can be found in the table below.

=== Jmols of the HOMOs and LUMOS of Butadiene and Ethene ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 1 showing the HOMO and LUMO of ethene with relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Ethene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<title>Ethene HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_MINIMISATION_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.39228 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<title>Ethene LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_MINIMISATION_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.04256 E<sub>h</sub>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 2 showing the HOMO and LUMO of butadiene, with relative energies in Hartrees.
! colspan = "3" style="background: #0D4F8B; color: white;" | Butadiene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS_BUTADIENE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.35899 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS_BUTADIENE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01943 E<sub>h</sub>
|}

=== Jmols of the MOs in the Transition State ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 3 showing the four MOs produced from the interaction of the ethene and butadiene MOs with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 16
| <jmol>
<jmolApplet>
<title> MO 16 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.32754 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 17
| <jmol>
<jmolApplet>
<title> MO 17 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.32532 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 18
| <jmol>
<jmolApplet>
<title> MO 18 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.03</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01732 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 19
| <jmol>
<jmolApplet>
<title> MO 19 </title>
<color>white</color>
<size>300</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.03 </script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.03066 E<sub>h</sub>
|}

=== C-C Bond Lengths of Reactants, Transition State and Products ===

[[File:Reaction_scheme.png|550px|center]]

Reaction Scheme repeated for clarity when analysing the bond lengths below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 4 showing bond distances in the reactants.
! colspan = "2" style="background: #0D4F8B; color: white;" | Reactants
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.33344
|-
| C2-C3
| 1.47077
|-
| C3-C4
| 1.33344
|-
| C5-C6
| 1.32731
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 5 showing bond distances in the transition state
! colspan = "2" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.37978
|-
| C2-C3
| 1.41104
|-
| C3-C4
| 1.37981
|-
| C4-C5
| 2.11452
|-
| C5-C6
| 1.38177
|-
| C6-C1
| 2.11469
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 6 showing bond distances in the product
! colspan = "2" style="background: #0D4F8B; color: white;" | Cyclohexene
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.49118
|-
| C2-C3
| 1.36309
|-
| C3-C4
| 1.49118
|-
| C4-C5
| 1.58345
|-
| C5-C6
| 1.56027
|-
| C6-C1
| 1.58345
|}

==== Discussion of carbon-carbon (C-C) bond lengths ====

The C-C single bond length of typical n-hydrocarbon is 1.533 Å, and the bond length of a typical C-C double bond is 1.33 Å<sup>(2)</sup>. These lengths will be used as a point of comparison in the following discussion.

The two pairs of carbon atoms which make up the two alkene bonds in the butadiene (C1-C2 and C3-C4) lengthen from a separation of 1.33 Å to a separation of 1.49 Å. This can be rationalised by observing that these two double bonds in the butadiene reactant will be present in the cyclohexene product as single bonds in the cyclohexene ring.

The internal C-C bond in butadiene (C2-C3) shortens from a distance of 1.47 Å to a distance of 1.36 Å. Again, although this bond is shorter than a typical C-C single bond due to the conjugation of the butadiene, it shortens to a distance more typical of a C-C double bond which it adopts in the cyclohexene product.

The ethene C-C double bond lengthens from 1.327 Å to 1.560 Å. This is due to the carbons moving from the sp<sup>2</sup> hybridised environment of the ethene molecule to the sp<sup>3</sup> hybridised environment of the cyclohexene ring.

The two new C-C bonds which are formed upon the Diels-Alder [4+2] cycloaddition between the butadiene and ethene have a value of 2.115 Å in the transition state, which shortens to a value of 1.583 Å in the cyclohexene product. This change in bond distance shows a shortening of bond lengths from an effectively infinite value in the reactants, through to a bond distance of 1.583 Å in the cyclohexene product.

Van der Waals radius of a carbon atom is 1.7 Å <sup>(3)</sup>, and this can be used in discussion of the partially formed bond between the ethene and butadiene in the transition state.

The length of the partly formed C-C bonds between butadiene and ethene is 2.115 Å. This is less than two times the van der Waals radius of carbon. Therefore, although there is not formally a bond formed between the atoms, the atoms are close enough to interact through van der Waals forces.

==== Vibration corresponding to the transition state ====

<jmol>
<jmolApplet>
<title> Reaction Path Vibration </title>
<color>white</color>
<size>500</size>
<script>frame 15; vibration 2;rotate x -20;</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Jmol above shows the vibration that corresponds to the reaction path at the transition state. It shows that the formation of the two bonds is synchronous - both bonds form simultaneously<sup>(4)</sup>.

==Exercise 2 ==

=== Reaction Scheme ===

[[File:Ex2_reaction_scheme.png|500px|center]]

=== Log files ===

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - 1,3-Dioxole + Cyclohexadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Log Files - 1,3-Dioxole + Cyclohexadiene
|-
| Minimised Cyclohexadiene (B3LYP/6-31G(d))
| [[Media:CYCLOHEXADIENE_REPEAT_AGAIN_B3LYP_MINIMISATION.LOG|Minimised Cyclohexadiene (B3LYP/6-31G(d))]]
|-
| Minimised 1,3-Dioxole (B3LYP/6-31G(d))
| [[Media:13DIOXOLE_PROPER_MINIMISATION_B3LYP_ATTEMPT3.LOG|Minimised 1,3-Dioxole (B3LYP/6-31G(d))]]
|-
| Minimised exo-product (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_MINIMISATION.LOG|Minimised exo-product (B3LYP/6-31G(d))]]
|-
| Minimised endo-product (B3LYP/6-31G(d))
| [[Media:ENDO_FULL_MOLECULE_INITIAL_MINIMISATION_B3LYP.LOG|Minimised endo-product (B3LYP/6-31G(d))]]
|-
| Minimised exo-transition state (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG|Minimised exo-transition state (B3LYP/6-31G(d))]]
|-
| Minimised endo-transition state (B3LYP/6-31G(d))
| [[Media:ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG|Minimised endo-transition state (B3LYP/6-31G(d))]]
|-
| IRC on Exo Transition State (PM6)
| [[Media:EXO_FULL_MOLECULE_IRC_ATTEMPT1.LOG|IRC on Exo Transition State (PM6)]]
|-
| IRC on Endo Transition State (PM6)
| [[Media:ENDO_MOLECULE_PM6_IRC_ATTEMPT1.LOG|IRC on Endo Transition State (PM6)]]
|-
| Single Point Energy on Exo Transition State (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_SINGLEPOINTENERGY.LOG|Single Point Energy on Exo Transition State (B3LYP/6-31G(d))]]
|-
| Single Point Energy on Endo Transition State (B3LYP/6-31G(d))
| [[Media:ENDO_MOLECULE_B3LYP_SINGLEPOINTENERGY.LOG|Single Point Energy on Endo Transition State (B3LYP/6-31G(d))]]
|}

=== Jmols and Molecular Orbital Diagram for the Endo Reaction of Cyclohexadiene and 1,3-Dioxole ===

[[File:Ex2_MO_diagram_endo.png|500px|right| MO diagram for reaction with endo arrangement between 1,3-dioxole and cyclohexadiene]]

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Table 7 showing the MOs of the endo transition state with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 40 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 40 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19648 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 41 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 41 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19052 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 42 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 42 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.00462 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 43 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 43 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01543 E<sub>h</sub>
|}

Above is the new MO diagram from the endo reaction of cyclohexadiene and 1,3-dioxole. The endo reaction involves the two oxygen atoms of the 1,3-dioxole tucking under the cyclohexadiene. This leads to a stabilising secondary orbital interaction which shall be discussed later. The MO's produced by the interaction of the cyclohexadiene and 1,3-dioxole orbitals are shown in Table 7.

=== Jmols and Molecular Orbital Diagram for the Exo Reaction of Cyclohexadiene and 1,3-Dioxole ===

[[File:Ex2_MO_diagram_exo.png|500px|right| MO diagram for reaction with exo arrangement between 1,3-dioxole and cyclohexadiene]]

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Table 8 showing the MOs of the exo transition state with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 40 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 40 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19801 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 41 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 41 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.18560 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 42 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 42 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.00699 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 43 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 43 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01019 E<sub>h</sub>
|}

Above is the MO diagram from the exo transition state, with the MOs produced from interaction of the reactant HOMOs and LUMOs shown in Table 8. It should be noted that, similarly to the previous Diels-Alder reaction of butadiene and ethene, that only orbitals of like symmetry interact to give MOs in the transition state.

=== Inverse and Normal Electron Demand Diels-Alder Reactions ===

The reaction between 1,3-dioxole and cyclohexadiene is an inverse electron demand Diels-Alder reaction. Inverse electron demand Diels-Alder reactions are characterised by there being a smaller energy gap between the HOMO of the dienophile (1,3-dioxole) and the LUMO of the diene (cyclohexadiene) than the energy gap between the HOMO of the diene and the LUMO of the dienophile<sup>(5)</sup>.

[[File:Inverse_normal_DA.png|400px|center|Figure highlighting the relative energy differences that lead to definition of normal and inverse electron demand Diels-Alder reactions.]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:12, 23 March 2018 (UTC) This is correct however you have just stated it with no values. You have even done a single point energy calculation too! Why not use the numbers for the MOs that you have calculated to prove your hypothesis.

=== Thermochemistry ===

If the formation of more than one product is possible from a given set of reactants, knowledge of reaction energies and activation energies can lead to assignment of the kinetic and thermodynamic products. The kinetically favourable product is that from the reaction which has the lowest energy barrier to conversion between reactants and products. The thermodynamically favourable product is the lower energy product relative to the reactant(s).

In the case that there are two possible products of a reaction, as is the situation in this Diels-Alder reaction between 1,3-dioxole and cyclohexadiene, it is not necessary for one product to be the thermodynamic product and the other product to be the kinetic product. It may be the case that one of the products is both the thermodynamic and kinetic product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Energies Endo Reaction
|-
! style="background: #0D4F8B; color: white;" | Molecule
! style="background: #0D4F8B; color: white;" | Gibbs Free Energy (kJ/mol)
|-
| 1,3dioxole
| -701,188.414
|-
| cyclohexadiene
| -612,592.877
|-
| 1,3dioxole and cyclohexadiene
| -1,313,781.291
|-
| Endo Transition State
| -1,313,621.479
|-
| Endo Product
| -1,313,848.695
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Endo Reaction Parameters
|-
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
| 159.811
|-
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
| -67.404
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Energies Exo Reaction
|-
! style="background: #0D4F8B; color: white;" | Molecule
! style="background: #0D4F8B; color: white;" | Gibbs Free Energy (kJ/mol)
|-
| 1,3dioxole
| -701,188.414
|-
| cyclohexadiene
| -612,592.877
|-
| 1,3dioxole and cyclohexadiene
| -1,313,781.291
|-
| Exo Transition State
| -1,313,613.639
|-
| Exo Product
| -1,313,845.098
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Exo Reaction Parameters
|-
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
| 167.651
|-
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
| -63.807
|}

As shown in the above tables, the reaction barrier for the exo reaction is higher at a value of 167.651 kJ/mol, due to the transition state through which the reaction proceeds being of higher energy. Therefore, due to the lower reaction barrier of 159.811 kJ/mol, the endo product is kinetic product.

The endo product proceeds through a lower energy transition state due to the secondary orbital interactions between the oxygen p orbitals and the p orbitals of the internal carbons of the cis-butadiene fragment<sup>(5)</sup>.

The Jmol of the HOMO of the endo transition state is repeated here, where it can be seen that there is a stabilising interaction between the orbitals which lie on the oxygens of 1,3-dioxole and the two carbons which eventually form the double bond in the product, for the portion of the orbital located in these areas is the same phase.

<jmol>
<jmolApplet>
<title> MO 41 - Endo Transition State </title>
<color>white</color>
<size>350</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The endo product is again the thermodynamic product, as the energy of the endo product (-67.404 kJ/mol) is lower than that of the exo product (-63.807) - although the difference in energy is less in the products than in the reactants. This reason for the greater stabilisation of the endo product is possibly due to this same orbital interaction between the p orbitals on the oxygens with the alkene pi system. The fact that the difference in energy between the products is less than the difference in energy of the transition states is a consequence of this orbital interaction being poorer in the products.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:14, 23 March 2018 (UTC) This is a good section. You have got the correct energies and come to the correct conclusions. However there are part where you could have gone into more detail. Such as the thermo and kinetic theory, or the electron demand.

==Exercise 3 ==

[[File:Ex3_reaction_scheme.png|500px|center]]

=== Log Files ===

==== Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Dioxide + Exo-Cyclic Butadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment
|-
| Xylylene Minimisation (PM6)
|[[File:XYLYLENE_MINIMISATION_PM6.LOG| Xylylene Minimisation (PM6)]]
|-
| Sulfur Dioxide Minimisation (PM6)
| [[File:SULFUR_DIOXIDE.LOG| Sulfur Dioxide Minimisation (PM6)]]
|-
| Cheletropic Transition State (PM6)]
| [[File:CHELETROPIC_PM6_PRODUCT_TRANSITIONSTATE_NOTFROZEN.LOG| Cheletropic Transition State (PM6)]]
|-
| Cheletropic Product (PM6)]
| [[File:CHELETROPIC_PRODUCT_INITIAL_MINIMISATION_2.LOG| Cheletropic Product (PM6)]]
|-
| Endo (Xylylene-SO2) Transition State (PM6)
| [[File:DA_ENDO_PM6_TRANSITIONSTATE_ATTEMPT1.LOG| Endo (Xylylene-SO2) Transition State (PM6)]]
|-
| Endo (Xylylene-SO2) Product (PM6)]
| [[File:DA_ENDO_PM6_PRODUCT_ATTEMPT1_NOTFROZEN_MINIMISATION.LOG| Endo (Xylylene-SO2) Product (PM6)]]
|-
| Exo (Xylylene-SO2) Transition State (PM6)]
| [[File:DA_EXO_PM6_TRANSITIONSTATE_SECOND.LOG| Exo (Xylylene-SO2) Transition State (PM6)]]
|-
| Cheletropic IRC (PM6)]
| [[File:CHELETROPIC_PM6_IRC_ATTEMPT1.LOG | Cheletropic IRC (PM6)]]
|-
| Endo (Xylylene-SO2) IRC (PM6)
| [[File:DA_ENDO_PM6_IRC_ATTEMPT1.LOG| Endo (Xylylene-SO2) IRC (PM6)]]
|-
| Exo (Xylylene-SO2) IRC (PM6)]
| [[File:DA_EXO_PM6_IRC_ATTEMPT1.LOG| Exo (Xylylene-SO2) IRC (PM6)]]
|}

==== Reaction of Sulfur with Alternate, Endo-Cyclic Cis-Butadiene Fragment of Xylylene ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Dioxide + Endo-Cyclic Butadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment
|-
| Endo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]
|[[File:ENDO EXTRA NEW TRANSITIONSTATE ATTEMPT2.LOG| Endo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Endo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:ENDO_EXTRA_NEW_MINIMISATION_ATTEMPT1.LOG| Endo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Exo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:EXO_EXTRA_TRANSITIONSTATE_ATTEMPT1.LOG| Exo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Exo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:EXO_EXTRA_MINIMISATION_ATTEMPT1.LOG| Exo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Cheletropic Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:CHELETROPIC_EXTRA_TRANSITIONSTATE_NOTFROZEN_ATTEMPT2.LOG| Cheletropic Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Cheletropic Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:CHELETROPIC_PRODUC_MINIMISATION_HOPEFULLY_ATTEMPT2.LOG| Cheletropic Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|}

=== GIFs of IRC for Reaction of Sulfur Dioxide and Xylylene ===

It can be seen in all of the GIFs of the reactions below that the 6-membered ring of the highly unstable xylylene molecule becomes aromatic on reaction with sulfur dioxide.

==== GIF for Endo Reaction ====

[[File:Endo_IRC_GIF.gif]]

==== GIF for Exo Reaction ====

[[File:Exo_IRC_GIF.gif]]

This reaction goes from products to reactants.

==== GIF for Cheletropic Reaction ====

[[File:Cheletropic_IRC_GIF.gif]]

=== Thermochemistry ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "3" style="background: #0D4F8B; color: white;" | Reaction Parameters For Reaction of Sulfur Dioxide With Xylylene
|-
! style="background: #0D4F8B; color: white;" | Reaction Type
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
|-
| style="background: #0D4F8B; color: white;" | Endo
| 81.724
| -99.050
|-
| style="background: #0D4F8B; color: white;" | Exo
| 85.709
| -99.714
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| 104.049
| -156.041
|}

The data above shows that the kinetic product is the endo product, due to it having the lowest reaction barrier of 111.946 kJ/mol. This is probably a consequence of the secondary orbitals interactions that were previously discussed, between the second sulfur oxygen and the carbon p orbitals that eventually form the alkene. The cheletropic reaction has the highest reaction barrier of 140.666 kJ/mol. This is potentially due to the 5-membered transition states that forms being of higher energy than that of the 6-membered transition states that form in the endo and exo forms of the reaction.

(The barriers in this text refer to the alternate reactions [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:32, 16 March 2018 (UTC))

The thermodynamic product is also that from the endo reaction, due to it having the lowest energy (-156.041 kJ/mol). This is best explained in terms of bond enthalpies. In the endo and exo reactions, a sulfur-oxygen bond is broken and a carbon-oxygen and sulfur-carbon bond are formed, whereas in the cheletropic reaction, no bonds are broken, and two bonds are formed.

Although the cheletropic reaction proceeds through a higher energy transition states, the formation of two bonds with the loss of none leads to a lower energy product.

=== Reaction Profile for the Reaction of Sulfur Dioxide and the Exo-Cyclic Cis-Butadiene Fragment of Xylylene ===

[[File:Reaction_Profile_for_Exercise_3.png|500px|center]]

=== Further Comment ===

==== Discussion of Stability of Xylylene ====

Xylylene is an 8 electron system, and therefore anti-aromatic (Huckel's 4n rule, with n=2)<sup>(5)</sup>. These systems are often bent to avoid planarity of the p orbitals of the molecule, however xylylene is somewhat constrained to a planar configuration due to the sp<sup>2</sup>) nature of the 6 ring carbons. This makes for a very strained molecule with a high relative energy of 467.460 kJ/mol.

=== Reaction at the Endo-Cyclic, Cis-Butadiene Fragment ===

[[File:Ex3 reaction scheme extension.png|500px|center]]

Reaction scheme above shows the same reactions are possible at the endo-cyclic cis-butadiene fragment of xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "3" style="background: #0D4F8B; color: white;" | Reaction Parameters For Reaction at the Alternate Cis-Butadiene Site of Xylylene
|-
! style="background: #0D4F8B; color: white;" | Reaction Type
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
|-
| style="background: #0D4F8B; color: white;" | Endo
| 111.946
| 16.197
|-
| style="background: #0D4F8B; color: white;" | Exo
| 119.783
| 20.668
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| 140.666
| 47.238
|}

The values for activation energy (reaction barrier) and reaction energy above show these reactions are far less favoured. All the reactions are endothermic, and also have larger reactions barriers than the reactions at the original cis-butadiene fragment.

The reason for the positive values for the reaction energy is due to the fact that there is no gain of aromaticity in these reactions, like there was previously.

The reason for the higher activation barrier is potentially a consequence of the endo-cyclic cis-butadiene fragment being harder to access, therefore the molecules need to adopt higher energy conformations in the transition states to yield the products

== Further Work ==

=== Ring Opening of the Dimethyl Ester Cyclobutene ===

[[File:Cyclobutene.png|500px|center]]

==== Log Files ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Ring Opening of the Dimethyl Ester Cyclobutene
! colspan = "2" style="background: #0D4F8B; color: white;" | Ring Opening of the Dimethyl Ester Cyclobutene
|-
| Dimethyl Ester of Cyclobutene
| [[Media:CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG|Dimethyl Ester of Cyclobutene]]
|-
| Transition State
| [[Media:FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG|Transition State]]
|-
| Diene Product
| [[Media:DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG|Diene Product]]
|-
| IRC Calculation
| [[Media:BIS_CYCLOHEXENE_IRC_ATTEMPT1.LOG| IRC Calculations]]
|}

==== Jmols of MOs ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Jmols of MOs for Ring Opening of the Dimethyl Ester Cyclobutene
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
|-
| Reactant (ring closed)
| <jmol>
<jmolApplet>
<title> Reactant HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Reactant LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Transition State
| <jmol>
<jmolApplet>
<title> Transition State HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Transition State LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product (ring open)
| <jmol>
<jmolApplet>
<title> Product HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Product LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Disrotatory or Conrotatory? ====

Due to running out of time, I have not been able to put the correct MO for the transition state into the table above (I am doing something wrong, but I am sure that the marker will be able to work out what it is I have done). However, the reaction proceeds in a conrotatory fashion, as expected due to it being a 4n cyclisation under thermal conditions<sup>(5)</sup>.

(So what's happened is that you're showing the MOs of the initial geometries of the calculations eg product frame should be 64 not 2. Yes this reaction is conrotatory as you're on the ground state [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:41, 16 March 2018 (UTC))

=== Cyclisation of [1,1']bicyclohexyl-1,1'-diene ===

[[File:Diene_one.png|500px|center]]

==== Log Files ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Cyclisation of [1,1']bicyclohexyl-1,1'-diene
! colspan = "2" style="background: #0D4F8B; color: white;" | Cyclisation of [1,1']bicyclohexyl-1,1'-diene
|-
| [1,1']bicyclohexyl-1,1'-diene
| [[Media:REACTANT_EXTENSION_MINIMISATION.LOG|[1,1']bicyclohexyl-1,1'-diene]]
|-
| Transition State
| [[Media:PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG|Transition State]]
|-
| Cyclised Product
| [[Media:PRODUCT_INITIAL_MINIMISATION.LOG|Cyclised Product]]
|-
| IRC Calculation
| [[Media:FRESHCYCLOBUTENE_PM6_IRC_ATTEMPT1.LOG|IRC Calculation]]
|}

==== Jmols of MOs ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Jmols of MOs for Cyclisation of [1,1']bicyclohexyl-1,1'-diene
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
|-
| Reactant (ring open)
| <jmol>
<jmolApplet>
<title> Reactant HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REACTANT_EXTENSION_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Reactant LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REACTANT_EXTENSION_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Transition State
| <jmol>
<jmolApplet>
<title> Transition State HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Transition State LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product (ring closed)
| <jmol>
<jmolApplet>
<title> Product HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_INITIAL_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Product LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_INITIAL_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(The same problem as before, but perhaps worse here. You've started with geometries that have a plane of symmetry, which in this case have favoured MOs with the same symmetry (just happen to correspond to the orbitals that would be populated under photochemical conditions). If you use the correct frame you'll see that it is all conrotation. Also observing the IRC should show the same result. Perhaps important to know is PM6 is a ground state, single-reference method [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:41, 16 March 2018 (UTC))

==== Disrotatory or Conrotatory? ====

As can be seen from the MOs of the transition state structures for the cyclisation of this [1,1']bicyclohexyl-1,1'-diene, the cyclisation proceeds in a disrotatory fashion, with either end of the butadiene fragment twisting in the opposite direction. This is anticipated due to it being a 4n cyclisation performed under photochemical conditions<sup>(5)</sup>.

==Conclusion==

A computational analysis of three different reactions of increasingly complexity were studied. Through the introduction to Gaussian, two computational methods were used (PM6 and B3LYP/6-31(d)) to optimise both the reactants and products of a reaction. From these initial minimisations, and using chemical intuition, the transition states for these reactions were located.

From using the relative energies of the transition states, reactants and products, thermodynamic properties of the systems were calculated (the activation energy (reaction barrier) and reaction energy). These values were used in discussion of the thermodynamic and kinetic products of the reaction.

Further work was carried out on two electrocyclic reactions, however the student ran out of time to conduct a full analysis of these reactions, for said was enjoying carrying out the calculations too much.

The tutorial and further reading provided facilitated an introduction to potential energy surfaces and the underlying quantum mechanics of the Gaussian code. A computational chemist must marry a working knowledge of the computational methods (and underlying approximations) with the savoir-faire of an experimental chemist.

==References==
{{Reflist}}

1. W. J. Ot, Computational quantum chemistry, 1990, vol. 207.

2. L. S. Bartell, J. Am. Chem. Soc., 1959, 81, 3497–3498.

3. A. Bondi, J. Phys. Chem., 1964, 68, 441–451.

4. B. R. Beno, K. N. Houk and D. A. Singleton, J. Am. Chem. Soc., 1996, 118, 9984–9985.

5. J.Clayden, Organic Chemistry, OUP, Oxford, 2001

6. E. Białkowska-Jaworska, M. Jaworski and Z. Kisiel, J. Mol. Struct., 1995, 350, 247–254.

Rep:MOD:TS Yiming Xu

2018-03-28T09:57:13Z

Fv611: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

= Introduction =

The potential energy surface (PES) is the mathematical relationship between the energy of a molcule and its geometry. <ref>E. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics, Springer Netherlands, Dordrecht, 2nd edn., 2011.</ref> By taking advantage of the Born-Oppenheimer approximation, the PES represents the electronic energy of the molecule at all possible arrangements of the atoms. Vibrational zero-point energy is sometimes added to the PES for increased accuracy.

For a molecule with N atoms, this represents a surface with 3N-6 dimensions (degrees of freedom for a non-linear molecule). Naïvely, this could be found by evaluating the energy of the molecule over all points in space using specific methods suitable for the molecule at hand. However, the effectively infinite number of possible configurations renders this approach computationally impossible. Luckily, during a reaction, only a limited "patch" of the PES is explored by the molecule, and any analysis of a reaction can be reasonably limited to studies of the reactants, products, and any surface that they traversed from the reactants to products (the reaction profile).

The reactants and products are (relatively) stable chemical species. Intuitively, they reside in minima on the PES - as stable chemical species, they tend to return to their configuration from slight perturbations. On the other hand, a reaction path is physical, and must necessarily be continuous and differentiable (where the PES itself might not be). In this case, a reaction profile joining two minima (i.e. reactants and products) will pass through one (or more) maxima along the reaction coordinate. These properties can be used to deduce structures from the PES.

== Critical points on the PES ==

Both minima and maxima are stationary points on the PES. For a stationary point at <math>\vec{q}</math>, the following relationship must hold:

<math display="block"> \nabla U(\vec{q})= 0</math>,

where <math>\nabla</math> is the gradient function, <math>\vec{q}</math> is any geometric parameter (e.g. mass-weighted coordinates), and <math>U(\vec{q})</math> is the potential energy surface. In order to determine if it is a local maximum or minimum, the second derivative test must be conducted. First, a square <math>n\times n</math> matrix, where <math>n</math> is the number of geometric parameters, can be defined:

<math display="block"> H_{i,j} = \frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}}</math>

where <math>H_{i,j}</math> is the i-th and j-th term of the Hessian matrix, <math>H</math>. The second partial derivative test is conducted by looking at the eigenvalue of the Hessian matrix at the stationary points <math>\vec{q}</math>, assuming that <math>H</math> is invertible: - If all eigenvalues are positive, <math>\vec{q}</math> is at a local maximum. - If all eigenvalues are negative, <math>\vec{q}</math> is at a local minimum. - If there is a mix of positive and negative eigenvalues, <math>\vec{q}</math> is at a saddle point. - And inconclusive otherwise.

In essence, the second partial derivative test is looking at direction of the local curvature at the station points.

== Harmonic Approximation and the Transition State ==

When deviation from equilibrium stationary points are small, the harmonic approximation can be used. The general expression of the harmonic approximation is as follows:

<math display="block">U \approx \frac{1}{2}\sum_{i,j=1}\frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}} q_i q_j</math>

As the force is related to energy as well as position,

<math display="block">\begin{align}
\vec{F} &= -\nabla U\\
& = -k\vec{X}
\end{align}
</math>

where <math>\vec{F}</math> is the column vector of the forces <math>[\vec{F_1},\vec{F_2}, ...]^T</math>, <math>X</math> is the column displacement vector of the coordinates <math>[\vec{q_1},\vec{q_2}, ...]^T</math>, and <math>k</math> is the force tensor connecting the force to the displacement of the atoms from their equilibrium positions. The differential equation admits a solution of the form:

<math display="block"> \vec{F} = -\omega ^2 \vec{X}</math>

where <math>\omega</math> is the frequency of vibration of the harmonic oscillator. It is obvious that it is an eigenvalue problem to obtain values of <math>\omega</math>, with the associated eigenvectors being the normal modes of vibrations. In practice, this is often referred to diagonalising the Hessian matrix, as the elements of the diagonalised matrix are the eigenvalues of the matrix. If we compare the form of the harmonic approximation with the second partial derivative test, it could be immediately seen that:

<math display="block"> k_{i,j} = H_{i,j} = \frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}}</math>

We could then restate the relationship between curvature and vibration as follows:

# The frequency of vibration is proportional to the square root of the local curvature at the point.
# A local minimum along coordinate <math>q_i</math> will have a positive frequency of vibration along coordinate <math>q_i</math>; and
# A local maximum along coordinate <math>q_i</math> will have an imaginary frequency of vibration (<math>\sqrt{-x} = i\sqrt{x}</math>); and
# A saddle point will have a mixture of positive and imaginary vibrational frequencies.

A transition state is defined to be a point on the PES that lies at the minimum along all coordinates, except for the reaction coordinate along which it lies at the maximum. <ref>E. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics, Springer Netherlands, Dordrecht, 2nd edn., 2011.</ref> In this case, a transition state will have one and only one imaginary vibrational frequency in its structure.

From the transition state, optimization of the structure along the coordinate following the steepest descent (as informed by the imaginary vibration frequency or negative force constant) allows one to reach the reactant and product state. The path traced out by such a procedure is called the Intrinsic Reaction Coordinate (IRC), and may or may not represent an actual physical reactive path due to other energy contributions (e.g. vibrational, kinetic, etc.). In either case, the IRC allows us to understand the changes in the molecular geometry, along with its electronic properties and molecule wavefunction, through the course of an reaction.

== Computational Approaches ==

In quantum mechanics, all information about a quantum system is encoded In its wavefunction, <math>\Psi</math>. The wavefunction obeys the Schrödinger equation, generally stated (in its time-independent form) ss below:

<math display="block">\hat{H} \Psi = E \Psi</math>

where <math>\hat{H}</math> is the Hamiltonian operator and <math> E </math> is the energy of the system. The Schrödinger equation is not analytically solvable in general, and many techniques have been developed since to find an approximate solution to the Schrödinger equation. One of the earliest approaches was the Hartree–Fock method. It was an ''ab initio'' computational method to directly compute the molecule wavefunction. Along with post-Hartree–Fock methods and alternatives approaches such as the Density Functional Theory (DFT). The different approaches share broadly similar features.

One of the most useful computational methods for finding the ground state solution is the variational method, based on the variational principle. It requires the use of trial solutions (''ansatz''), often a basis set of orbitals, to evaluate the energy eigenvalue. As the variational principle states that the true ground state has the lowest energy, the wavefunction (or rather coefficients to the basis set) can be found by locating the global minimum of the ansatz. Often, the basis set of orbitals are orthogonal to each other and uses either Slater Type Orbitals (STOs) or Gaussian Type Orbitals (GTOs) to save computation time.

Different methods employ different formalism and assumptions to simplify calculations. For example, Hartree–Fock implies the mean-field assumption and ignores electron correlation. The ansatz for the variational method is the Slater determinant of the basis sets and solves for the molecular wavefunction directly. DFT works by recognising the equivalence of finding the electron density of the molecule with its ground state wavefunction, allowing the optimizing of a single electron Schrödinger equation, shortening computation time. Modern methods with hybrid functionals (e.g. B3LYP) may use features from both to obtain more accurate results.

Unlike the ''ab initio'' methods above, semi-empirical methods drastically shorten computation time by making assumptions and correcting for them using parameters. These can include the zero differential overlap assumption, reducing the computational complexity scaling from <math>N^4</math> to <math>N^2</math>, where <math>N</math> is the number of electrons. One common semi-empirical method is the Huckle method for π-electrons. However, the parametrization requirement means that different parameters or assumptions must be used for different systems (valence electron vs п-electrons, transition metals, small vs heavy elements, etc.). When properly parameterized, semi-empirical methods can produce results more accurately than ''ab initio'' methods with much greater computation efficiency. Even if general purpose semi-empiricle methods (e.g. PM6) are less accurate than ''ab initio'' methods, its computational efficiency means that it is often used as an initial step in an optimization.

= Experimental Methods =

In this experiment, the Diels-Alder reaction was investigated in 3 different systems: reaction of butadiene with ethylene, reaction of cyclohexadiene with 1,3-dioxole, and reaction between o-xylylene and sulphur dioxide. The calculations are carried out with Gaussian 09 on Windows 7. Unless otherwise specified, initial geometry optimizations and IRC calculations were carried out in PM6 at default settings, with IRC calculations allowed to carry out to PES minima. Reactant, product and transition state molecular orbital calculations were carried out with B3LYP/6-31G(d) unless otherwise specified.

Results were extracted and analysed with GuassView (v5.0.9), as well as with cclib (v1.5) on Jupyter Notebook using Python (v3.6.4). Python analysis script is available on request. Surfaces were visualized via generation of Cube files from Gaussian, then converted to .jvxl files for faster loading and subsequently visualized on JSmol.

= Exercise 1: Reaction of Butadiene with Ethylene =

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Unfortunately this section is very confused. The MO diagram is incorrect, and even though you have correctly stated the symmetry requirements for the combination of reactant fragment orbitals you did not apply that to your computed orbitals. Additionally you didn't include jmols or log files so it is impossible to know if you have uploaded the wrong pictures or ran the wrong calculation.)

[[File:Yx6015 mechanism butadiene ethene.png|thumb|300px|'''Figure 1'''. Arrow-pushing mechanism of the Diels-Alder reaction between buta-1,3-diene and ethene showing concerted addition.]]

The reaction between buta-1,3-diene with ethene is the simplest example of a Diels-Alder reaction. The Diels-Alder reaction is a concerted pericyclic reaction between a diene (i.e. buta-1,3-diene) and a dieneophile (i.e. ethene). It in general proceeds via a single transition state with no intermediates, and is thus classified as a [4π<sub>S</sub>+2π<sub>S</sub>], and is thermally allowed under the Woodward-Hoffmann rules.

[[File:Yx6015 modiagram TS butadiene ethene.png|center|thumb|800px|'''Figure 2''': Molecular orbital diagram for the reaction between buta-1,3-diene in s-cis conformation (left) and ethene (right), along with the predicted transition state (middle).]]

Using the Hückel method, we could restrict our analysis to only π-electrons. An illustration of the molecular orbitals is found in Figure 2. It is important to note that there are additional interactions betwene the sigma and pi frameworks of the molecules. From the MO diagram, it could be seen that there are significant interactions throughout the pi system. For example, the TS orbital
π<sub>3s</sub> is due to the net interaction of 3 orbitals: butadiene π<sub>1s</sub> and π<sub>3s</sub>, and ethene π<sub>1s</sub>. Using frontier orbital molecular theory, we could further simplify analysis by, looking at only the HOMO/LUMO of the reactants and their interactions.

{| class="wikitable" style="text-align: center; margin: auto;"
|
!Buta-1,3-diene
!colspan = 2| Transition State
!Ethene
|- style="vertical-align:bottom;"
! scope="row" style="vertical-align:middle;"| LUMOs
| [[File:Yx6015 butadiene lumo.png|center|thumb|200px|'''Figure 3a''': Molecular orbital of the LUMO of buta-1,3-diene (MO 12, energy = +0.01104 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS4.png|center|thumb|200px|'''Figure 5a''': Molecular orbital of the LUMO of the TS (MO 16, energy = -0.32755 a.u.). Corresponds to π<sub>5a</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS3.png|center|thumb|200px|'''Figure 5b''': Molecular orbital of the LUMO+1 of the TS (MO 17, energy = -0.32533 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 ethene lumo.png|center|thumb|200px|'''Figure 4a''': Molecular orbital of the LUMO of ethene (MO 7, energy = +0.04256 a.u.). Corresponds to π<sub>4s</sub> from Fig 2.]]
|- style="vertical-align:bottom;"
! scope="row" style="vertical-align:middle;"| HOMOs
| [[File:Yx6015 butadiene homonew.png|center|thumb|200px|'''Figure 3b''': Molecular orbital of the HOMO of buta-1,3-diene(MO 11, energy = -0.35169 a.u.). Corresponds to π<sub>2a</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS2.png|center|thumb|200px|'''Figure 5c''': Molecular orbital of the HOMO-1 of the TS MO 18, energy = +0.01732 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS1.png|center|thumb|200px|'''Figure 5d''': Molecular orbital of the HOMO of the TS (MO 19, energy = +0.03067 a.u.). Corresponds to π<sub>2a</sub> from Fig 2.]]
| [[File:Yx6015 ethene homo.png|center|thumb|200px|'''Figure 4b''': Molecular orbital of the HOMO of ethene (MO 6, energy = -0.39228a.u.). Corresponds to π<sub>1s</sub> from Fig 2.]]
|}

For Figures 3, 4, and 5, only the MOs that would be directly relevant from the frontier orbitals are shown. It can be obviously seen that the frontier orbital theory is sufficient for this case - MO 16 and MO 18 cannot be generated from the HOMO and LUMO of the reactants only. A more correct interpretatin and diagram is depicted in Figure 2. In addition, it is clear the symmetry of the orbitals are important for their interaction and for a reaction to proceed - with orbitals only interacting with each other if they have the same symmetry. This can be formalized by the orbital overlap integral:

<math display = "block">
S_{AB} = <\psi^*_A|\psi_B>
</math>

where <math>S_{AB}</math> is the overlap integral for wavefunctions A and B, <math>\psi^*_A</math> is the Hermitian adjoint of wavefunction A, and <math>\psi_B</math> is wavefunction B. It is immediately evident that where <math>\psi_A</math> and <math>\psi_B</math> are of opposite phase, <math>\psi_A \times \psi_B</math> is an odd function and <math>S_{AB}</math> evaluates to 0. Specifically:

* the overlap integral is zero for a symmetric-antisymmetric interaction;
* the overlap integral is non-zero for a symmetric-symmetric interaction; and
* the overlap integral is non-zero for a antisymmetric-antisymmetric interaction.

The transition state for this reaction could be quite easily found as it is a simple molecular system. As detailed above, it was verified to be correct as it contains only 1 imaginary frequency, and the vibration corresponds to the desired reaction path. The transition state is visualized below.

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015_TS_reaction_path.gif|center|frame|300px|'''Figure 6a''': Transition state vibration at 948.67i cm<sup>-1</sup>. Calculated E(RPM6] = 0.11286018 at ultrafine grid.]]
| [[File:Yx6015 anim irc butadiene ethene.gif|center|frame|300px|'''Figure 6b''': IRC path for reaction between buta-1,3-diene and ethene.]]
|}

From the transition, an IRC optimization was carried out to find the reaction path, and to confirm that the transition state is indeed the transition state. The IRC path is also shown above, illustrating the correct TS and transition state is found. The changes to the bond lengths of the products and reactants could be visualized from the IRC.

| [[File:Yx6015 ccbonds butadiene ethene.png|center|thumb|800px|'''Figure 7a''': All bond lengths over the reaction coordiante. Reactant on negative reaction coordinate.]]
| [[File:Yx6015 chbonds butadiene ethene.png|center|thumb|800px|'''Figure 7b''': C-H bond lengths over the reaction coordinate. Reactant on negative reaction coordinate.]]

As can be seen from Figure 7, the bond lengths of the various C-C and C-H bonds vary across the reaction coordinate as expected. In general, variation comes from the change in hybridization of the terminal carbons bonds on butadiene and ethene from double bond to single bond, and the change from 'middle' carbons on butadiene from single to double bond. Similar variations are seen for C-H bonds, although the trend is not as straightforward. Notably, differences in the products are seen depending on the position of the hydrogen - axial vs equitorial, bowspirit vs flagpole. The two forming C-C bonds could also be seen approaching each other over time.

From the animation as well as the overlapped nature of the graph (each line has another line underneath), it is clear that the formation of the two bonds was synchronous. This was to be expected as the reactants, transition state and product all have the same plane of symmetry.

= Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole =

[[File:Yx6015 mechanism cyclohexadiene dioxole.png|thumb|300px|'''Figure 8'''. Arrow-pushing mechanism of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole showing concerted addition.]]

The reaction is another example of a Diels-Alder reaction. Changing the dienenophile from ethene to dioxole allowed the possibility of the product having two stereoisomers - the endo product and the exo product. The IRC paths for the respective products are as follow:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc cyclohexadiene dioxole exo.gif|center|frame|300px|'''Figure 9a''': IRC path for the reaction between cyclohexadiene and 1,3-dioxole with the exo product.]]
| [[File:Yx6015 anim irc cyclohexadiene dioxole endo.gif|center|frame|300px|'''Figure 9b''': IRC path for the reaction between cyclohexadiene and 1,3-dioxole with the endo product.]]
|}

From Figure 9, it could be seen that the transition state leading to the different products had different transition structures. The reactants' MO should however be identical:

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Cyclohexadiene
! 1,3-Dioxole
|-
! scope = "row"| LUMO
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/c/c1/Yx6015_cyclohexadiene_631Gd_mo23.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 cyclohexadiene 631Gd mo22.cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 23, energy = -0.01710 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/3/30/Yx6015_Dioxole_631Gd_mo20.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 Dioxole 631Gd mo20cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 20, energy = +0.03794 a.u., symmetric
|-
! scope = "row"| HOMO
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/c/cc/Yx6015_cyclohexadiene_631Gd_mo22.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 cyclohexadiene 631Gd mo22.cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 22, energy = -0.20551 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/60/Yx6015_Dioxole_631Gd_mo19.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 Dioxole 631Gd mo20cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 19, energy = -0.19594 a.u., antisymmetric
|}

From the molecular orbitals of the reactants, the transition state MO could be inferred. As with the previous section, only orbitals with the same symmetry have significant interactions. The reactant molecules overlap in either an endo or exo orientation. The molecular orbitals of the transition state is visualized as below:

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Endo Transition State
! Exo Transition State
|-
! scope = "row"| LUMO +1 (MO43)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/65/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo43.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = +0.01550 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/e/e6/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo43.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = +0.01024 a.u., antisymmetric
|-
! scope = "row"| LUMO (MO42)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/3/3f/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo42.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.00466 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/b/b2/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo42.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.00703 a.u., symmetric
|-
! scope = "row"| HOMO (MO41)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/69/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo41.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19047 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/8/85/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo41.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.18561 a.u., symmetric
|-
! scope = "row"| HOMO-1 (MO40)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/b/bf/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo40.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19650 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/4/48/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo40.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19803 a.u., antisymmetric
|}

The relevant endo and exo TS MOs show similar characteristics, with the exception of the HOMO. For the endo TS, in addition to the normal overlap between the reacting carbons as shown on the exo TS, there were secondary orbital overlaps between the oxygen with the middle two carbon atoms of the diene. This stabilizes the interactions, lowering the overall TS energy. In addition, additional repulsive non-covation interactions (i.e. steric clash) can be seen in the exo transition state. The energy difference can be seen in the energy profile of the reaction as below:

[[File:Yx6015_energyprofile_endo_exo.png|center|frame|700px|'''Figure 10''': Energy profile of the reaction over the IRC path. Reactants on the left.]]

From the reaction profile, it could be seen that the endo pathway has slightly lower energy at transition state, as discussed above. According to the Arrhenius equation, <math> k = Ae^{\frac{-E_a}{RT}} </math>, a lower activation energy would lend to a fastor rate of reaction, thus the endo product would be formed preferentially. However, it is noted that the endo product has a lower energy than the exo product - this would imply that the endo product is thermodynamically more stable. This is the opposite of what was expected - the exo product is usually the more thermodynamically stable one due to the steric clash present in the endo product. In this case, steric clash is seen in both products. The thermodynamics of the reaction was calculated using B3LYP/6-31G(d) and is given below. The results correspond with what was seen from PM6 above.

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Cyclohexadiene
! Dioxole
! Sum of Reactants
! Endo TS
! Exo TS
! Endo Product
! Exo Product
|-
! <math>\Delta G^o </math>/kJ mol<sup>-1</sup>
| -612591
| -701188
| -1313780
| -1313622
| -1313614
| -1313849
| -1313845
|}

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Reaction Energy /kJ mol<sup>-1</sup>
! Reaction Barrier /kJ mol<sup>-1</sup>
|-
! Endo
| -69
| +158
|-
! Exo
| -65
| +166
|}

Using results from the MO calculations, a MO diagram for the formation of the TS could be plotted. As previously mentioned, only orbitals of the same symmetry can interact with each other.

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 energy level endo cyclohexadiene dioxole.png|center|thumb|400px|'''Figure 11a''': MO diagram for the endo TS. Secondary orbital interactions in red.]]
| [[File:Yx6015 energy level exo cyclohexadiene dioxole.png|center|thumb|400px|'''Figure 11b''': MO diagram for the exo TS.]]
|}

From the MO diagrams, it can be seen that the dienenopphile, 1,3-dioxole, has a HOMO of a higher energy due to electron donation by the oxygens. This reaction is thus an inverse-demand Diels-Alder reaction.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Your MO diagrams are correct but they do not have proper labelling. You also should have inserted your calculation .LOG files.)

= Exercise 3: Diels-Alder vs Cheletropic =

The reaction between o-xylylene and SO<sub>2</sub> form two different types of bicyclic products - a Diels-Alder product with two six-membered rings, and a cheletropic product with one six-membered ring and one five-membered ring:

[[File:Yx6015 mechanism so2.png|center|thumb|600px|'''Figure 12'''. Arrow-pushing mechanism of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole showing concerted addition.]]

The hallmark of a chelotropic reaction is both bond form reactions happen on the same atom. In this case, both bond formation occur on the sulphur atom. Together with the two stereoisomers from the Diels-Alder reaction, a total of 3 products could be obtained with 3 different reaction paths:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc so2 exo.gif|center|frame|400px|'''Figure 13a''': IRC path for the Diels-Alder reaction resulting in the exo product.]]
| [[File:Yx6015 anim irc so2 endo.gif|center|frame|400px|'''Figure 13b''': IRC path for the Diels-Alder reaction resulting in the endo product.]]
|-
| colspan=2|[[File:Yx6015 anim irc cheletropic.gif|center|frame|400px|'''Figure 13c''': IRC path for the cheletropic reaction.]]
|}

From the IRC animation, it could be seen that the new bonds are formed asynchronously. This is due to the lack of the mirror plane, as could be found in the previous two exercises. However, as symmetry was maintained in the cheletropic reaction, the bonds were formed synchronously.

The energy along the reaction path could be followed in a similar manner:
[[File:Yx6015_energyprofile_so2.png|center|thumb|800px|'''Figure 14''': Energy profile of the reactions along the IRC path. Reactants on the left.]]

(The problem with overlaying IRCs is that they don't exist in the same reference frame. The reaction coordinate is different for all three. Another issue is the IRC gives you the electronic energy when we want the free energies of the stationary points. However it's ok to get a qualitative comparison of the three. [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:14, 16 March 2018 (UTC))

While PM6 was not able to give accurate results for the reactant and product energies, the overall trend in the reactions was clear. As with other Diels-Alder reactions investigated above, the endo TS showed a slightly energy than the exo TS, making the endo TS the kinetic product. The cheletropic product showed significantly higher transition state energies, and may not be readily observed. More accurate results were obtained using B3LYP/6-31G(d):

{| class="wikitable" style="text-align: center; margin: auto;"
|
! o-xylylene
! SO<sub>2</sub>
! Sum of Reactants
! Endo TS
! Exo TS
! Cheletropic TS
! Endo Product
! Exo Product
! Cheletropic Product
|-
! <math>\Delta G^o </math>/kJ mol<sup>-1</sup>
| -812870
| -1440316
| -2253186
| -2253200
| -2253200
| -2253181
| -2253333
| -2253335
| -2253324
|}

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Reaction Energy /kJ mol<sup>-1</sup>
! Reaction Barrier /kJ mol<sup>-1</sup>
|-
! Endo
| -147
| -14
|-
! Exo
| -149
| -14
|-
! Cheletropic
| -138
| +5
|}

(You should definitely not be getting negative barriers! There must be a minimum in between your reactants and TS, or, more likely, your SO2 energy is wrong [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:14, 16 March 2018 (UTC))

Calculation using B3LYP/6-31G(d) show different trend as compared to PM6 previously. The energy TS for the endo and exo products are essentially identical, possibly owing to minimal sterics and interaction due to the small SO<sub>2</sub> size. In addition, they appear below the energy of the reactants. This could be a quirk of the optimization or due to the aromatization energy. However, as expected, the exo product is the most thermodynamic product, with the cheletropic pathway being quite unfavourable. The generated reaction profile is as follow:

[[File:Yx6015 final rxn profile.png|center|thumb|800px|'''Figure 15''': Reaction profile of the reactions.]]

== The ''Other'' Diels-Alder Reaction ==
[[File:Yx6015 mechanism other.png|thumb|300px|'''Figure 16''': Arrow-pushing mechanism for the ''other'' Diels-Alder reaction.]]

The Diels-Alder reaction could also take place at the other pair (non-terminal) of diene to form another two (exo and endo) products. The reactions proceed as below:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc otherexo.gif|center|frame|400px|'''Figure 17a''': IRC path for the ''other'' Diels-Alder reaction resulting in the exo product.]]
| [[File:Yx6015 anim irc otherendo.gif|center|frame|400px|'''Figure 17b''': IRC path for the ''other'' Diels-Alder reaction resulting in the endo product.]]
|}

Due to the loss of the free energy of aromatization in this reaction, the reaction was expected to be much more unfavourable. The energy from IRC was plotted and compared to the normal positions above:

[[File:Yx6015_energyprofile_other.png|center|thumb|800px|'''Figure 18''': Energy profile of different possible reactions between o-xylylene and SO<sub>2</sub> along the IRC path. Reactants on the left.]]

From the graph, it could be clearly seen that the Diels-Alder reactions at the non-terminal dienes are kinetically much less favourable. Due to the loss in aromaticity, the products are also less thermodynamically stable. As such, Diels-Alder reactions would not happen at this position.

= Conclusion =

Some examples of Diels-Alder reactions were investigated in this experiment. The reaction proceed in a single step with a single transition state, without intermediates. In general, the bond-forming reaction proceed in a synchronous manner. The reaction barrier for the reaction may be reduced through secondary orbital interactions, preferring endo products over exo products where secondary orbital interactions are possible. Additional interactions, such as sterics or aromatization may also promote specific regio or stereoisomers of the Diels-Alder product. The cheletropic reaction was also investigated, and was found to have higher reaction barrier, but produces more stable 5-membered adduct.

= References =

Rep:MOD:TS Yiming Xu

2018-03-28T09:52:31Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene */

= Introduction =

The potential energy surface (PES) is the mathematical relationship between the energy of a molcule and its geometry. <ref>E. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics, Springer Netherlands, Dordrecht, 2nd edn., 2011.</ref> By taking advantage of the Born-Oppenheimer approximation, the PES represents the electronic energy of the molecule at all possible arrangements of the atoms. Vibrational zero-point energy is sometimes added to the PES for increased accuracy.

For a molecule with N atoms, this represents a surface with 3N-6 dimensions (degrees of freedom for a non-linear molecule). Naïvely, this could be found by evaluating the energy of the molecule over all points in space using specific methods suitable for the molecule at hand. However, the effectively infinite number of possible configurations renders this approach computationally impossible. Luckily, during a reaction, only a limited "patch" of the PES is explored by the molecule, and any analysis of a reaction can be reasonably limited to studies of the reactants, products, and any surface that they traversed from the reactants to products (the reaction profile).

The reactants and products are (relatively) stable chemical species. Intuitively, they reside in minima on the PES - as stable chemical species, they tend to return to their configuration from slight perturbations. On the other hand, a reaction path is physical, and must necessarily be continuous and differentiable (where the PES itself might not be). In this case, a reaction profile joining two minima (i.e. reactants and products) will pass through one (or more) maxima along the reaction coordinate. These properties can be used to deduce structures from the PES.

== Critical points on the PES ==

Both minima and maxima are stationary points on the PES. For a stationary point at <math>\vec{q}</math>, the following relationship must hold:

<math display="block"> \nabla U(\vec{q})= 0</math>,

where <math>\nabla</math> is the gradient function, <math>\vec{q}</math> is any geometric parameter (e.g. mass-weighted coordinates), and <math>U(\vec{q})</math> is the potential energy surface. In order to determine if it is a local maximum or minimum, the second derivative test must be conducted. First, a square <math>n\times n</math> matrix, where <math>n</math> is the number of geometric parameters, can be defined:

<math display="block"> H_{i,j} = \frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}}</math>

where <math>H_{i,j}</math> is the i-th and j-th term of the Hessian matrix, <math>H</math>. The second partial derivative test is conducted by looking at the eigenvalue of the Hessian matrix at the stationary points <math>\vec{q}</math>, assuming that <math>H</math> is invertible: - If all eigenvalues are positive, <math>\vec{q}</math> is at a local maximum. - If all eigenvalues are negative, <math>\vec{q}</math> is at a local minimum. - If there is a mix of positive and negative eigenvalues, <math>\vec{q}</math> is at a saddle point. - And inconclusive otherwise.

In essence, the second partial derivative test is looking at direction of the local curvature at the station points.

== Harmonic Approximation and the Transition State ==

When deviation from equilibrium stationary points are small, the harmonic approximation can be used. The general expression of the harmonic approximation is as follows:

<math display="block">U \approx \frac{1}{2}\sum_{i,j=1}\frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}} q_i q_j</math>

As the force is related to energy as well as position,

<math display="block">\begin{align}
\vec{F} &= -\nabla U\\
& = -k\vec{X}
\end{align}
</math>

where <math>\vec{F}</math> is the column vector of the forces <math>[\vec{F_1},\vec{F_2}, ...]^T</math>, <math>X</math> is the column displacement vector of the coordinates <math>[\vec{q_1},\vec{q_2}, ...]^T</math>, and <math>k</math> is the force tensor connecting the force to the displacement of the atoms from their equilibrium positions. The differential equation admits a solution of the form:

<math display="block"> \vec{F} = -\omega ^2 \vec{X}</math>

where <math>\omega</math> is the frequency of vibration of the harmonic oscillator. It is obvious that it is an eigenvalue problem to obtain values of <math>\omega</math>, with the associated eigenvectors being the normal modes of vibrations. In practice, this is often referred to diagonalising the Hessian matrix, as the elements of the diagonalised matrix are the eigenvalues of the matrix. If we compare the form of the harmonic approximation with the second partial derivative test, it could be immediately seen that:

<math display="block"> k_{i,j} = H_{i,j} = \frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}}</math>

We could then restate the relationship between curvature and vibration as follows:

# The frequency of vibration is proportional to the square root of the local curvature at the point.
# A local minimum along coordinate <math>q_i</math> will have a positive frequency of vibration along coordinate <math>q_i</math>; and
# A local maximum along coordinate <math>q_i</math> will have an imaginary frequency of vibration (<math>\sqrt{-x} = i\sqrt{x}</math>); and
# A saddle point will have a mixture of positive and imaginary vibrational frequencies.

A transition state is defined to be a point on the PES that lies at the minimum along all coordinates, except for the reaction coordinate along which it lies at the maximum. <ref>E. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics, Springer Netherlands, Dordrecht, 2nd edn., 2011.</ref> In this case, a transition state will have one and only one imaginary vibrational frequency in its structure.

From the transition state, optimization of the structure along the coordinate following the steepest descent (as informed by the imaginary vibration frequency or negative force constant) allows one to reach the reactant and product state. The path traced out by such a procedure is called the Intrinsic Reaction Coordinate (IRC), and may or may not represent an actual physical reactive path due to other energy contributions (e.g. vibrational, kinetic, etc.). In either case, the IRC allows us to understand the changes in the molecular geometry, along with its electronic properties and molecule wavefunction, through the course of an reaction.

== Computational Approaches ==

In quantum mechanics, all information about a quantum system is encoded In its wavefunction, <math>\Psi</math>. The wavefunction obeys the Schrödinger equation, generally stated (in its time-independent form) ss below:

<math display="block">\hat{H} \Psi = E \Psi</math>

where <math>\hat{H}</math> is the Hamiltonian operator and <math> E </math> is the energy of the system. The Schrödinger equation is not analytically solvable in general, and many techniques have been developed since to find an approximate solution to the Schrödinger equation. One of the earliest approaches was the Hartree–Fock method. It was an ''ab initio'' computational method to directly compute the molecule wavefunction. Along with post-Hartree–Fock methods and alternatives approaches such as the Density Functional Theory (DFT). The different approaches share broadly similar features.

One of the most useful computational methods for finding the ground state solution is the variational method, based on the variational principle. It requires the use of trial solutions (''ansatz''), often a basis set of orbitals, to evaluate the energy eigenvalue. As the variational principle states that the true ground state has the lowest energy, the wavefunction (or rather coefficients to the basis set) can be found by locating the global minimum of the ansatz. Often, the basis set of orbitals are orthogonal to each other and uses either Slater Type Orbitals (STOs) or Gaussian Type Orbitals (GTOs) to save computation time.

Different methods employ different formalism and assumptions to simplify calculations. For example, Hartree–Fock implies the mean-field assumption and ignores electron correlation. The ansatz for the variational method is the Slater determinant of the basis sets and solves for the molecular wavefunction directly. DFT works by recognising the equivalence of finding the electron density of the molecule with its ground state wavefunction, allowing the optimizing of a single electron Schrödinger equation, shortening computation time. Modern methods with hybrid functionals (e.g. B3LYP) may use features from both to obtain more accurate results.

Unlike the ''ab initio'' methods above, semi-empirical methods drastically shorten computation time by making assumptions and correcting for them using parameters. These can include the zero differential overlap assumption, reducing the computational complexity scaling from <math>N^4</math> to <math>N^2</math>, where <math>N</math> is the number of electrons. One common semi-empirical method is the Huckle method for π-electrons. However, the parametrization requirement means that different parameters or assumptions must be used for different systems (valence electron vs п-electrons, transition metals, small vs heavy elements, etc.). When properly parameterized, semi-empirical methods can produce results more accurately than ''ab initio'' methods with much greater computation efficiency. Even if general purpose semi-empiricle methods (e.g. PM6) are less accurate than ''ab initio'' methods, its computational efficiency means that it is often used as an initial step in an optimization.

= Experimental Methods =

In this experiment, the Diels-Alder reaction was investigated in 3 different systems: reaction of butadiene with ethylene, reaction of cyclohexadiene with 1,3-dioxole, and reaction between o-xylylene and sulphur dioxide. The calculations are carried out with Gaussian 09 on Windows 7. Unless otherwise specified, initial geometry optimizations and IRC calculations were carried out in PM6 at default settings, with IRC calculations allowed to carry out to PES minima. Reactant, product and transition state molecular orbital calculations were carried out with B3LYP/6-31G(d) unless otherwise specified.

Results were extracted and analysed with GuassView (v5.0.9), as well as with cclib (v1.5) on Jupyter Notebook using Python (v3.6.4). Python analysis script is available on request. Surfaces were visualized via generation of Cube files from Gaussian, then converted to .jvxl files for faster loading and subsequently visualized on JSmol.

= Exercise 1: Reaction of Butadiene with Ethylene =

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Unfortunately this section is very confused. The MO diagram is incorrect, and even though you have correctly stated the symmetry requirements for the combination of reactant fragment orbitals you did not apply that to your computed orbitals. Additionally you didn't include jmols or log files so it is impossible to know if you have uploaded the wrong pictures or ran the wrong calculation.)

[[File:Yx6015 mechanism butadiene ethene.png|thumb|300px|'''Figure 1'''. Arrow-pushing mechanism of the Diels-Alder reaction between buta-1,3-diene and ethene showing concerted addition.]]

The reaction between buta-1,3-diene with ethene is the simplest example of a Diels-Alder reaction. The Diels-Alder reaction is a concerted pericyclic reaction between a diene (i.e. buta-1,3-diene) and a dieneophile (i.e. ethene). It in general proceeds via a single transition state with no intermediates, and is thus classified as a [4π<sub>S</sub>+2π<sub>S</sub>], and is thermally allowed under the Woodward-Hoffmann rules.

[[File:Yx6015 modiagram TS butadiene ethene.png|center|thumb|800px|'''Figure 2''': Molecular orbital diagram for the reaction between buta-1,3-diene in s-cis conformation (left) and ethene (right), along with the predicted transition state (middle).]]

Using the Hückel method, we could restrict our analysis to only π-electrons. An illustration of the molecular orbitals is found in Figure 2. It is important to note that there are additional interactions betwene the sigma and pi frameworks of the molecules. From the MO diagram, it could be seen that there are significant interactions throughout the pi system. For example, the TS orbital
π<sub>3s</sub> is due to the net interaction of 3 orbitals: butadiene π<sub>1s</sub> and π<sub>3s</sub>, and ethene π<sub>1s</sub>. Using frontier orbital molecular theory, we could further simplify analysis by, looking at only the HOMO/LUMO of the reactants and their interactions.

{| class="wikitable" style="text-align: center; margin: auto;"
|
!Buta-1,3-diene
!colspan = 2| Transition State
!Ethene
|- style="vertical-align:bottom;"
! scope="row" style="vertical-align:middle;"| LUMOs
| [[File:Yx6015 butadiene lumo.png|center|thumb|200px|'''Figure 3a''': Molecular orbital of the LUMO of buta-1,3-diene (MO 12, energy = +0.01104 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS4.png|center|thumb|200px|'''Figure 5a''': Molecular orbital of the LUMO of the TS (MO 16, energy = -0.32755 a.u.). Corresponds to π<sub>5a</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS3.png|center|thumb|200px|'''Figure 5b''': Molecular orbital of the LUMO+1 of the TS (MO 17, energy = -0.32533 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 ethene lumo.png|center|thumb|200px|'''Figure 4a''': Molecular orbital of the LUMO of ethene (MO 7, energy = +0.04256 a.u.). Corresponds to π<sub>4s</sub> from Fig 2.]]
|- style="vertical-align:bottom;"
! scope="row" style="vertical-align:middle;"| HOMOs
| [[File:Yx6015 butadiene homonew.png|center|thumb|200px|'''Figure 3b''': Molecular orbital of the HOMO of buta-1,3-diene(MO 11, energy = -0.35169 a.u.). Corresponds to π<sub>2a</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS2.png|center|thumb|200px|'''Figure 5c''': Molecular orbital of the HOMO-1 of the TS MO 18, energy = +0.01732 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS1.png|center|thumb|200px|'''Figure 5d''': Molecular orbital of the HOMO of the TS (MO 19, energy = +0.03067 a.u.). Corresponds to π<sub>2a</sub> from Fig 2.]]
| [[File:Yx6015 ethene homo.png|center|thumb|200px|'''Figure 4b''': Molecular orbital of the HOMO of ethene (MO 6, energy = -0.39228a.u.). Corresponds to π<sub>1s</sub> from Fig 2.]]
|}

For Figures 3, 4, and 5, only the MOs that would be directly relevant from the frontier orbitals are shown. It can be obviously seen that the frontier orbital theory is sufficient for this case - MO 16 and MO 18 cannot be generated from the HOMO and LUMO of the reactants only. A more correct interpretatin and diagram is depicted in Figure 2. In addition, it is clear the symmetry of the orbitals are important for their interaction and for a reaction to proceed - with orbitals only interacting with each other if they have the same symmetry. This can be formalized by the orbital overlap integral:

<math display = "block">
S_{AB} = <\psi^*_A|\psi_B>
</math>

where <math>S_{AB}</math> is the overlap integral for wavefunctions A and B, <math>\psi^*_A</math> is the Hermitian adjoint of wavefunction A, and <math>\psi_B</math> is wavefunction B. It is immediately evident that where <math>\psi_A</math> and <math>\psi_B</math> are of opposite phase, <math>\psi_A \times \psi_B</math> is an odd function and <math>S_{AB}</math> evaluates to 0. Specifically:

* the overlap integral is zero for a symmetric-antisymmetric interaction;
* the overlap integral is non-zero for a symmetric-symmetric interaction; and
* the overlap integral is non-zero for a antisymmetric-antisymmetric interaction.

The transition state for this reaction could be quite easily found as it is a simple molecular system. As detailed above, it was verified to be correct as it contains only 1 imaginary frequency, and the vibration corresponds to the desired reaction path. The transition state is visualized below.

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015_TS_reaction_path.gif|center|frame|300px|'''Figure 6a''': Transition state vibration at 948.67i cm<sup>-1</sup>. Calculated E(RPM6] = 0.11286018 at ultrafine grid.]]
| [[File:Yx6015 anim irc butadiene ethene.gif|center|frame|300px|'''Figure 6b''': IRC path for reaction between buta-1,3-diene and ethene.]]
|}

From the transition, an IRC optimization was carried out to find the reaction path, and to confirm that the transition state is indeed the transition state. The IRC path is also shown above, illustrating the correct TS and transition state is found. The changes to the bond lengths of the products and reactants could be visualized from the IRC.

| [[File:Yx6015 ccbonds butadiene ethene.png|center|thumb|800px|'''Figure 7a''': All bond lengths over the reaction coordiante. Reactant on negative reaction coordinate.]]
| [[File:Yx6015 chbonds butadiene ethene.png|center|thumb|800px|'''Figure 7b''': C-H bond lengths over the reaction coordinate. Reactant on negative reaction coordinate.]]

As can be seen from Figure 7, the bond lengths of the various C-C and C-H bonds vary across the reaction coordinate as expected. In general, variation comes from the change in hybridization of the terminal carbons bonds on butadiene and ethene from double bond to single bond, and the change from 'middle' carbons on butadiene from single to double bond. Similar variations are seen for C-H bonds, although the trend is not as straightforward. Notably, differences in the products are seen depending on the position of the hydrogen - axial vs equitorial, bowspirit vs flagpole. The two forming C-C bonds could also be seen approaching each other over time.

From the animation as well as the overlapped nature of the graph (each line has another line underneath), it is clear that the formation of the two bonds was synchronous. This was to be expected as the reactants, transition state and product all have the same plane of symmetry.

= Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole =

[[File:Yx6015 mechanism cyclohexadiene dioxole.png|thumb|300px|'''Figure 8'''. Arrow-pushing mechanism of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole showing concerted addition.]]

The reaction is another example of a Diels-Alder reaction. Changing the dienenophile from ethene to dioxole allowed the possibility of the product having two stereoisomers - the endo product and the exo product. The IRC paths for the respective products are as follow:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc cyclohexadiene dioxole exo.gif|center|frame|300px|'''Figure 9a''': IRC path for the reaction between cyclohexadiene and 1,3-dioxole with the exo product.]]
| [[File:Yx6015 anim irc cyclohexadiene dioxole endo.gif|center|frame|300px|'''Figure 9b''': IRC path for the reaction between cyclohexadiene and 1,3-dioxole with the endo product.]]
|}

From Figure 9, it could be seen that the transition state leading to the different products had different transition structures. The reactants' MO should however be identical:

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Cyclohexadiene
! 1,3-Dioxole
|-
! scope = "row"| LUMO
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/c/c1/Yx6015_cyclohexadiene_631Gd_mo23.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 cyclohexadiene 631Gd mo22.cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 23, energy = -0.01710 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/3/30/Yx6015_Dioxole_631Gd_mo20.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 Dioxole 631Gd mo20cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 20, energy = +0.03794 a.u., symmetric
|-
! scope = "row"| HOMO
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/c/cc/Yx6015_cyclohexadiene_631Gd_mo22.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 cyclohexadiene 631Gd mo22.cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 22, energy = -0.20551 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/60/Yx6015_Dioxole_631Gd_mo19.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 Dioxole 631Gd mo20cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 19, energy = -0.19594 a.u., antisymmetric
|}

From the molecular orbitals of the reactants, the transition state MO could be inferred. As with the previous section, only orbitals with the same symmetry have significant interactions. The reactant molecules overlap in either an endo or exo orientation. The molecular orbitals of the transition state is visualized as below:

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Endo Transition State
! Exo Transition State
|-
! scope = "row"| LUMO +1 (MO43)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/65/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo43.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = +0.01550 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/e/e6/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo43.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = +0.01024 a.u., antisymmetric
|-
! scope = "row"| LUMO (MO42)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/3/3f/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo42.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.00466 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/b/b2/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo42.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.00703 a.u., symmetric
|-
! scope = "row"| HOMO (MO41)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/69/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo41.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19047 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/8/85/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo41.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.18561 a.u., symmetric
|-
! scope = "row"| HOMO-1 (MO40)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/b/bf/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo40.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19650 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/4/48/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo40.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19803 a.u., antisymmetric
|}

The relevant endo and exo TS MOs show similar characteristics, with the exception of the HOMO. For the endo TS, in addition to the normal overlap between the reacting carbons as shown on the exo TS, there were secondary orbital overlaps between the oxygen with the middle two carbon atoms of the diene. This stabilizes the interactions, lowering the overall TS energy. In addition, additional repulsive non-covation interactions (i.e. steric clash) can be seen in the exo transition state. The energy difference can be seen in the energy profile of the reaction as below:

[[File:Yx6015_energyprofile_endo_exo.png|center|frame|700px|'''Figure 10''': Energy profile of the reaction over the IRC path. Reactants on the left.]]

From the reaction profile, it could be seen that the endo pathway has slightly lower energy at transition state, as discussed above. According to the Arrhenius equation, <math> k = Ae^{\frac{-E_a}{RT}} </math>, a lower activation energy would lend to a fastor rate of reaction, thus the endo product would be formed preferentially. However, it is noted that the endo product has a lower energy than the exo product - this would imply that the endo product is thermodynamically more stable. This is the opposite of what was expected - the exo product is usually the more thermodynamically stable one due to the steric clash present in the endo product. In this case, steric clash is seen in both products. The thermodynamics of the reaction was calculated using B3LYP/6-31G(d) and is given below. The results correspond with what was seen from PM6 above.

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Cyclohexadiene
! Dioxole
! Sum of Reactants
! Endo TS
! Exo TS
! Endo Product
! Exo Product
|-
! <math>\Delta G^o </math>/kJ mol<sup>-1</sup>
| -612591
| -701188
| -1313780
| -1313622
| -1313614
| -1313849
| -1313845
|}

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Reaction Energy /kJ mol<sup>-1</sup>
! Reaction Barrier /kJ mol<sup>-1</sup>
|-
! Endo
| -69
| +158
|-
! Exo
| -65
| +166
|}

Using results from the MO calculations, a MO diagram for the formation of the TS could be plotted. As previously mentioned, only orbitals of the same symmetry can interact with each other.

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 energy level endo cyclohexadiene dioxole.png|center|thumb|400px|'''Figure 11a''': MO diagram for the endo TS. Secondary orbital interactions in red.]]
| [[File:Yx6015 energy level exo cyclohexadiene dioxole.png|center|thumb|400px|'''Figure 11b''': MO diagram for the exo TS.]]
|}

From the MO diagrams, it can be seen that the dienenopphile, 1,3-dioxole, has a HOMO of a higher energy due to electron donation by the oxygens. This reaction is thus an inverse-demand Diels-Alder reaction.

= Exercise 3: Diels-Alder vs Cheletropic =

The reaction between o-xylylene and SO<sub>2</sub> form two different types of bicyclic products - a Diels-Alder product with two six-membered rings, and a cheletropic product with one six-membered ring and one five-membered ring:

[[File:Yx6015 mechanism so2.png|center|thumb|600px|'''Figure 12'''. Arrow-pushing mechanism of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole showing concerted addition.]]

The hallmark of a chelotropic reaction is both bond form reactions happen on the same atom. In this case, both bond formation occur on the sulphur atom. Together with the two stereoisomers from the Diels-Alder reaction, a total of 3 products could be obtained with 3 different reaction paths:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc so2 exo.gif|center|frame|400px|'''Figure 13a''': IRC path for the Diels-Alder reaction resulting in the exo product.]]
| [[File:Yx6015 anim irc so2 endo.gif|center|frame|400px|'''Figure 13b''': IRC path for the Diels-Alder reaction resulting in the endo product.]]
|-
| colspan=2|[[File:Yx6015 anim irc cheletropic.gif|center|frame|400px|'''Figure 13c''': IRC path for the cheletropic reaction.]]
|}

From the IRC animation, it could be seen that the new bonds are formed asynchronously. This is due to the lack of the mirror plane, as could be found in the previous two exercises. However, as symmetry was maintained in the cheletropic reaction, the bonds were formed synchronously.

The energy along the reaction path could be followed in a similar manner:
[[File:Yx6015_energyprofile_so2.png|center|thumb|800px|'''Figure 14''': Energy profile of the reactions along the IRC path. Reactants on the left.]]

(The problem with overlaying IRCs is that they don't exist in the same reference frame. The reaction coordinate is different for all three. Another issue is the IRC gives you the electronic energy when we want the free energies of the stationary points. However it's ok to get a qualitative comparison of the three. [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:14, 16 March 2018 (UTC))

While PM6 was not able to give accurate results for the reactant and product energies, the overall trend in the reactions was clear. As with other Diels-Alder reactions investigated above, the endo TS showed a slightly energy than the exo TS, making the endo TS the kinetic product. The cheletropic product showed significantly higher transition state energies, and may not be readily observed. More accurate results were obtained using B3LYP/6-31G(d):

{| class="wikitable" style="text-align: center; margin: auto;"
|
! o-xylylene
! SO<sub>2</sub>
! Sum of Reactants
! Endo TS
! Exo TS
! Cheletropic TS
! Endo Product
! Exo Product
! Cheletropic Product
|-
! <math>\Delta G^o </math>/kJ mol<sup>-1</sup>
| -812870
| -1440316
| -2253186
| -2253200
| -2253200
| -2253181
| -2253333
| -2253335
| -2253324
|}

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Reaction Energy /kJ mol<sup>-1</sup>
! Reaction Barrier /kJ mol<sup>-1</sup>
|-
! Endo
| -147
| -14
|-
! Exo
| -149
| -14
|-
! Cheletropic
| -138
| +5
|}

(You should definitely not be getting negative barriers! There must be a minimum in between your reactants and TS, or, more likely, your SO2 energy is wrong [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:14, 16 March 2018 (UTC))

Calculation using B3LYP/6-31G(d) show different trend as compared to PM6 previously. The energy TS for the endo and exo products are essentially identical, possibly owing to minimal sterics and interaction due to the small SO<sub>2</sub> size. In addition, they appear below the energy of the reactants. This could be a quirk of the optimization or due to the aromatization energy. However, as expected, the exo product is the most thermodynamic product, with the cheletropic pathway being quite unfavourable. The generated reaction profile is as follow:

[[File:Yx6015 final rxn profile.png|center|thumb|800px|'''Figure 15''': Reaction profile of the reactions.]]

== The ''Other'' Diels-Alder Reaction ==
[[File:Yx6015 mechanism other.png|thumb|300px|'''Figure 16''': Arrow-pushing mechanism for the ''other'' Diels-Alder reaction.]]

The Diels-Alder reaction could also take place at the other pair (non-terminal) of diene to form another two (exo and endo) products. The reactions proceed as below:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc otherexo.gif|center|frame|400px|'''Figure 17a''': IRC path for the ''other'' Diels-Alder reaction resulting in the exo product.]]
| [[File:Yx6015 anim irc otherendo.gif|center|frame|400px|'''Figure 17b''': IRC path for the ''other'' Diels-Alder reaction resulting in the endo product.]]
|}

Due to the loss of the free energy of aromatization in this reaction, the reaction was expected to be much more unfavourable. The energy from IRC was plotted and compared to the normal positions above:

[[File:Yx6015_energyprofile_other.png|center|thumb|800px|'''Figure 18''': Energy profile of different possible reactions between o-xylylene and SO<sub>2</sub> along the IRC path. Reactants on the left.]]

From the graph, it could be clearly seen that the Diels-Alder reactions at the non-terminal dienes are kinetically much less favourable. Due to the loss in aromaticity, the products are also less thermodynamically stable. As such, Diels-Alder reactions would not happen at this position.

= Conclusion =

Some examples of Diels-Alder reactions were investigated in this experiment. The reaction proceed in a single step with a single transition state, without intermediates. In general, the bond-forming reaction proceed in a synchronous manner. The reaction barrier for the reaction may be reduced through secondary orbital interactions, preferring endo products over exo products where secondary orbital interactions are possible. Additional interactions, such as sterics or aromatization may also promote specific regio or stereoisomers of the Diels-Alder product. The cheletropic reaction was also investigated, and was found to have higher reaction barrier, but produces more stable 5-membered adduct.

= References =

Rep:Zw4415:TSexercise

2018-03-28T08:54:02Z

Fv611: /* Visualized HOMOs and LUMOs,frequency check and Gibbs free energies */

=Introduction=

===The Transition State===

According to '''Computational Quantum Chemistry''' the reaction coordinate was functionalised by all 3N<sub>atoms</sub>-6 internal coordinates.

Potenyial energy surface describes the energy of a specific system where energy was tabulated by a set of reaction coordinates. [1]

The reactant and product with stationary structure are the minimum points on the potential energy surface.It could be calculated by :

[[File:Zinan_Wang_eq1.png|thumb|center|Equation. 1 [1] ]]

where '''R''' is a set of all internal coordinates and q is normal coordinates which is a linear combination of all internal coordinates.

The transition state is the point with the highest energy along the reaction pathway. The second derivative should be all positive except the one along the reaction coordinate.
Thus it could be calculated as below.
[[File:Zinan_Wang_eq2.png|thumb|center|Equation. 2 [1] ]]
[[File:Zinan_Wang_eq3.png|thumb|center|Equation. 3 [1] ]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 08:53, 23 March 2018 (UTC) You get this info by diagonalising the hessian matrix which is second derivatives in the basis of the degrees of freedom. the diagonalisation give the normal modes as eigenvectors and the force constants as eigenvalues.

===The computational method===
In this exercise, PM6 and B3LYP/6-31G(d) methods have been used to calculate the optimized structure of the reactants, products and the transition state. PM6 method is generally a faster method to give a rough approximation of the structure. A more precise optimization could be carried out by B3LYP with basis set of 6-31G(d) while it often takes quite a long time.

===Freqrency check===
All the normal modes for stationary structure ,thus the reactants and products, should have positive values as they represent the minimum energy points on the PES.
For all the transition state structures, only 1 negative value should be seen. It is because when calculating from a harmonic oscillator with negative force constant (The negative value of the second derivative along the reaction coordinate), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate the imaginary number (e.g. 526.7i).

===IRC check===
IRC was obtained with the same basis set used to calculate the transition structrue. The gradient of the energy graph (thus the first derivative along the reaction coordinate) shows 0 at the Transition state, reactants and product, which confirms the success of obtaining transition state.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 08:54, 23 March 2018 (UTC) This section was ok you could have done abit more reading and gone into more detail.

=Exercise 1: Reaction of Butadiene with Ethylene=
In exercise 1, the simplest Diels-Alder reaction between butadiene and ethene was calculated.

The net reaction was visualized by the bond length measurment which represent the change of bond order.

===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level with frequency checked to only have one negative value at around -930.

[[File: Zinan_Wang_EX1_IRC.PNG|thumb|The IRC for optimized transition state|300px]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You did a good work in this exercise overall but you got a bit confused here in reporting the energies of your TS LUMOs. Both the LUMO and LUMO+1 are higher in energy than what you have used here in the diagram.)

The MO energy level of both reactant was obtained by Energy calculation using PM6 method. For this specific Diels-Alder reaction between butadiene and ethene with no substituents, the electrons are in normal demand (Diene being electron rich and ethene being electron poor).

The Transition state MO generated by both reactant has higher energy then the HOMO of ethene. That is due to the fact that it is MO for transition state (not the product) which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole=

This is a reaction between cyclohexadiene and 1,3-Dioxole. There are 2 pathways of Diels-Alder reaction, Endo and Exo. For both pathway, reactants, TS and products were approximated using PM6 method then reoptimized by B3LYP method with 6-31G(d) basis set. Frequencies were checked, Gibbs free energies were extracted and MO diagrams were constructed and adjusted.

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===
([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You have compared PM6 optimised reactants with a B3LYP optimised transition state, so your MO diagrams are incorrect.)

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy (Hatree)
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 08:58, 23 March 2018 (UTC) Well done as long as these are optimised this should give you the right answer

===Secondary orbital interactions===

In the endo position, there are 2 oxygen p orbitals from oxygen lone pair which has the silimar energy and same symmetry of the cyclohexadiene LUMO, therefore they would have non-zero overlap integral. This interaction would lower the energy of LUMO producing a stabalising effect for the whole structrue. Thus more thermodynamically favored.

In the exo position, the two orbitals mentioned above were too far apart, thus almost no overlap integral. Moreover, there is a steric clash between the ring structure of 1,3-Dioxole and the half of the ring structure of cyclohexadiene, which rise up the energy of the net structure, thus less stable.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:02, 23 March 2018 (UTC) This was a good section your study of the MO energies was particularly good.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise 3: Diels-Alder vs Cheletropic=

In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.

The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is most thermodynamic favored.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

(Too many significant figures. You need to think about the errors related to to the convergence criteria you are using [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:03, 16 March 2018 (UTC))

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

In this computational lab, 3 pericyclic reactions were investigated. Gaussian was used to optimized the structure of the reactants, products and transition states using either PM6 or B3LYP method with IRC and frequency checked to confirm the transition states. Gibbs free energy was extracted from the log file for each species and the reaction barriers and reaction energies were calculated from them. The kinetic favored pathway were determined by the lowest reaction barrier and thermodynamic favored pathway was determined by the lowest reaction energy.

This computational method could be carried out for more reactions to determine the reaction route under different conditions.

=Reference=

[1] J. J. W. McDouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, The Royal Society of Chemistry, London,
2013, ch. 1, pp. 1-62.

Rep:Zw4415:TSexercise

2018-03-28T08:37:20Z

Fv611: /* MO diagram for the formation of the butadiene/ethene transition state */

=Introduction=

===The Transition State===

According to '''Computational Quantum Chemistry''' the reaction coordinate was functionalised by all 3N<sub>atoms</sub>-6 internal coordinates.

Potenyial energy surface describes the energy of a specific system where energy was tabulated by a set of reaction coordinates. [1]

The reactant and product with stationary structure are the minimum points on the potential energy surface.It could be calculated by :

[[File:Zinan_Wang_eq1.png|thumb|center|Equation. 1 [1] ]]

where '''R''' is a set of all internal coordinates and q is normal coordinates which is a linear combination of all internal coordinates.

The transition state is the point with the highest energy along the reaction pathway. The second derivative should be all positive except the one along the reaction coordinate.
Thus it could be calculated as below.
[[File:Zinan_Wang_eq2.png|thumb|center|Equation. 2 [1] ]]
[[File:Zinan_Wang_eq3.png|thumb|center|Equation. 3 [1] ]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 08:53, 23 March 2018 (UTC) You get this info by diagonalising the hessian matrix which is second derivatives in the basis of the degrees of freedom. the diagonalisation give the normal modes as eigenvectors and the force constants as eigenvalues.

===The computational method===
In this exercise, PM6 and B3LYP/6-31G(d) methods have been used to calculate the optimized structure of the reactants, products and the transition state. PM6 method is generally a faster method to give a rough approximation of the structure. A more precise optimization could be carried out by B3LYP with basis set of 6-31G(d) while it often takes quite a long time.

===Freqrency check===
All the normal modes for stationary structure ,thus the reactants and products, should have positive values as they represent the minimum energy points on the PES.
For all the transition state structures, only 1 negative value should be seen. It is because when calculating from a harmonic oscillator with negative force constant (The negative value of the second derivative along the reaction coordinate), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate the imaginary number (e.g. 526.7i).

===IRC check===
IRC was obtained with the same basis set used to calculate the transition structrue. The gradient of the energy graph (thus the first derivative along the reaction coordinate) shows 0 at the Transition state, reactants and product, which confirms the success of obtaining transition state.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 08:54, 23 March 2018 (UTC) This section was ok you could have done abit more reading and gone into more detail.

=Exercise 1: Reaction of Butadiene with Ethylene=
In exercise 1, the simplest Diels-Alder reaction between butadiene and ethene was calculated.

The net reaction was visualized by the bond length measurment which represent the change of bond order.

===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level with frequency checked to only have one negative value at around -930.

[[File: Zinan_Wang_EX1_IRC.PNG|thumb|The IRC for optimized transition state|300px]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You did a good work in this exercise overall but you got a bit confused here in reporting the energies of your TS LUMOs. Both the LUMO and LUMO+1 are higher in energy than what you have used here in the diagram.)

The MO energy level of both reactant was obtained by Energy calculation using PM6 method. For this specific Diels-Alder reaction between butadiene and ethene with no substituents, the electrons are in normal demand (Diene being electron rich and ethene being electron poor).

The Transition state MO generated by both reactant has higher energy then the HOMO of ethene. That is due to the fact that it is MO for transition state (not the product) which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole=

This is a reaction between cyclohexadiene and 1,3-Dioxole. There are 2 pathways of Diels-Alder reaction, Endo and Exo. For both pathway, reactants, TS and products were approximated using PM6 method then reoptimized by B3LYP method with 6-31G(d) basis set. Frequencies were checked, Gibbs free energies were extracted and MO diagrams were constructed and adjusted.

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy (Hatree)
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 08:58, 23 March 2018 (UTC) Well done as long as these are optimised this should give you the right answer

===Secondary orbital interactions===

In the endo position, there are 2 oxygen p orbitals from oxygen lone pair which has the silimar energy and same symmetry of the cyclohexadiene LUMO, therefore they would have non-zero overlap integral. This interaction would lower the energy of LUMO producing a stabalising effect for the whole structrue. Thus more thermodynamically favored.

In the exo position, the two orbitals mentioned above were too far apart, thus almost no overlap integral. Moreover, there is a steric clash between the ring structure of 1,3-Dioxole and the half of the ring structure of cyclohexadiene, which rise up the energy of the net structure, thus less stable.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:02, 23 March 2018 (UTC) This was a good section your study of the MO energies was particularly good.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise 3: Diels-Alder vs Cheletropic=

In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.

The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is most thermodynamic favored.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

(Too many significant figures. You need to think about the errors related to to the convergence criteria you are using [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:03, 16 March 2018 (UTC))

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

In this computational lab, 3 pericyclic reactions were investigated. Gaussian was used to optimized the structure of the reactants, products and transition states using either PM6 or B3LYP method with IRC and frequency checked to confirm the transition states. Gibbs free energy was extracted from the log file for each species and the reaction barriers and reaction energies were calculated from them. The kinetic favored pathway were determined by the lowest reaction barrier and thermodynamic favored pathway was determined by the lowest reaction energy.

This computational method could be carried out for more reactions to determine the reaction route under different conditions.

=Reference=

[1] J. J. W. McDouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, The Royal Society of Chemistry, London,
2013, ch. 1, pp. 1-62.

Rep:PS4615 Transition States and Reactivity

2018-03-27T16:21:16Z

Fv611: /* Transition State MO Diagram and Analysis */

=Introduction=

In this experiment, the reactivity of different Diels-Alder reactions were explored computationally by carrying out energy calculations of the reactants, products and more importantly the transition states. The two computational methods used are the PM6 (semi-empirical) and B3LYP (Density Functional Theory).

==<i>Potential Energy Surface (PES) and Transition States</i>==

A potential energy surface (PES) describes the potential energy of a system, especially a collection of atoms or molecules, in terms of certain parameters. In this case, the PES describes the potential energy of the system when it is in different geometries. Its dimensionality depends on the number of atoms in the system. Using 3-dimensional cartesian coordinates to describe the position of the atoms in the system, it can be deduced that the dimensionality would be <math>3N</math>. Although, the potential energy, hence the PES does not depend on the absolute position of the atoms, but only their relative positions. As a result, the translational and rotational degrees of freedom (3 each) can be removed from the dimensionality of the PES. As a result, the dimensionality of the PES becomes:

<center><math>3N - 6 </math> <b>(1)</b></center>

where N is the number of atoms in the system.

The most interesting points on PES's are stationary points. A stationary point on a PES is a point with nuclear configuration where all the forces vanish. In other words, it is where every component of the gradient in all directions/dimensions <math>\alpha</math> is zero.

<center><math>\frac{{\delta}V(X)}{{\delta}X_{\alpha}} = 0</math> <b>(2)</b></center>

where <math>V(X)</math> represents the potential energy of a particular coordinate <math>X</math>. <math>\alpha</math> represents a particular dimension in the PES where <math>\alpha \epsilon [3N-6]</math>. The following summarises the three points:

<b>1. Minima</b>: corresponds to stable (global minimum) species or quasi-stable (local minima) species. Examples include the reactants, intermediates and products.

<b>2. Transition states</b>: saddle points which are minimum in all dimensions in the PES except for one, where it is a maximum in that dimension. In other words, the transition state is the true kinetic barrier of a reaction.

<b>3. Higher-order saddle points</b>: a minimum in all dimensions except for <math>n</math> number of dimensions, where <math>n > 1</math>. It is the maximum points in the <math>n</math> dimensions.

At the stationary point, since the first derivative of the potential energy (which is the force) is zero, the leading terms of a Taylor expansion of the potential energy <math>V(Q)</math> at a stationary point <math>M</math>, where <math>Q = X - M</math> are quadratic.

<center><math> V(Q) = \frac{1}{2}\sum^{3N-6}_{\alpha=1}\omega^2_{\alpha}Q^2_{\alpha} + K</math> <b>(3)</b></center>

where <math>Q_{\alpha}</math> represents the <math>\alpha</math> component of <math>Q</math>, <math>\omega_\alpha </math> represents the Hessian eigenvalues of <math>\alpha</math> of <math>Q</math> and <math>K</math> represents the higher order terms in the Taylor expansion (Harmonic Approximation).

The Hessian eigenvalues determine the characteristic of the stationary points. More importantly, the Hessian index, which is the number of negative Hessian eigenvalues, determines whether the stationary point is a minimum, transition state or high order saddle point. It also corresponds to the number of imaginary (negative) vibrational frequencies. For minimum points, the Hessian index is zero. This means all the vibrational frequencies must be positive. On the other hand, a transition state is a stationary point with a Hessian index of 1. This means that the frequency analysis of the transition state must result in one imaginary/negative vibrational frequency. A saddle point has a Hessian index of more than 1, which again can be observed from the output frequencies after running a vibrational analysis.<ref>D. J. Wales, Energy landscapes, Cambridge University Press, Cambridge, UK, 2003, ch. 4</ref>

[[File:PS615_TS_PES.GIF|thumb|center|700px|alt=|<b>Figure 1</b>. The transition state (TS) indicated on a sample PES. MEP stands for the minimum energy path, which in this case is the IRC.<ref>Nino Runeberg, 2018.
</ref>]]

In this experiment, the energies of the reactants, transition states and the products of different pericyclic reactions were computed. The difference between the energy of the reactions' transition state and reactants were used to quantify the kinetic barriers of the reactions. In addition, the minimum energy paths that connect the reactants, transition states and products were visualised to show the reaction coordinate of the reactions (IRC).

==<I>Methods</i>==

Gaussian was used for the computations in this experiment, where GaussView was used as a user interface and visualisation of the molecular orbitals. There are three methods that can be used to compute the transition state geometries and energies of the pericyclic reactions in this experiment. The following outlines the methods available:

<b>Method 1</b>. This method only work for small systems, where a guessed transition state is optimised in one single step with the PM6 method. This only work for simple systems because for complex systems with many atoms, the PES will be very complex with multiple higher order saddle points around the true transition state. It is the fastest method but at the same time the least reliable as the converged structure might actually be a higher order saddle point due to the complex PES.

<b>Method 2</b>. Again, this method requires guessing the transition state structure. Although, the atoms that is involved in the reaction are frozen, with the resulting structure optimised to a minimum before the whole guessed transition state is optimised to find the converged structure. This ensures that the guessed structure is as close to the transition state as possible in the PES, providing the fastest reliable method for computing the geometry of transition states.

<b>Method 3</b>. Compared to the other 2, this method does not require the guessing of the transition state. It is the most reliable method of the three, but take the longest time due to additional steps required. The product or the reactants of the reaction is optimised individually to a minima. This is followed by altering the bond lengths so that the structure resembles the transition state. The atoms involved in the reactions are then frozen like Method 2, optimised to a minimum before being optimised again to get the converged structure.

From earlier, it was mentioned how the PES can be used to determine the geometries and energies of transition states, but not how they can be generated. For very simple systems, the PES can be fitted to experimental data. For more complex and reactive systems, the PES must be generated by quantum mechanical calculations (eg. semi-empirical, DFT, etc).

The <b>Parameterisation Method 6 (PM6)</b> method, which is a semi-emipirical method, is an approximate version of the Hartree-Fock method. Many approximations are made to calculate the Hamiltonian of the Schrodinger equation of the system. Namely, some two-electron and sometimes one-electron integrals are neglected to speed up the computation and reduce the computation cost. To make up for this, empirical parameters are used to make up for these approximations. For the remaining integrals, some are computed exactly, but some are computed using parameters obtained from experiments (hence semi-empirical). This means that the method will work well for systems that experimental parameters are available, but not reliable otherwise.

The <b>B3LYP</b> method used in this experiment is a hybrid method that contains elements from Density Functional Theory (DFT) and Hartree-Fock theory. The 'B3' part specifies the exchange functional (Hartree-Fock) used to run the computation, whereas the 'LYP' specifies the correlation functional (DFT). In other words, it utilises the Hartree-Fock theory to calculate the exchange integral terms in the Hamiltonian. In addition to that, it uses DFT to approximate the correlated motions of electrons in the system. 6-31G basis set was used to model the electronic wavefunctions. Overall, B3LYP carry out calculations more accurately compared to PM6, but takes longer time and computation cost. <ref>J. J. W. McDouall, Computational quantum chemistry: molecular structure and properties in silico, Royal Society of Chemistry, Cambridge, 2013, ch. 1</ref>

=Exercise 1: Reaction of Butadiene with Ethylene=

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very well done across the whole exercise. Good job!)

[[File:Ex1_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 2</b>. The reaction scheme between butadiene and ethylene to make cyclohexene.]]

<b>Corresponding Log files</b>

[[Media:PS4615_1_ETHENE_MIN_OPT_FREQ_PM6.LOG|PS4615_1_ETHENE_MIN_OPT_FREQ_PM6.LOG]]

[[Media:PS4615_1_BUTADIENE_MIN_OPT_FREQ_PM6_AGAIN_BREAK_SYM.LOG|PS4615_1_BUTADIENE_MIN_OPT_FREQ_PM6_AGAIN_BREAK_SYM.LOG]]

[[Media:PS4615_1_CYCLOHEXENE_MIN_PM6.LOG|PS4615_1_CYCLOHEXENE_MIN_PM6.LOG]]

[[Media:PS4615_1_TS_BERNY_PM6_2.LOG|PS4615_1_TS_BERNY_PM6_2.LOG]]

[[Media:PS4615_1_TS_IRC_PM6.LOG|PS4615_1_TS_IRC_PM6.LOG]]

==<i>Transition State MO diagram</i>==

[[File:Exercise_1_MO.png|thumb|center|1000px|alt=|<b>Figure 3</b>. The transition state MO diagram of the reaction. Note that the energies of the MOs are obtained (in Hartrees) from Gaussian.]]

The MO diagram as shown in <b>figure 3</b> was constructed using the MOs from the reactants optimised using Gaussian. In addition, the MOs of the transition state were obtained using <b>Method 3</b>, where they were used to correlate the reactants' MOs that interacted to make up the TS MOs. The MOs obtained from the calculation are shown below in <b>table 1</b>. The symmetry of the MOs were determined by following the steps as described below:

1. Identify a plane of symmetry in the MOs.

2. If the phase of the atomic orbitals on both sides of the plane are the same, then the MO is symmetric (S). If it is in the opposite phase, then it must be antisymmetric (A).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 1</b>. The HOMO and LUMO of butadiene, ethylene and the transition state of the reaction.'''

!Butadiene HOMO

!Butadiene LUMO

!Ethylene HOMO

!Ethylene LUMO

|-

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|-

!'''Transition State HOMO-1'''

!Transition State HOMO

!Transition State LUMO

!Transition State LUMO + 1

|-

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Firstly, the HOMO and LUMO of the transition structure was analysed. It can be seen from the MOs that it is a result of the interaction between the HOMO of the reactant ethylene and LUMO of butadiene, both of which are symmetric. As a result, the transition state MOs must be symmetric. This was further confirmed by carrying the symmetry analysis described on the TS MOs. As for the HOMO-1 and LUMO+1 of the TS, it was determined that they are the result of the interaction between the LUMO of ethylene and HOMO of the butadiene. The reactants' MOs are all antisymmetric, which resulted in antisymmetric HOMO-1 and LUMO+1 of the TS.

From this, it can be concluded that only orbitals with the same symmetry can interact to produce molecular orbitals. Furthermore, it is possible to draw up the conclusion that in order to determine whether the reaction is forbidden or allowed, the MOs of the reactants must be analysed. For an allowed reaction, the orbitals of the reactants must have the same symmetry. On the other hand, if the orbitals of the reactants does not have the same symmetry, the reaction is then said to be forbidden. This can be explained further by considering the overlap integrals <math>S_{AB}</math> of the orbitals. It is a quantitative way of analysing the extent of interaction between the orbitals. For symmetric-symmetric or antisymmetric-antisymmetric orbital interaction, the overall overlap integral is non-zero, leading to two new MOs (the TS MOs in this case). As for antisymmetric-symmetric orbital interaction, the overlap integral is zero leading to no MOs formed.

==<i>Carbon-Carbon Bond Length Analysis</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 2</b>. The Carbon-Carbon bond lengths for the reaction obtained from the calculation.'''
!
! colspan="4" style="text-align: center; font-weight: bold;" | Bond Length (Å)
|-
| style="text-align: center; font-weight: bold;" | C-C Bond
| style="text-align: center; font-weight: bold;" | Butadiene (Reactant)
| style="text-align: center; font-weight: bold;" | Ethylene (Reactant)
| style="text-align: center; font-weight: bold;" | Transition State
| style="text-align: center; font-weight: bold;" | Cyclohexene (Product)
|-
| style="text-align: center; font-weight: bold;" | C1-C2
| style="text-align: center;" | 1.333
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.380
| style="text-align: center;" | 1.491
|-
| style="text-align: center; font-weight: bold;" | C2-C3
| style="text-align: center;" | 1.471
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.411
| style="text-align: center;" | 1.363
|-
| style="text-align: center; font-weight: bold;" | C3-C4
| style="text-align: center;" | 1.333
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.380
| style="text-align: center;" | 1.491
|-
| style="text-align: center; font-weight: bold;" | C4-C5
| style="text-align: center;" | N/A
| style="text-align: center;" | N/A
| style="text-align: center;" | 2.116
| style="text-align: center;" | 1.583
|-
| style="text-align: center; font-weight: bold;" | C5-C6
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.327
| style="text-align: center;" | 1.382
| style="text-align: center;" | 1.560
|-
| style="text-align: center; font-weight: bold;" | C6-C1
| style="text-align: center;" | N/A
| style="text-align: center;" | N/A
| style="text-align: center;" | 2.113
| style="text-align: center;" | 1.583
|}

During the course of the reaction, the different C-C bonds change as it progresses from the reactant to the transition state and finally the product. Firstly, the hybridisation of the carbons in the reactants and products must be discussed to make the explanation easier. It is clear from the reaction scheme that all of the carbons in the reactants are <math>sp^2</math> hybridised. After the reaction has proceeded to the product, the hybridisation of C2 and C3 stays the same, whereas the rest of the carbons changed their hybridisation to <math>sp^3</math>.

The analysis of the hybridisation of the carbons are essentially for identifying the change in the bond lengths. From <b>Table 2</b>, it can seen that C1-C2/ C3-C4 bond lengths (they are the same due to symmetry) changes from 1.333 Å (double bond) to 1.491 Å (<math>sp^{2}-sp^{3}</math> single bond), with the bond length of 1.380 Å for the transition state. One of the reasons why the bond length increases is because the bond length changes from being a double bond to being a single bond. Moreover, the hybridisation of the carbons that make up the bonds changes from being <math>sp^{2}-sp^{2}</math> to <math>sp^{2}-sp^{3}</math>. Having less s-character in the hybridisation increases the bond length, as s-orbital electron densities are closer to the nucleus.

As for C5-C6, the bond changes from 1.327 Å (double bond) to 1.560 Å (<math>sp^{3}-sp^{3}</math> single bond), with the bond length of 1.382 Å for the transition state. Again, the same analysis can be made for the discussion of the changes in the C-C bond lengths. Although, it is worth noting that the C5-C6 bond length is greater than the C1-C2 / C3-C4 bond lengths in product. One possible explanation is that even though both of the bonds has a bond order of 1, the hybridisation of C5-C6 bond is <math>sp^3-sp^3</math>. Hence, there is less s-character in the bond, making it longer. For C2-C3, the bond length changes from 1.471 Å (<math>sp^{2}-sp^{2}</math> single bond) to 1.362 Å (double bond) with the bond length of 1.411 Å for the transition state. For this case, the transition state bond length is observed to be shorter than the reactants compare to the other cases discussed. This is because for this case, instead of the double bonds in the reactant partially breaking (decreasing in electron density) in the transition state, a double bond is partially forming (increasing electron density) here, making the bond length decrease.

As for the new bonds created (C1-C6 and C4-C5), the corresponding bond lengths for both of them is 1.583 Å (<math>sp^{3}-sp^{3}</math> single bond). As for the transition states, the corresponding partially formed bond lengths are 2.113 Å and 2.116 Å for C1-C6 and C4-C5 respectively. This is shorter than Van der Waals radii between two carbons of 3.4 Å (each being 1.7 Å) but at the same time longer than a typical C-C single bond. This indicates that the orbitals in the carbons involved are drawn together, interacting, and about to form new bonds in the transition state.

From this, it can be approximated that the typical bond length for C-C double bonds is 1.3 Å (lit. 1.34 Å), 1.6 Å (lit. 1.54 Å) for <math>sp^{3}-sp^{3}</math> single bonds, and 1.5 Å for <math>sp^{2}-sp^{3}</math>/<math>sp^{2}-sp^{2}</math> single bonds, with <math>sp^{2}-sp^{2}</math> single bonds slightly shorter than <math>sp^{2}-sp^{3}</math> single bonds (lit. 1.50 Å for <math>sp^{2}-sp^{3}</math> and 1.47 Å for <math>sp^{2}-sp^{2}</math>) <ref>Fox, Marye Anne., and James K. Whitesell. Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen. Heidelberg: Spektrum Akademischer Verlag, 1995.</ref>.

==<i>Transition State Vibrations</I>==

[[File:PS4615_IRC_exersize_1.PNG|thumb|center|600px|alt=|<b>Figure 4</b>. The IRC of the reaction.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

!<b>Figure 5</b> shows the vibration of the transition state.
|-
|

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|
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By running an IRC calculation, the vibration calculation was confirmed to be successful (see <b>Figure 4</b>). In addition, vibration corresponding to the transition state is illustrated (<b>Figure 5</b>). As described in the introduction, the frequency of this particular vibration of the transition state is negative. From the IRC of the reaction, it can be deduced that the bond formation between terminal carbons in butadiene and ethylene is synchronous, as the bond formation occurred at the same time. Also, it can be seen from the Jmol that the carbons involved in forming the new bonds approach each other at the same time and synchronously. This results in synchronous bond formation.

=Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole=

[[File:ex2_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 6</b>. The reaction scheme of the reaction. Note that there are two possible products from the reaction.]]

<b>Corresponding Log files</b>

Reactants:

[[Media:PS4615_2_CYCLOHEXADIENE_MIN_PM6.LOG|PS4615_2_CYCLOHEXADIENE_MIN_PM6.LOG]]

[[Media:PS4615_2_CYCLOHEXADIENE_MIN_B3LYP.LOG|PS4615_2_CYCLOHEXADIENE_MIN_B3LYP.LOG]]

[[Media:PS4615_2_1_3_DIOXOLE_MIN_PM6.LOG|PS4615_2_1_3_DIOXOLE_MIN_PM6.LOG]]

[[Media:PS4615_2_1_3_DIOXOLE_MIN_B3LYP.LOG|PS4615_2_1_3_DIOXOLE_MIN_B3LYP.LOG]]

ENDO TS and products:

[[Media:PS4615_2_TS_BERNY_ENDO_PM6.LOG|PS4615_2_TS_BERNY_ENDO_PM6.LOG]]

[[Media:PS4615_2_TS_BERNY_ENDO_B3LYP.LOG|PS4615_2_TS_BERNY_ENDO_B3LYP.LOG]]

[[Media:PS4615_2_PRODUCT_ENDO_MIN_PM6.LOG|PS4615_2_PRODUCT_ENDO_MIN_PM6.LOG]]

[[Media:PS4615_2_PRODUCT_ENDO_MIN_B3LYP.LOG|PS4615_2_PRODUCT_ENDO_MIN_B3LYP.LOG]]

[[Media:PS4615_2_TS_IRC_ENDO_PM6.LOG|PS4615_2_TS_IRC_ENDO_PM6.LOG]]

EXO TS and products:

[[Media:PS4615_2_TS_BERNY_EXO_PM6.LOG|PS4615_2_TS_BERNY_EXO_PM6.LOG]]

[[Media:PS4615_2_TS_BERNY_EXO_B3LYP.LOG|PS4615_2_TS_BERNY_EXO_B3LYP.LOG]]

[[Media:PS4615_2_PRODUCT_EXO_MIN_PM6.LOG|PS4615_2_PRODUCT_EXO_MIN_PM6.LOG]]

[[Media:PS4615_2_PRODUCT_EXO_MIN_B3LYP.LOG|PS4615_2_PRODUCT_EXO_MIN_B3LYP.LOG]]

[[Media:PS4615_2_TS_EXO_IRC_PM6.LOG|PS4615_2_TS_EXO_IRC_PM6.LOG]]

==<i>Transition State MO Diagram and Analysis</i>==
([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Nice MO diagrams. Could have extended the discussion a little bit.)
[[File:PS4615_Ex2MO_ENDO.png|thumb|center|600px|alt=|<b>Figure 7</b>. The transition state MO diagram of the reaction (ENDO). Note that the energies of the MOs are obtained (in Hartree) from Gaussian.]]
[[File:PS4615_Ex2ExoMO.png|thumb|center|600px|alt=|<b>Figure 8</b>. The transition state MO diagram of the reaction (EXO). Note that the energies of the MOs are obtained (in Hartree) from Gaussian.]]

<b>Figure 7</b> illustrates the molecular orbital diagram of the transition states for the Diels-Alder reaction. The MO diagrams were constructed by carrying out the same analysis on the relevant MOs of the reaction's transition states (see <b>table 3</b> for the MOs of the transition states). Again, it was observed that MOs that has the same symmetry interact to form the TS MOs. It can be seen that for each case, the overall energy of the transition state for the ENDO case is lower compared to the transition state for the EXO product. Qualitatively speaking, this indicates that the kinetic barrier/activation energy for the EXO case is higher, resulting in the pathway being kinetically stable compared to the ENDO pathway. A more quantitative analysis is discussed in the <I>Thermochemistry</I> section below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 3</b>. The relevant molecular orbitals of the transition states of the Diels-Alder reaction.'''

!TS ENDO HOMO-1

!TS ENDO HOMO

!TS ENDO LUMO

!TS ENDO LUMO+1

|-

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!'''TS ENDO HOMO-1'''

!TS ENDO HOMO

!TS ENDO LUMO

!TS ENDO LUMO+1

|-

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Diels-Alder reactions such as this case can be classified as either normal or inverse electron-demand. For a qualitative analysis, it can be said that for a normal electron-demand Diels-Alder reaction, the diene is electron rich whereas the dienophile is electron deficient. On the other hand, the diene is required to be electron deficient, where the dienophile is electron rich for an inverse electron-demand Diels-Alder reaction. For a more quantitative analysis, whether the reaction is normal or inverse electron-demand depends on the relative energies of the HOMO and LUMO of the reactants involved in the reaction. For a normal electron-demand reaction, the HOMO and LUMO of the dienophile is lower in energy compared to the respective HOMO and LUMO of the diene. As a result, there is a strong interaction between the HOMO of the diene and the LUMO of the dienenophile as they have similar energies, forming the HOMO and LUMO of the product. An example of this is the Diels-Alder reaction in Exercise 1 (see <b>figure 3</b> for the MO diagram). For an inverse electron-demand reaction, the HOMO and LUMO of the dienophile is higher in energy compared to the respective HOMO and LUMO of the diene. For this case, the HOMO of the dienophile and LUMO of the diene interact strongly to produce the HOMO and LUMO of the product. For the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the reaction is an inverse electron-demand reaction, with explanations as described above. One of the reasons why the HOMO and LUMO of the dienophile has such high energies, surpassing the MOs of the diene, is because of the electron donating effect of the two oxygens next to the alkene, raising the energy of MOs of the dienophile. <b>Figure 9</b> illustrates the inverse electron-demand characteristic of the (ENDO) reaction nicely, with the energies of the product MOs calculated by running an optimisation on the product structure (B3LYP).

[[File:PS4615_Ex2MO_ENDO_product_INV.png|thumb|center|600px|alt=|<b>Figure 9</b>. A simplified MO diagram (ENDO product) illustrating the inverse electron demand nature of the reaction.]]

==<i>Thermochemistry</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 4</b> The table shows activation energies and the Gibbs free energies of the ENDO and EXO Diels-Alder reaction.'''
! style="text-align: center;" |
! style="text-align: center; font-weight: bold;" | Activation Energy / <math>kJmol^{-1}</math>
! style="text-align: center; font-weight: bold;" | Gibbs Free Energy / <math>kJmol^{-1}</math>
|-
| style="text-align: center; font-weight: bold;" | ENDO
| style="text-align: center;" | +159.8
| style="text-align: center;" | -67.4
|-
| style="text-align: center; font-weight: bold;" | EXO
| style="text-align: center;" | +167.7
| style="text-align: center;" | -63.8
|}

From <b>table 4</b>, it can be seen that the ENDO pathway has a lower activation energy compared to the EXO pathway, making it kinetically favourable. This is because the HOMO of the ENDO transition state is further stabilised by secondary orbital interactions. From <b>table 5</b>, it can be seen that the p orbitals on the oxygens of the dienophile interacts with the delocalised π orbitals on the diene, which has a stabilising effect on the transition state. Secondary orbital interaction is absent in the EXO pathway, as transition state does not have the correct geometry for it. This makes the energy of the ENDO transition state lower than that of the EXO pathway, making it kinetically favoured.

In addition, the ENDO pathway is more exothermic compared to the EXO pathway, making it the thermodynamically favoured compared to the other pathway. As a result, this makes the ENDO product thermodynamically more stable than the EXO product. Secondary orbital interactions within the ENDO product is one of the factors that make the energy of the ENDO product lower than the EXO product. This is the same interaction as described above, with the EXO product lacking in the stabilising interaction due to its geometry. Furthermore, unfavourable steric interactions between the dioxole group and the ethylene bridgehead in the EXO product may have played a significant role in increasing its energy, making it less exothermic. This effect is likely to be less significant for the ENDO product, as the dioxole is closest to the saturated bridgehead, resulting in less interaction with the hydrogen atoms (see <b>table 6</b> for illustration).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 5</b> The table shows the HOMO of the transition states with the isovalue set to 0.01 to show secondary orbital interactions.'''

!TS ENDO HOMO

!TS EXO HOMO

|-

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{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 6</b> The table shows the steric interactions in the ENDO and EXO product.'''

!ENDO product

!EXO product

|-

|[[File:PS4615_Sterics_ENDO_product.png|500px]]|
|[[File:PS4615_Sterics_EXO_product.png|500px]]|

|}

=Exercise 3: Diels-Alder vs Cheletropic=

[[File:PS4615_ex3_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 10</b>. The reaction scheme of the reaction. Note that there are two possible reaction pathways, including Diels-ALder and Cheletropic.]]

<b>Corresponding Log files</b>

Reactants:

[[Media:PS4615_3_REACTANT_DIENE_MIN_PM6.LOG|PS4615_3_REACTANT_DIENE_MIN_PM6.LOG]]

[[Media:PS4615_3_REACTANT_SO2_MIN_PM6.LOG|PS4615_3_REACTANT_SO2_MIN_PM6.LOG]]

Diels-Alder ENDO TS and products:

[[Media:PS4615_3_DA_TS_BERNY_ENDO_PM6.LOG|PS4615_3_DA_TS_BERNY_ENDO_PM6.LOG]]

[[Media:PS4615_3_DA_TS_IRC_ENDO_PM6.LOG|PS4615_3_DA_TS_IRC_ENDO_PM6.LOG]]

[[Media:PS4615_3_DA_PRODUCT_MIN_ENDO_PM6.LOG|PS4615_3_DA_PRODUCT_MIN_ENDO_PM6.LOG]]

Diels-Alder EXO TS and products:

[[Media:PS4615_3_DA_EXO_TS_BERNY_PM6.LOG|PS4615_3_DA_EXO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_DA_EXO_TS_IRC_PM6.LOG|PS4615_3_DA_EXO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_DA_EXO_PRODUCT_MIN_PM6.LOG|PS4615_3_DA_EXO_PRODUCT_MIN_PM6.LOG]]

Cheletropic TS and products:

[[Media:PS4615_3_CHELETROPIC_TS_BERNY_PM6.LOG|PS4615_3_CHELETROPIC_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_CHELETROPIC_TS_IRC_PM6.LOG|PS4615_3_CHELETROPIC_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_CHELETROPIC_PRODUCT_MIN_PM6.LOG|PS4615_3_CHELETROPIC_PRODUCT_MIN_PM6.LOG]]

Alternative Diels-Alder ENDO TS and products:

[[Media:PS4615_3_ALT_DA_ENDO_TS_BERNY_PM6.LOG|PS4615_3_ALT_DA_ENDO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_ENDO_TS_IRC_PM6.LOG|PS4615_3_ALT_DA_ENDO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_ENDO_PRODUCT_MIN_PM6.LOG|PS4615_3_ALT_DA_ENDO_PRODUCT_MIN_PM6.LOG]]

Alternative Diels-Alder EXO TS and products:

[[Media:PS4615_3_ALT_DA_EXO_TS_BERNY_PM6.LOG|PS4615_3_ALT_DA_EXO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_EXO_TS_IRC_PM6.LOG|PS4615_3_ALT_DA_EXO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_EXO_PRODUCT_MIN_PM6.LOG|PS4615_3_ALT_DA_EXO_PRODUCT_MIN_PM6.LOG]]

==<i>IRC</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 7</b> The table shows the different IRC of the Diels-Alder and Cheletropic reaction. Note that the IRC of the Diels-Alder EXO IRC is in the opposite direction.'''

!Diels-Alder ENDO IRC

!Diels-Alder EXO IRC

!Cheletropic IRC

!Alternative Diels-Alder ENDO IRC

!Alternative Diels-Alder EXO IRC

|-

|[[File:PS4615_endo_DA_IRC.png|400px]]|
|[[File:PS4615_exo_DA_IRC.png|400px]]|
|[[File:PS4615_cheletropic_IRC.png|400px]]|
|[[File:PS4615_ALT_endo_DA_IRC.png|400px]]|
|[[File:PS4615_ALT_exo_DA_IRC.png|400px]]|

|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 8</b> visualises the IRC path of the Diels-Alder and Cheletropic reactions. Click on the links to see the animations.'''

!Diels-Alder ENDO IRC

!Diels-Alder EXO IRC

!Cheletropic IRC

!Alternative Diels-Alder ENDO IRC

!Alternative Diels-Alder EXO IRC

|-

|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ENDO_DA_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_EXO_DA_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_cheletropic_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ALT_ENDO_DA_IRC_movie_NEW.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ALT_EXO_DA_IRC_movie_NEW.gif]]|

|}

<b>Table 7</b> and <b>table 8</b> Shows the IRC (described in the Introduction section) of the reaction pathways of this exercise, including the movie file links that illustrates the nature of bond formations of the pathways. From the movies, it can be seen that all the Diels-Alder reaction pathways (including the reaction at the high energy site) form new bonds asynchronously. On the other hand, the bond formation of the cheletropic pathway is synchronous. It is worth noting that xylylene is an extremely reactive species, as it is only one oxidation state away from forming a 6-membered aromatic ring. In fact, this can be seen during the reaction of xylylene with sulphur dioxide (see the IRC animation), where the ring becomes aromatised when transition states are formed. This is not the case for the alternative pathway at the inner diene site, resulting in the reaction being highly unfavourable.

==<i>Thermochemistry</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 9</b> shows the activation energies and Gibbs free energies of the different reaction pathways.'''

!
! style="text-align: center; font-weight: bold;" | Activation Energy / <math>kJmol^{-1}</math>
! style="font-weight: bold;" | Gibbs Free Energy / <math>kJmol^{-1}</math>
|-
| style="text-align: center; font-weight: bold;" | DA ENDO
| style="text-align: center;" | +84.4
| style="text-align: center;" | -96.4
|-
| style="text-align: center; font-weight: bold;" | DA EXO
| style="text-align: center;" | +88.4
| style="text-align: center;" | -97.0
|-
| style="text-align: center; font-weight: bold;" | Cheletropic
| style="text-align: center;" | +106.7
| style="text-align: center;" | -153.4
|-
| style="text-align: center; font-weight: bold;" | Alternative DA ENDO
| style="text-align: center;" | +114.7
| style="text-align: center;" | +18.9
|-
| style="text-align: center; font-weight: bold;" | Alternative DA EXO
| style="text-align: center;" | +122.5
| style="text-align: center;" | +23.4
|}

(This is really a change in free energy. Best to just call it a reaction energy [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:42, 16 March 2018 (UTC))

[[File:PS4615_3_energy_diagram_FULL.png|thumb|center|1000px|alt=|<b>Figure 11</b>. The energy diagram illustrating the relative activation energies and Gibbs free energies of the Diels-Alder and Cheletropic reaction.]]

From <b>figure 11</b>, it can be seen that out of all the reaction pathways (excluding the alternative Diels-Alder), the cheletropic pathway has the greatest activation energy, making it the most kinetically stable compared to the other 2 pathways. One of the possible explanation for this is the fact that the reaction forms a new 5-membered ring, compared to 6-membered rings for the other pathways. The ring strain in the 5-membered ring raises the energy of the transition state, raising its activation energy. Even though it is the most kinetically inert compared to the other three, the cheletropic path is the most thermodynamically favourable, as it is the most exothermic pathway (most negative Gibbs free energy of reaction). This is because of the stabilisation of the product by the 2 strong S=O bonds (bond enthalpy of 518 kJ/mol each <ref>Luo, Yu-Ran. Comprehensive handbook of chemical bond energies. Boca Raton, Fla.: CRC Press, 2007.
</ref>) compared to only one S=O and one S-O (S-O contributes 348 kJ/mol <ref>Cottrell, T. L. The strengths of chemical bonds. New York: Academic Press, 1961.
</ref>) in the Diels-Alder products. The two S=O bonds has a much greater effect than the ring strain in the 5-membered ring, making it the most exothermic reaction of the three.

Contrarily, the ENDO Diels-Alder pathway has the lowest activation energy, making it the fastest kinetically compared to the other two paths. This is due to the stabilisation of the transition state by secondary orbital interactions (similar to Exercise 2 case). This involves the interaction between the p orbital of the oxygen in sulphur dioxide and the delocalised π orbitals of xylylene. This is not possible for the EXO case as it does not have the correct geometry for the interaction, making its activation energy higher (but still lower than cheletropic path) than the ENDO transition state. Due to steric repulsions between the oxygen in the S=O and the rest of the molecule, the ENDO product energy is slightly above the EXO product. This makes the EXO path more thermodynamically favourable than the ENDO pathway, as it is slightly more exothermic. If the reaction is carried out under equilibrating conditions, the cheletropic product will be the major product of the reaction between sulphur dioxide and xylylene, as it is the most thermonamically favourable pathway.

The energy diagram (<b>figure 11</b>) shows that the alternative Diels-Alder reaction at the inner site is both thermodynamically and kinetically unfavourable. Firstly, the activation energy of the reaction is greater than any of the pathways described before. The reactions (EXO and ENDO) are endothermic, which means that they require energy to convert from reactants to product overall. The ENDO product here is both the kinetic and thermodynamic product compared to the EXO case. The transition states for this alternative pathway is higher in energy than the preferred path because it lacks the aromatic ring formed at the 6-membered ring. This also explains the why the reaction is endothermic, as the products does not have the aromatic 6-membered ring in it like the normal Diels-Alder and cheletropic products.

=Extension: Electrocyclic reaction=

[[File:Ext_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 12</b>. The reaction scheme of the electrocyclic reaction of cyclobutene.]]

<b>Corresponding Log Files</b>

[[Media:PS4615_EXT_CYCLOBUTENE_MIN_PM6.LOG|PS4615_EXT_CYCLOBUTENE_MIN_PM6.LOG]]

[[Media:PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG|PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG]]

[[Media:PS4615_EXT_TS_BERNY_PM6.LOG|PS4615_EXT_TS_BERNY_PM6.LOG]]

[[Media:PS4615_EXT_TS_BERNY_B3LYP.LOG|PS4615_EXT_TS_BERNY_B3LYP.LOG]]

[[Media:PS4615_EXT_TS_IRC_PM6.LOG|PS4615_EXT_TS_IRC_PM6.LOG]]

[[Media:PS4615_EXT_PRODUCT_B3LYP.LOG|PS4615_EXT_PRODUCT_B3LYP.LOG]]

In this extension, the thermal electrocyclic ring opening of the molecule shown in the reaction scheme above was studied. Since electrocyclic reactions is a class of a pericyclic reaction, the stereochemistry of the product can be determined using the Woodward-Hoffman rules. From this, it was determined that the reaction undergoes conrotatory electrocyclic ring opening, which agrees with the calculations carried out using B3LYP (see the animation in <b>table 10</b> and the vibrations of the transition state at <b>figure 13</b>). The activation energy of the reaction was found to be <math> +122.4 kJmol^{-1} </math>, with the Gibbs free energy of the reaction at <math>-64.1 kJmol^{-1}</math>. This shows that the reaction has a significantly high activation energy, making it kinetically inert. One possible explanation to this is the raise in the TS energy due to steric interactions between the bulky methyl ester groups during the transition from the reactant to product (see animations). Since the reaction is significantly exothermic, the reaction is considered thermodynamically favourable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

!<b>Figure 13</b> shows the vibration of the transition state.
|-
|

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size><align>centre</align>
<uploadedFileContents>PS4615_EXT_TS_BERNY_B3LYP.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 29; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>EXT_TS_VIBRATION</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>EXT_TS_VIBRATION</target>
</jmolbutton>
</jmol>

|
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 10</b> shows the IRC of the reaction, where the movie shows that the reaction is conrotatory.'''

!The reaction's IRC

|-

|[[File:PS4615_EXT_IRC.png|400px]]|

|-

!IRC movie. Click on the link for movie.

|-

|[[https://wiki.ch.ic.ac.uk/wiki/images/d/d1/PS4615_EXT_IRC_movie.gif]]|

|}

It is clear from the animations and the transition state vibrations that the reaction is a conrotatory electrocyclic ring opening. Aside from using the Woodward-Hoffmann rules, this can be determined and illustrated by looking the the HOMO of the reactants and products (see <b>table 11</b>). From the HOMO of the product, it can be seen that the only way that the reaction can proceed (working backwards) is through antarafacial interactions of the MOs at the terminal carbons, as this is the only way to achieve constructive interaction between the orbitals. In terms of the symmetry (when considering just the diene fragment), the HOMO is asymmetric. By following through with the reaction to the reactants, it can be seen that the terminal carbons rotate in the same direction to form the cyclobutene. This is illustrated in the in <b>figure 14</b>.

[[File:PS4615_EXT_orbitals_interaction_NEW.png|thumb|center|600px|alt=|<b>Figure 14</b>. This illustrates the Frontier orbital (HOMO) approach to determining the stereochemistry of the reaction.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 11</b>. The relevant molecular orbitals of the reaction.'''

!Cyclobutene HOMO

!Transition state HOMO

!Product HOMO

|-

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 122; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02</script>
<uploadedFileContents>PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG</uploadedFileContents>
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</jmol>
|<jmol>
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|<jmol>
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<uploadedFileContents>PS4615_EXT_PRODUCT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
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|-

!Cyclobutene LUMO

!Transition state LUMO

!Product LUMO

|-

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 122; mo 46; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02</script>
<uploadedFileContents>PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG</uploadedFileContents>
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|<jmol>
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<color>white</color>
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|<jmol>
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<color>white</color>
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<script>frame 38; mo 46; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02</script>
<uploadedFileContents>PS4615_EXT_PRODUCT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

(It is actually the HOMO-1 in the TS that has the orbitals that you are looking for [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:49, 16 March 2018 (UTC))

=Conclusion=

In this experiment, a semi-empirical method PM6 and a hybrid method B3LYP were used to calculate the geometries and vibrations of 4 different transition states of 4 different pericyclic reactions successfully. Method three was used for all of the calculations, as it is the most accurate method out of the three. Starting with the first exercise, the C-C bond lengths involved in the reaction were analysed as the reaction progresses from the reactants, to the transition states and finally the product. It was also found that the bond formation is synchronous, which is not the case for the reactions in exercise 3. The activation energies and Gibbs free energies of the ENDO and EXO Diels-Alder reactions were calculated in exercise 2 up to the B3LYP level of accuracy. The relevant MOs were visualised to qualitatively show the effect of secondary orbital interactions and steric repulsions on the thermochemistry of the reactions. From the energies of the relavant MOs, it was proven that the Diels-Alder reaction in exercise 2 is an inverse electron-demand reaction. As for exercise 3, the different reaction paths were investigated for the reaction between sulphur dioxide and xylylene. It was found that the most thermodynamically favourable pathway is the Cheletropic path, whereas the ENDO Diels-Alder reaction path is the most kinetically driven. Lastly, calculations up to B3LYP level of accuracy for a thermal electrocyclic ring opening of cyclobutene was carried out. The IRC animation and the transition state vibrations showed that the reaction is conrotatory, which is in agreement with the Woodward-Hoffmann rules.

=Bibliography=

Rep:PS4615 Transition States and Reactivity

2018-03-27T16:15:04Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene */

=Introduction=

In this experiment, the reactivity of different Diels-Alder reactions were explored computationally by carrying out energy calculations of the reactants, products and more importantly the transition states. The two computational methods used are the PM6 (semi-empirical) and B3LYP (Density Functional Theory).

==<i>Potential Energy Surface (PES) and Transition States</i>==

A potential energy surface (PES) describes the potential energy of a system, especially a collection of atoms or molecules, in terms of certain parameters. In this case, the PES describes the potential energy of the system when it is in different geometries. Its dimensionality depends on the number of atoms in the system. Using 3-dimensional cartesian coordinates to describe the position of the atoms in the system, it can be deduced that the dimensionality would be <math>3N</math>. Although, the potential energy, hence the PES does not depend on the absolute position of the atoms, but only their relative positions. As a result, the translational and rotational degrees of freedom (3 each) can be removed from the dimensionality of the PES. As a result, the dimensionality of the PES becomes:

<center><math>3N - 6 </math> <b>(1)</b></center>

where N is the number of atoms in the system.

The most interesting points on PES's are stationary points. A stationary point on a PES is a point with nuclear configuration where all the forces vanish. In other words, it is where every component of the gradient in all directions/dimensions <math>\alpha</math> is zero.

<center><math>\frac{{\delta}V(X)}{{\delta}X_{\alpha}} = 0</math> <b>(2)</b></center>

where <math>V(X)</math> represents the potential energy of a particular coordinate <math>X</math>. <math>\alpha</math> represents a particular dimension in the PES where <math>\alpha \epsilon [3N-6]</math>. The following summarises the three points:

<b>1. Minima</b>: corresponds to stable (global minimum) species or quasi-stable (local minima) species. Examples include the reactants, intermediates and products.

<b>2. Transition states</b>: saddle points which are minimum in all dimensions in the PES except for one, where it is a maximum in that dimension. In other words, the transition state is the true kinetic barrier of a reaction.

<b>3. Higher-order saddle points</b>: a minimum in all dimensions except for <math>n</math> number of dimensions, where <math>n > 1</math>. It is the maximum points in the <math>n</math> dimensions.

At the stationary point, since the first derivative of the potential energy (which is the force) is zero, the leading terms of a Taylor expansion of the potential energy <math>V(Q)</math> at a stationary point <math>M</math>, where <math>Q = X - M</math> are quadratic.

<center><math> V(Q) = \frac{1}{2}\sum^{3N-6}_{\alpha=1}\omega^2_{\alpha}Q^2_{\alpha} + K</math> <b>(3)</b></center>

where <math>Q_{\alpha}</math> represents the <math>\alpha</math> component of <math>Q</math>, <math>\omega_\alpha </math> represents the Hessian eigenvalues of <math>\alpha</math> of <math>Q</math> and <math>K</math> represents the higher order terms in the Taylor expansion (Harmonic Approximation).

The Hessian eigenvalues determine the characteristic of the stationary points. More importantly, the Hessian index, which is the number of negative Hessian eigenvalues, determines whether the stationary point is a minimum, transition state or high order saddle point. It also corresponds to the number of imaginary (negative) vibrational frequencies. For minimum points, the Hessian index is zero. This means all the vibrational frequencies must be positive. On the other hand, a transition state is a stationary point with a Hessian index of 1. This means that the frequency analysis of the transition state must result in one imaginary/negative vibrational frequency. A saddle point has a Hessian index of more than 1, which again can be observed from the output frequencies after running a vibrational analysis.<ref>D. J. Wales, Energy landscapes, Cambridge University Press, Cambridge, UK, 2003, ch. 4</ref>

[[File:PS615_TS_PES.GIF|thumb|center|700px|alt=|<b>Figure 1</b>. The transition state (TS) indicated on a sample PES. MEP stands for the minimum energy path, which in this case is the IRC.<ref>Nino Runeberg, 2018.
</ref>]]

In this experiment, the energies of the reactants, transition states and the products of different pericyclic reactions were computed. The difference between the energy of the reactions' transition state and reactants were used to quantify the kinetic barriers of the reactions. In addition, the minimum energy paths that connect the reactants, transition states and products were visualised to show the reaction coordinate of the reactions (IRC).

==<I>Methods</i>==

Gaussian was used for the computations in this experiment, where GaussView was used as a user interface and visualisation of the molecular orbitals. There are three methods that can be used to compute the transition state geometries and energies of the pericyclic reactions in this experiment. The following outlines the methods available:

<b>Method 1</b>. This method only work for small systems, where a guessed transition state is optimised in one single step with the PM6 method. This only work for simple systems because for complex systems with many atoms, the PES will be very complex with multiple higher order saddle points around the true transition state. It is the fastest method but at the same time the least reliable as the converged structure might actually be a higher order saddle point due to the complex PES.

<b>Method 2</b>. Again, this method requires guessing the transition state structure. Although, the atoms that is involved in the reaction are frozen, with the resulting structure optimised to a minimum before the whole guessed transition state is optimised to find the converged structure. This ensures that the guessed structure is as close to the transition state as possible in the PES, providing the fastest reliable method for computing the geometry of transition states.

<b>Method 3</b>. Compared to the other 2, this method does not require the guessing of the transition state. It is the most reliable method of the three, but take the longest time due to additional steps required. The product or the reactants of the reaction is optimised individually to a minima. This is followed by altering the bond lengths so that the structure resembles the transition state. The atoms involved in the reactions are then frozen like Method 2, optimised to a minimum before being optimised again to get the converged structure.

From earlier, it was mentioned how the PES can be used to determine the geometries and energies of transition states, but not how they can be generated. For very simple systems, the PES can be fitted to experimental data. For more complex and reactive systems, the PES must be generated by quantum mechanical calculations (eg. semi-empirical, DFT, etc).

The <b>Parameterisation Method 6 (PM6)</b> method, which is a semi-emipirical method, is an approximate version of the Hartree-Fock method. Many approximations are made to calculate the Hamiltonian of the Schrodinger equation of the system. Namely, some two-electron and sometimes one-electron integrals are neglected to speed up the computation and reduce the computation cost. To make up for this, empirical parameters are used to make up for these approximations. For the remaining integrals, some are computed exactly, but some are computed using parameters obtained from experiments (hence semi-empirical). This means that the method will work well for systems that experimental parameters are available, but not reliable otherwise.

The <b>B3LYP</b> method used in this experiment is a hybrid method that contains elements from Density Functional Theory (DFT) and Hartree-Fock theory. The 'B3' part specifies the exchange functional (Hartree-Fock) used to run the computation, whereas the 'LYP' specifies the correlation functional (DFT). In other words, it utilises the Hartree-Fock theory to calculate the exchange integral terms in the Hamiltonian. In addition to that, it uses DFT to approximate the correlated motions of electrons in the system. 6-31G basis set was used to model the electronic wavefunctions. Overall, B3LYP carry out calculations more accurately compared to PM6, but takes longer time and computation cost. <ref>J. J. W. McDouall, Computational quantum chemistry: molecular structure and properties in silico, Royal Society of Chemistry, Cambridge, 2013, ch. 1</ref>

=Exercise 1: Reaction of Butadiene with Ethylene=

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very well done across the whole exercise. Good job!)

[[File:Ex1_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 2</b>. The reaction scheme between butadiene and ethylene to make cyclohexene.]]

<b>Corresponding Log files</b>

[[Media:PS4615_1_ETHENE_MIN_OPT_FREQ_PM6.LOG|PS4615_1_ETHENE_MIN_OPT_FREQ_PM6.LOG]]

[[Media:PS4615_1_BUTADIENE_MIN_OPT_FREQ_PM6_AGAIN_BREAK_SYM.LOG|PS4615_1_BUTADIENE_MIN_OPT_FREQ_PM6_AGAIN_BREAK_SYM.LOG]]

[[Media:PS4615_1_CYCLOHEXENE_MIN_PM6.LOG|PS4615_1_CYCLOHEXENE_MIN_PM6.LOG]]

[[Media:PS4615_1_TS_BERNY_PM6_2.LOG|PS4615_1_TS_BERNY_PM6_2.LOG]]

[[Media:PS4615_1_TS_IRC_PM6.LOG|PS4615_1_TS_IRC_PM6.LOG]]

==<i>Transition State MO diagram</i>==

[[File:Exercise_1_MO.png|thumb|center|1000px|alt=|<b>Figure 3</b>. The transition state MO diagram of the reaction. Note that the energies of the MOs are obtained (in Hartrees) from Gaussian.]]

The MO diagram as shown in <b>figure 3</b> was constructed using the MOs from the reactants optimised using Gaussian. In addition, the MOs of the transition state were obtained using <b>Method 3</b>, where they were used to correlate the reactants' MOs that interacted to make up the TS MOs. The MOs obtained from the calculation are shown below in <b>table 1</b>. The symmetry of the MOs were determined by following the steps as described below:

1. Identify a plane of symmetry in the MOs.

2. If the phase of the atomic orbitals on both sides of the plane are the same, then the MO is symmetric (S). If it is in the opposite phase, then it must be antisymmetric (A).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 1</b>. The HOMO and LUMO of butadiene, ethylene and the transition state of the reaction.'''

!Butadiene HOMO

!Butadiene LUMO

!Ethylene HOMO

!Ethylene LUMO

|-

|<jmol>
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|-

!'''Transition State HOMO-1'''

!Transition State HOMO

!Transition State LUMO

!Transition State LUMO + 1

|-

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Firstly, the HOMO and LUMO of the transition structure was analysed. It can be seen from the MOs that it is a result of the interaction between the HOMO of the reactant ethylene and LUMO of butadiene, both of which are symmetric. As a result, the transition state MOs must be symmetric. This was further confirmed by carrying the symmetry analysis described on the TS MOs. As for the HOMO-1 and LUMO+1 of the TS, it was determined that they are the result of the interaction between the LUMO of ethylene and HOMO of the butadiene. The reactants' MOs are all antisymmetric, which resulted in antisymmetric HOMO-1 and LUMO+1 of the TS.

From this, it can be concluded that only orbitals with the same symmetry can interact to produce molecular orbitals. Furthermore, it is possible to draw up the conclusion that in order to determine whether the reaction is forbidden or allowed, the MOs of the reactants must be analysed. For an allowed reaction, the orbitals of the reactants must have the same symmetry. On the other hand, if the orbitals of the reactants does not have the same symmetry, the reaction is then said to be forbidden. This can be explained further by considering the overlap integrals <math>S_{AB}</math> of the orbitals. It is a quantitative way of analysing the extent of interaction between the orbitals. For symmetric-symmetric or antisymmetric-antisymmetric orbital interaction, the overall overlap integral is non-zero, leading to two new MOs (the TS MOs in this case). As for antisymmetric-symmetric orbital interaction, the overlap integral is zero leading to no MOs formed.

==<i>Carbon-Carbon Bond Length Analysis</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 2</b>. The Carbon-Carbon bond lengths for the reaction obtained from the calculation.'''
!
! colspan="4" style="text-align: center; font-weight: bold;" | Bond Length (Å)
|-
| style="text-align: center; font-weight: bold;" | C-C Bond
| style="text-align: center; font-weight: bold;" | Butadiene (Reactant)
| style="text-align: center; font-weight: bold;" | Ethylene (Reactant)
| style="text-align: center; font-weight: bold;" | Transition State
| style="text-align: center; font-weight: bold;" | Cyclohexene (Product)
|-
| style="text-align: center; font-weight: bold;" | C1-C2
| style="text-align: center;" | 1.333
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.380
| style="text-align: center;" | 1.491
|-
| style="text-align: center; font-weight: bold;" | C2-C3
| style="text-align: center;" | 1.471
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.411
| style="text-align: center;" | 1.363
|-
| style="text-align: center; font-weight: bold;" | C3-C4
| style="text-align: center;" | 1.333
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.380
| style="text-align: center;" | 1.491
|-
| style="text-align: center; font-weight: bold;" | C4-C5
| style="text-align: center;" | N/A
| style="text-align: center;" | N/A
| style="text-align: center;" | 2.116
| style="text-align: center;" | 1.583
|-
| style="text-align: center; font-weight: bold;" | C5-C6
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.327
| style="text-align: center;" | 1.382
| style="text-align: center;" | 1.560
|-
| style="text-align: center; font-weight: bold;" | C6-C1
| style="text-align: center;" | N/A
| style="text-align: center;" | N/A
| style="text-align: center;" | 2.113
| style="text-align: center;" | 1.583
|}

During the course of the reaction, the different C-C bonds change as it progresses from the reactant to the transition state and finally the product. Firstly, the hybridisation of the carbons in the reactants and products must be discussed to make the explanation easier. It is clear from the reaction scheme that all of the carbons in the reactants are <math>sp^2</math> hybridised. After the reaction has proceeded to the product, the hybridisation of C2 and C3 stays the same, whereas the rest of the carbons changed their hybridisation to <math>sp^3</math>.

The analysis of the hybridisation of the carbons are essentially for identifying the change in the bond lengths. From <b>Table 2</b>, it can seen that C1-C2/ C3-C4 bond lengths (they are the same due to symmetry) changes from 1.333 Å (double bond) to 1.491 Å (<math>sp^{2}-sp^{3}</math> single bond), with the bond length of 1.380 Å for the transition state. One of the reasons why the bond length increases is because the bond length changes from being a double bond to being a single bond. Moreover, the hybridisation of the carbons that make up the bonds changes from being <math>sp^{2}-sp^{2}</math> to <math>sp^{2}-sp^{3}</math>. Having less s-character in the hybridisation increases the bond length, as s-orbital electron densities are closer to the nucleus.

As for C5-C6, the bond changes from 1.327 Å (double bond) to 1.560 Å (<math>sp^{3}-sp^{3}</math> single bond), with the bond length of 1.382 Å for the transition state. Again, the same analysis can be made for the discussion of the changes in the C-C bond lengths. Although, it is worth noting that the C5-C6 bond length is greater than the C1-C2 / C3-C4 bond lengths in product. One possible explanation is that even though both of the bonds has a bond order of 1, the hybridisation of C5-C6 bond is <math>sp^3-sp^3</math>. Hence, there is less s-character in the bond, making it longer. For C2-C3, the bond length changes from 1.471 Å (<math>sp^{2}-sp^{2}</math> single bond) to 1.362 Å (double bond) with the bond length of 1.411 Å for the transition state. For this case, the transition state bond length is observed to be shorter than the reactants compare to the other cases discussed. This is because for this case, instead of the double bonds in the reactant partially breaking (decreasing in electron density) in the transition state, a double bond is partially forming (increasing electron density) here, making the bond length decrease.

As for the new bonds created (C1-C6 and C4-C5), the corresponding bond lengths for both of them is 1.583 Å (<math>sp^{3}-sp^{3}</math> single bond). As for the transition states, the corresponding partially formed bond lengths are 2.113 Å and 2.116 Å for C1-C6 and C4-C5 respectively. This is shorter than Van der Waals radii between two carbons of 3.4 Å (each being 1.7 Å) but at the same time longer than a typical C-C single bond. This indicates that the orbitals in the carbons involved are drawn together, interacting, and about to form new bonds in the transition state.

From this, it can be approximated that the typical bond length for C-C double bonds is 1.3 Å (lit. 1.34 Å), 1.6 Å (lit. 1.54 Å) for <math>sp^{3}-sp^{3}</math> single bonds, and 1.5 Å for <math>sp^{2}-sp^{3}</math>/<math>sp^{2}-sp^{2}</math> single bonds, with <math>sp^{2}-sp^{2}</math> single bonds slightly shorter than <math>sp^{2}-sp^{3}</math> single bonds (lit. 1.50 Å for <math>sp^{2}-sp^{3}</math> and 1.47 Å for <math>sp^{2}-sp^{2}</math>) <ref>Fox, Marye Anne., and James K. Whitesell. Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen. Heidelberg: Spektrum Akademischer Verlag, 1995.</ref>.

==<i>Transition State Vibrations</I>==

[[File:PS4615_IRC_exersize_1.PNG|thumb|center|600px|alt=|<b>Figure 4</b>. The IRC of the reaction.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

!<b>Figure 5</b> shows the vibration of the transition state.
|-
|

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<script>vibrating=0; spinning=0; frame 15; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
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|
|}

By running an IRC calculation, the vibration calculation was confirmed to be successful (see <b>Figure 4</b>). In addition, vibration corresponding to the transition state is illustrated (<b>Figure 5</b>). As described in the introduction, the frequency of this particular vibration of the transition state is negative. From the IRC of the reaction, it can be deduced that the bond formation between terminal carbons in butadiene and ethylene is synchronous, as the bond formation occurred at the same time. Also, it can be seen from the Jmol that the carbons involved in forming the new bonds approach each other at the same time and synchronously. This results in synchronous bond formation.

=Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole=

[[File:ex2_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 6</b>. The reaction scheme of the reaction. Note that there are two possible products from the reaction.]]

<b>Corresponding Log files</b>

Reactants:

[[Media:PS4615_2_CYCLOHEXADIENE_MIN_PM6.LOG|PS4615_2_CYCLOHEXADIENE_MIN_PM6.LOG]]

[[Media:PS4615_2_CYCLOHEXADIENE_MIN_B3LYP.LOG|PS4615_2_CYCLOHEXADIENE_MIN_B3LYP.LOG]]

[[Media:PS4615_2_1_3_DIOXOLE_MIN_PM6.LOG|PS4615_2_1_3_DIOXOLE_MIN_PM6.LOG]]

[[Media:PS4615_2_1_3_DIOXOLE_MIN_B3LYP.LOG|PS4615_2_1_3_DIOXOLE_MIN_B3LYP.LOG]]

ENDO TS and products:

[[Media:PS4615_2_TS_BERNY_ENDO_PM6.LOG|PS4615_2_TS_BERNY_ENDO_PM6.LOG]]

[[Media:PS4615_2_TS_BERNY_ENDO_B3LYP.LOG|PS4615_2_TS_BERNY_ENDO_B3LYP.LOG]]

[[Media:PS4615_2_PRODUCT_ENDO_MIN_PM6.LOG|PS4615_2_PRODUCT_ENDO_MIN_PM6.LOG]]

[[Media:PS4615_2_PRODUCT_ENDO_MIN_B3LYP.LOG|PS4615_2_PRODUCT_ENDO_MIN_B3LYP.LOG]]

[[Media:PS4615_2_TS_IRC_ENDO_PM6.LOG|PS4615_2_TS_IRC_ENDO_PM6.LOG]]

EXO TS and products:

[[Media:PS4615_2_TS_BERNY_EXO_PM6.LOG|PS4615_2_TS_BERNY_EXO_PM6.LOG]]

[[Media:PS4615_2_TS_BERNY_EXO_B3LYP.LOG|PS4615_2_TS_BERNY_EXO_B3LYP.LOG]]

[[Media:PS4615_2_PRODUCT_EXO_MIN_PM6.LOG|PS4615_2_PRODUCT_EXO_MIN_PM6.LOG]]

[[Media:PS4615_2_PRODUCT_EXO_MIN_B3LYP.LOG|PS4615_2_PRODUCT_EXO_MIN_B3LYP.LOG]]

[[Media:PS4615_2_TS_EXO_IRC_PM6.LOG|PS4615_2_TS_EXO_IRC_PM6.LOG]]

==<i>Transition State MO Diagram and Analysis</i>==

[[File:PS4615_Ex2MO_ENDO.png|thumb|center|600px|alt=|<b>Figure 7</b>. The transition state MO diagram of the reaction (ENDO). Note that the energies of the MOs are obtained (in Hartree) from Gaussian.]]
[[File:PS4615_Ex2ExoMO.png|thumb|center|600px|alt=|<b>Figure 8</b>. The transition state MO diagram of the reaction (EXO). Note that the energies of the MOs are obtained (in Hartree) from Gaussian.]]

<b>Figure 7</b> illustrates the molecular orbital diagram of the transition states for the Diels-Alder reaction. The MO diagrams were constructed by carrying out the same analysis on the relevant MOs of the reaction's transition states (see <b>table 3</b> for the MOs of the transition states). Again, it was observed that MOs that has the same symmetry interact to form the TS MOs. It can be seen that for each case, the overall energy of the transition state for the ENDO case is lower compared to the transition state for the EXO product. Qualitatively speaking, this indicates that the kinetic barrier/activation energy for the EXO case is higher, resulting in the pathway being kinetically stable compared to the ENDO pathway. A more quantitative analysis is discussed in the <I>Thermochemistry</I> section below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 3</b>. The relevant molecular orbitals of the transition states of the Diels-Alder reaction.'''

!TS ENDO HOMO-1

!TS ENDO HOMO

!TS ENDO LUMO

!TS ENDO LUMO+1

|-

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|-

!'''TS ENDO HOMO-1'''

!TS ENDO HOMO

!TS ENDO LUMO

!TS ENDO LUMO+1

|-

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Diels-Alder reactions such as this case can be classified as either normal or inverse electron-demand. For a qualitative analysis, it can be said that for a normal electron-demand Diels-Alder reaction, the diene is electron rich whereas the dienophile is electron deficient. On the other hand, the diene is required to be electron deficient, where the dienophile is electron rich for an inverse electron-demand Diels-Alder reaction. For a more quantitative analysis, whether the reaction is normal or inverse electron-demand depends on the relative energies of the HOMO and LUMO of the reactants involved in the reaction. For a normal electron-demand reaction, the HOMO and LUMO of the dienophile is lower in energy compared to the respective HOMO and LUMO of the diene. As a result, there is a strong interaction between the HOMO of the diene and the LUMO of the dienenophile as they have similar energies, forming the HOMO and LUMO of the product. An example of this is the Diels-Alder reaction in Exercise 1 (see <b>figure 3</b> for the MO diagram). For an inverse electron-demand reaction, the HOMO and LUMO of the dienophile is higher in energy compared to the respective HOMO and LUMO of the diene. For this case, the HOMO of the dienophile and LUMO of the diene interact strongly to produce the HOMO and LUMO of the product. For the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the reaction is an inverse electron-demand reaction, with explanations as described above. One of the reasons why the HOMO and LUMO of the dienophile has such high energies, surpassing the MOs of the diene, is because of the electron donating effect of the two oxygens next to the alkene, raising the energy of MOs of the dienophile. <b>Figure 9</b> illustrates the inverse electron-demand characteristic of the (ENDO) reaction nicely, with the energies of the product MOs calculated by running an optimisation on the product structure (B3LYP).

[[File:PS4615_Ex2MO_ENDO_product_INV.png|thumb|center|600px|alt=|<b>Figure 9</b>. A simplified MO diagram (ENDO product) illustrating the inverse electron demand nature of the reaction.]]

==<i>Thermochemistry</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 4</b> The table shows activation energies and the Gibbs free energies of the ENDO and EXO Diels-Alder reaction.'''
! style="text-align: center;" |
! style="text-align: center; font-weight: bold;" | Activation Energy / <math>kJmol^{-1}</math>
! style="text-align: center; font-weight: bold;" | Gibbs Free Energy / <math>kJmol^{-1}</math>
|-
| style="text-align: center; font-weight: bold;" | ENDO
| style="text-align: center;" | +159.8
| style="text-align: center;" | -67.4
|-
| style="text-align: center; font-weight: bold;" | EXO
| style="text-align: center;" | +167.7
| style="text-align: center;" | -63.8
|}

From <b>table 4</b>, it can be seen that the ENDO pathway has a lower activation energy compared to the EXO pathway, making it kinetically favourable. This is because the HOMO of the ENDO transition state is further stabilised by secondary orbital interactions. From <b>table 5</b>, it can be seen that the p orbitals on the oxygens of the dienophile interacts with the delocalised π orbitals on the diene, which has a stabilising effect on the transition state. Secondary orbital interaction is absent in the EXO pathway, as transition state does not have the correct geometry for it. This makes the energy of the ENDO transition state lower than that of the EXO pathway, making it kinetically favoured.

In addition, the ENDO pathway is more exothermic compared to the EXO pathway, making it the thermodynamically favoured compared to the other pathway. As a result, this makes the ENDO product thermodynamically more stable than the EXO product. Secondary orbital interactions within the ENDO product is one of the factors that make the energy of the ENDO product lower than the EXO product. This is the same interaction as described above, with the EXO product lacking in the stabilising interaction due to its geometry. Furthermore, unfavourable steric interactions between the dioxole group and the ethylene bridgehead in the EXO product may have played a significant role in increasing its energy, making it less exothermic. This effect is likely to be less significant for the ENDO product, as the dioxole is closest to the saturated bridgehead, resulting in less interaction with the hydrogen atoms (see <b>table 6</b> for illustration).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 5</b> The table shows the HOMO of the transition states with the isovalue set to 0.01 to show secondary orbital interactions.'''

!TS ENDO HOMO

!TS EXO HOMO

|-

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{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 6</b> The table shows the steric interactions in the ENDO and EXO product.'''

!ENDO product

!EXO product

|-

|[[File:PS4615_Sterics_ENDO_product.png|500px]]|
|[[File:PS4615_Sterics_EXO_product.png|500px]]|

|}

=Exercise 3: Diels-Alder vs Cheletropic=

[[File:PS4615_ex3_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 10</b>. The reaction scheme of the reaction. Note that there are two possible reaction pathways, including Diels-ALder and Cheletropic.]]

<b>Corresponding Log files</b>

Reactants:

[[Media:PS4615_3_REACTANT_DIENE_MIN_PM6.LOG|PS4615_3_REACTANT_DIENE_MIN_PM6.LOG]]

[[Media:PS4615_3_REACTANT_SO2_MIN_PM6.LOG|PS4615_3_REACTANT_SO2_MIN_PM6.LOG]]

Diels-Alder ENDO TS and products:

[[Media:PS4615_3_DA_TS_BERNY_ENDO_PM6.LOG|PS4615_3_DA_TS_BERNY_ENDO_PM6.LOG]]

[[Media:PS4615_3_DA_TS_IRC_ENDO_PM6.LOG|PS4615_3_DA_TS_IRC_ENDO_PM6.LOG]]

[[Media:PS4615_3_DA_PRODUCT_MIN_ENDO_PM6.LOG|PS4615_3_DA_PRODUCT_MIN_ENDO_PM6.LOG]]

Diels-Alder EXO TS and products:

[[Media:PS4615_3_DA_EXO_TS_BERNY_PM6.LOG|PS4615_3_DA_EXO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_DA_EXO_TS_IRC_PM6.LOG|PS4615_3_DA_EXO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_DA_EXO_PRODUCT_MIN_PM6.LOG|PS4615_3_DA_EXO_PRODUCT_MIN_PM6.LOG]]

Cheletropic TS and products:

[[Media:PS4615_3_CHELETROPIC_TS_BERNY_PM6.LOG|PS4615_3_CHELETROPIC_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_CHELETROPIC_TS_IRC_PM6.LOG|PS4615_3_CHELETROPIC_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_CHELETROPIC_PRODUCT_MIN_PM6.LOG|PS4615_3_CHELETROPIC_PRODUCT_MIN_PM6.LOG]]

Alternative Diels-Alder ENDO TS and products:

[[Media:PS4615_3_ALT_DA_ENDO_TS_BERNY_PM6.LOG|PS4615_3_ALT_DA_ENDO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_ENDO_TS_IRC_PM6.LOG|PS4615_3_ALT_DA_ENDO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_ENDO_PRODUCT_MIN_PM6.LOG|PS4615_3_ALT_DA_ENDO_PRODUCT_MIN_PM6.LOG]]

Alternative Diels-Alder EXO TS and products:

[[Media:PS4615_3_ALT_DA_EXO_TS_BERNY_PM6.LOG|PS4615_3_ALT_DA_EXO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_EXO_TS_IRC_PM6.LOG|PS4615_3_ALT_DA_EXO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_EXO_PRODUCT_MIN_PM6.LOG|PS4615_3_ALT_DA_EXO_PRODUCT_MIN_PM6.LOG]]

==<i>IRC</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 7</b> The table shows the different IRC of the Diels-Alder and Cheletropic reaction. Note that the IRC of the Diels-Alder EXO IRC is in the opposite direction.'''

!Diels-Alder ENDO IRC

!Diels-Alder EXO IRC

!Cheletropic IRC

!Alternative Diels-Alder ENDO IRC

!Alternative Diels-Alder EXO IRC

|-

|[[File:PS4615_endo_DA_IRC.png|400px]]|
|[[File:PS4615_exo_DA_IRC.png|400px]]|
|[[File:PS4615_cheletropic_IRC.png|400px]]|
|[[File:PS4615_ALT_endo_DA_IRC.png|400px]]|
|[[File:PS4615_ALT_exo_DA_IRC.png|400px]]|

|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 8</b> visualises the IRC path of the Diels-Alder and Cheletropic reactions. Click on the links to see the animations.'''

!Diels-Alder ENDO IRC

!Diels-Alder EXO IRC

!Cheletropic IRC

!Alternative Diels-Alder ENDO IRC

!Alternative Diels-Alder EXO IRC

|-

|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ENDO_DA_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_EXO_DA_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_cheletropic_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ALT_ENDO_DA_IRC_movie_NEW.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ALT_EXO_DA_IRC_movie_NEW.gif]]|

|}

<b>Table 7</b> and <b>table 8</b> Shows the IRC (described in the Introduction section) of the reaction pathways of this exercise, including the movie file links that illustrates the nature of bond formations of the pathways. From the movies, it can be seen that all the Diels-Alder reaction pathways (including the reaction at the high energy site) form new bonds asynchronously. On the other hand, the bond formation of the cheletropic pathway is synchronous. It is worth noting that xylylene is an extremely reactive species, as it is only one oxidation state away from forming a 6-membered aromatic ring. In fact, this can be seen during the reaction of xylylene with sulphur dioxide (see the IRC animation), where the ring becomes aromatised when transition states are formed. This is not the case for the alternative pathway at the inner diene site, resulting in the reaction being highly unfavourable.

==<i>Thermochemistry</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 9</b> shows the activation energies and Gibbs free energies of the different reaction pathways.'''

!
! style="text-align: center; font-weight: bold;" | Activation Energy / <math>kJmol^{-1}</math>
! style="font-weight: bold;" | Gibbs Free Energy / <math>kJmol^{-1}</math>
|-
| style="text-align: center; font-weight: bold;" | DA ENDO
| style="text-align: center;" | +84.4
| style="text-align: center;" | -96.4
|-
| style="text-align: center; font-weight: bold;" | DA EXO
| style="text-align: center;" | +88.4
| style="text-align: center;" | -97.0
|-
| style="text-align: center; font-weight: bold;" | Cheletropic
| style="text-align: center;" | +106.7
| style="text-align: center;" | -153.4
|-
| style="text-align: center; font-weight: bold;" | Alternative DA ENDO
| style="text-align: center;" | +114.7
| style="text-align: center;" | +18.9
|-
| style="text-align: center; font-weight: bold;" | Alternative DA EXO
| style="text-align: center;" | +122.5
| style="text-align: center;" | +23.4
|}

(This is really a change in free energy. Best to just call it a reaction energy [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:42, 16 March 2018 (UTC))

[[File:PS4615_3_energy_diagram_FULL.png|thumb|center|1000px|alt=|<b>Figure 11</b>. The energy diagram illustrating the relative activation energies and Gibbs free energies of the Diels-Alder and Cheletropic reaction.]]

From <b>figure 11</b>, it can be seen that out of all the reaction pathways (excluding the alternative Diels-Alder), the cheletropic pathway has the greatest activation energy, making it the most kinetically stable compared to the other 2 pathways. One of the possible explanation for this is the fact that the reaction forms a new 5-membered ring, compared to 6-membered rings for the other pathways. The ring strain in the 5-membered ring raises the energy of the transition state, raising its activation energy. Even though it is the most kinetically inert compared to the other three, the cheletropic path is the most thermodynamically favourable, as it is the most exothermic pathway (most negative Gibbs free energy of reaction). This is because of the stabilisation of the product by the 2 strong S=O bonds (bond enthalpy of 518 kJ/mol each <ref>Luo, Yu-Ran. Comprehensive handbook of chemical bond energies. Boca Raton, Fla.: CRC Press, 2007.
</ref>) compared to only one S=O and one S-O (S-O contributes 348 kJ/mol <ref>Cottrell, T. L. The strengths of chemical bonds. New York: Academic Press, 1961.
</ref>) in the Diels-Alder products. The two S=O bonds has a much greater effect than the ring strain in the 5-membered ring, making it the most exothermic reaction of the three.

Contrarily, the ENDO Diels-Alder pathway has the lowest activation energy, making it the fastest kinetically compared to the other two paths. This is due to the stabilisation of the transition state by secondary orbital interactions (similar to Exercise 2 case). This involves the interaction between the p orbital of the oxygen in sulphur dioxide and the delocalised π orbitals of xylylene. This is not possible for the EXO case as it does not have the correct geometry for the interaction, making its activation energy higher (but still lower than cheletropic path) than the ENDO transition state. Due to steric repulsions between the oxygen in the S=O and the rest of the molecule, the ENDO product energy is slightly above the EXO product. This makes the EXO path more thermodynamically favourable than the ENDO pathway, as it is slightly more exothermic. If the reaction is carried out under equilibrating conditions, the cheletropic product will be the major product of the reaction between sulphur dioxide and xylylene, as it is the most thermonamically favourable pathway.

The energy diagram (<b>figure 11</b>) shows that the alternative Diels-Alder reaction at the inner site is both thermodynamically and kinetically unfavourable. Firstly, the activation energy of the reaction is greater than any of the pathways described before. The reactions (EXO and ENDO) are endothermic, which means that they require energy to convert from reactants to product overall. The ENDO product here is both the kinetic and thermodynamic product compared to the EXO case. The transition states for this alternative pathway is higher in energy than the preferred path because it lacks the aromatic ring formed at the 6-membered ring. This also explains the why the reaction is endothermic, as the products does not have the aromatic 6-membered ring in it like the normal Diels-Alder and cheletropic products.

=Extension: Electrocyclic reaction=

[[File:Ext_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 12</b>. The reaction scheme of the electrocyclic reaction of cyclobutene.]]

<b>Corresponding Log Files</b>

[[Media:PS4615_EXT_CYCLOBUTENE_MIN_PM6.LOG|PS4615_EXT_CYCLOBUTENE_MIN_PM6.LOG]]

[[Media:PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG|PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG]]

[[Media:PS4615_EXT_TS_BERNY_PM6.LOG|PS4615_EXT_TS_BERNY_PM6.LOG]]

[[Media:PS4615_EXT_TS_BERNY_B3LYP.LOG|PS4615_EXT_TS_BERNY_B3LYP.LOG]]

[[Media:PS4615_EXT_TS_IRC_PM6.LOG|PS4615_EXT_TS_IRC_PM6.LOG]]

[[Media:PS4615_EXT_PRODUCT_B3LYP.LOG|PS4615_EXT_PRODUCT_B3LYP.LOG]]

In this extension, the thermal electrocyclic ring opening of the molecule shown in the reaction scheme above was studied. Since electrocyclic reactions is a class of a pericyclic reaction, the stereochemistry of the product can be determined using the Woodward-Hoffman rules. From this, it was determined that the reaction undergoes conrotatory electrocyclic ring opening, which agrees with the calculations carried out using B3LYP (see the animation in <b>table 10</b> and the vibrations of the transition state at <b>figure 13</b>). The activation energy of the reaction was found to be <math> +122.4 kJmol^{-1} </math>, with the Gibbs free energy of the reaction at <math>-64.1 kJmol^{-1}</math>. This shows that the reaction has a significantly high activation energy, making it kinetically inert. One possible explanation to this is the raise in the TS energy due to steric interactions between the bulky methyl ester groups during the transition from the reactant to product (see animations). Since the reaction is significantly exothermic, the reaction is considered thermodynamically favourable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

!<b>Figure 13</b> shows the vibration of the transition state.
|-
|

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size><align>centre</align>
<uploadedFileContents>PS4615_EXT_TS_BERNY_B3LYP.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 29; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>EXT_TS_VIBRATION</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>EXT_TS_VIBRATION</target>
</jmolbutton>
</jmol>

|
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 10</b> shows the IRC of the reaction, where the movie shows that the reaction is conrotatory.'''

!The reaction's IRC

|-

|[[File:PS4615_EXT_IRC.png|400px]]|

|-

!IRC movie. Click on the link for movie.

|-

|[[https://wiki.ch.ic.ac.uk/wiki/images/d/d1/PS4615_EXT_IRC_movie.gif]]|

|}

It is clear from the animations and the transition state vibrations that the reaction is a conrotatory electrocyclic ring opening. Aside from using the Woodward-Hoffmann rules, this can be determined and illustrated by looking the the HOMO of the reactants and products (see <b>table 11</b>). From the HOMO of the product, it can be seen that the only way that the reaction can proceed (working backwards) is through antarafacial interactions of the MOs at the terminal carbons, as this is the only way to achieve constructive interaction between the orbitals. In terms of the symmetry (when considering just the diene fragment), the HOMO is asymmetric. By following through with the reaction to the reactants, it can be seen that the terminal carbons rotate in the same direction to form the cyclobutene. This is illustrated in the in <b>figure 14</b>.

[[File:PS4615_EXT_orbitals_interaction_NEW.png|thumb|center|600px|alt=|<b>Figure 14</b>. This illustrates the Frontier orbital (HOMO) approach to determining the stereochemistry of the reaction.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 11</b>. The relevant molecular orbitals of the reaction.'''

!Cyclobutene HOMO

!Transition state HOMO

!Product HOMO

|-

|<jmol>
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|-

!Cyclobutene LUMO

!Transition state LUMO

!Product LUMO

|-

|<jmol>
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|-
|}

(It is actually the HOMO-1 in the TS that has the orbitals that you are looking for [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:49, 16 March 2018 (UTC))

=Conclusion=

In this experiment, a semi-empirical method PM6 and a hybrid method B3LYP were used to calculate the geometries and vibrations of 4 different transition states of 4 different pericyclic reactions successfully. Method three was used for all of the calculations, as it is the most accurate method out of the three. Starting with the first exercise, the C-C bond lengths involved in the reaction were analysed as the reaction progresses from the reactants, to the transition states and finally the product. It was also found that the bond formation is synchronous, which is not the case for the reactions in exercise 3. The activation energies and Gibbs free energies of the ENDO and EXO Diels-Alder reactions were calculated in exercise 2 up to the B3LYP level of accuracy. The relevant MOs were visualised to qualitatively show the effect of secondary orbital interactions and steric repulsions on the thermochemistry of the reactions. From the energies of the relavant MOs, it was proven that the Diels-Alder reaction in exercise 2 is an inverse electron-demand reaction. As for exercise 3, the different reaction paths were investigated for the reaction between sulphur dioxide and xylylene. It was found that the most thermodynamically favourable pathway is the Cheletropic path, whereas the ENDO Diels-Alder reaction path is the most kinetically driven. Lastly, calculations up to B3LYP level of accuracy for a thermal electrocyclic ring opening of cyclobutene was carried out. The IRC animation and the transition state vibrations showed that the reaction is conrotatory, which is in agreement with the Woodward-Hoffmann rules.

=Bibliography=

Rep:Mod:mg5715TS

2018-03-27T15:59:07Z

Fv611: /* MO analysis of exercise 2 */

==Introduction==

===Potential energy surface===
[[File:MG5715_TS_INTRO_DIATOMIC.PNG|thumb|500px|x500px|center|Fig.1 The potential energy curve of a diatomic molecule<ref>L., D. J. (1957). Model of a potential energy surface. J. Chem. Educ., 34(5), 215.</ref>]]
The potential energy surface of a diatomic molecule is anharmonic oscillation (as shown in Fig.1). The lowest point in this energy potential is a stationary point, which means it has a zero first derivative:
<center><math>\frac{dE(R)}{dR}=0</math></center>
<small><center>Equation 1. First derivative of 1-D potential energy</center></small>

R stands for the bond length and the physical meaning of the first derivative of potential energy is the force acting on the atoms and the second derivative is the force constant (k). The bond will vibrate; so the vibration wavenumber could be calculated by Equation 2.
<center><math>\tilde{v}=\frac{1}{2c\pi}\sqrt{\frac{k}{\mu}}</math></center>
<small><center>Equation 2. Vibrational wavenumber of a diatomic molecule</center></small>
where <math>\mu</math> is the reduced mass and it could be calculated by Equation 3.
<center><math>\mu=\frac{M_AM_B}{M_A+M_B}</math></center>
<small><center>Equation 3. Reduced mass of a diatomic molecule</center></small>

[[File:MG5715_TS_INTRO_TRIATOMIC.PNG|thumb|500px|x500px|center|Fig.3 Potential energy surface of triatomic molecule<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). http://doi.org/10.1016/0166-1280(90)85035-L</ref>]]
For a triatomic molecule (e.g.H<sub>2</sub>O), the potential energy surface has two coordinates including bond length R and bond angle <math>\theta</math> and the potential energy surface is shown in Fig.3. For a non-linear molecule including N atoms, it will have '''3N-6''' independent geometric variables. For each atom, it will have three variables (bond length, bond angle and torsional angles).The three global rotations and three global translations should be subtracted, so it has 3N-6 degrees of freedom. If it is a linear molecule, there only have two rotation axes, so it has '''3N-5''' independent geometric variables.
A stationary point of the potential energy surface, which has 3N-6 degrees of freedom, could be defined by equation 4.

<center><math>\frac{dE(\mathbf{R})}{dR_i}=0 i=1,2,3,...3N-6</math></center>
<small><center>Equation 4. General equation of a stationary point with 3N-6 variables</center></small>
where '''R''' is the set of all nuclear coordiantes.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). http://doi.org/10.1016/0166-1280(90)85035-L</ref>

[[File:MG5715_TS_INTRO_PES.PNG|thumb|500px|x500px|center|Fig.4 The 1-D potential energy surface of a reaction<ref>L., D. J. (1957). Model of a potential energy surface. J. Chem. Educ., 34(5), 215.</ref>]]
Fig.4 is a 1-D potential energy surface of a reaction. Products and reactants are the minimum points on the lowest energy pathway. For transition state, it is the maximum point on the lowest energy pathway. All of reactants, products and transition state are the stationary points, which means that they satisfy this equation:
(<math>\frac{dE(\mathbf{R})}{dR}=0</math>). The second derivative of potential energy surface, the force constant, is used to distinguish the products and reactants with the transition state. Reactants and products are {{fontcolor1|blue|'''minima'''}}, so the second derivative is positive.(<math>\frac{d^2E(\mathbf{R})}{dR^2}>0</math>) Transition state is the {{fontcolor1|blue|'''saddle point'''}} of the potential energy surface, which means its second derivative is negative.(<math>\frac{d^2E(\mathbf{R})}{dR^2}<0</math>) The force constant of transition state is negative; so, the vibration wavenumber will be imaginary at transition state according to Equation 2.

===Approximations===
The time-independent Schrödinger equation is:
<Center><math>\hat{H}\Psi_A=E\Psi_A </math></center>
<center><small>Equation 5. Time-independent Schrödinger equation</small></center>
where <math>\hat{H}</math> is an operator called Hamiltonian, <math>\Psi_A</math> is the wavefunction of electron A, and E stands for the energy.
Schrödinger equation could be rewritten by Dirac notation (<math>\hat{H}|\Psi =E|\Psi</math>).Premultiply the complex conjugation of the wavefunction and integrate over all variables and then rearrange the equation, an euqation of E will be gained. (<math>E=\frac{<\Psi^*|\hat{H}|\Psi>} {<\Psi^*|\Psi>}</math>) where the denominator is the overlap integer. If the wavefunction is normalised, the overlap integer should be 1; so <math>E=<\Psi^*|\hat{H}|\Psi></math>.

The Hamiltonian operator for a molecule could be separated into kinetic and potential energies of individual particles (<math>\hat{E}=\hat{T}_n+\hat{T}_e+\hat{V}_{ee}+\hat{V}_{en}+\hat{V}_{nn}</math>).T stands for the kinetic energy and V is the potential energy.The {{fontcolor1|blue|'''Born-Oppenheimer approximation'''}} is the first key approximation for Schrödinger equation. Because the motion of electrons is much faster than that of nuclei, the kinetic energy of the nucleus could be ignored and the potential energy of nuclei's interaction will be constant. Hence, the Hamiltonian operator could be rewritten to <math>\hat{E}_{BO}=+\hat{T}_e+\hat{V}_{ee}+\hat{V}_{en}+constant</math>

In quantum chemistry, another very important approximation is that the wavefunction of a molecule is the {{fontcolor1|blue|'''linear combination of atomic orbitals (LCAO)'''}} as shown in Equation 6.
<center><math>\Psi(r)=\sum_{n}^N c_n \phi_n(r)</math></center>
<center><small>Equation 6. linear combination of atomic orbitals</small></center>
where <math>\phi_n(r)</math> is the basis set (atomic orbital). Therefore the hamiltonian could be rewriten as Equation 7.
<center><math>E=<\Psi^*|\hat{H}|\Psi>=\sum_{n}^N \sum_{m}^N c_m <\phi_m(r)|\phi_n(r)> c_n</math></center>
<center><small>Equation 7. linear combination of atomic orbitals</small></center>

The more basis sets are used, the more accurate the molcular orbital is, but increasing the basis sets will increase the cost of computational effort.

===Computational Methods===
Although Gauss View contains lots of different calculation method, only two of them are used in this lab: (1) Semi-empirical method PM6 and (2) Density Functional Theory(DFT) method B3LYP.

The Semi-empirical method is based on the experimental data, which will save time for calculating. The density functional theory is the calculation based on theory and does not include any experimental data. Therefore, this process is slower than semi-empirical method.

===Methods to find Transition State===
* '''Method 1'''
(1) predict and draw a guess transition state structure

(2) optimise the guess transition state structure to TS(Berny) and set ''Calculate force constants'' to '''once''' and the output is the optimised transition state (Only have '''one''' imaginary frequency)

This method is quite easy and it is the fastest method.However, this method is not very reliable and it only works for small systems because it will fail easily if the predicted transition state is not close to the real transition state.

* '''Method 2'''
(1) predict and draw a guess transition state structure

(2) freeze the distance between atoms where the bond will be formed in the reaction

(3) optimise the frozen-bond structure to a minimum

(4) repeat method 1(2)

This method is similar to method 1 but this one is more reliable than method 1 because it freezes the atoms to prevent them from moving. This makes sure the system close to the transition state before calculation. However, this also will fail easily.

* '''Method 3'''
(1) draw the reactant(s) or product(s) and choose the one which has fewer molecules.

(2) optimise the reactant(s) or product(s) to a minimum

(3) break or form the bond and freeze the distance between atoms

(4) repeat method 2 (2)-(4)

This method is much more reliable than the previous two methods and it does not need to predict the possible transition state. However, this method is more complicated and it requires more steps.

==Excercise 1: Reaction of Butadiene with Ethylene==
[[file:MG5715_TS_EX1_REACTION SCHEME.JPG|thumb|550px|center|Fig.5 The reaction scheme of cycloaddition of butadiene and ethylene]]
The reaction of butadiene with ethylene is a traditional '''[4+2] cycloaddition''', which also known as '''Diels-Alder reaction'''.In Diels-Alder reaction, a conjugated diene (butadiene) will react with a dienophile (ethylene) to form a cyclohexene and the reaction scheme is shown in Fig 5. Although the s-''trans'' conformation is more energetically favourable, the conformation of diene should be s-''cis'' because of the interaction between the frontier molecular orbitals(FMO). Moreover, the energy barrier between s-''trans'' and s-''cis'' is not extremely high. In this exercise, all reactants, products and transition state were optimised by {{fontcolor1|blue|'''semi-empirical method PM6 '''}} in Gauss View and {{fontcolor1|blue|'''Method 2'''}} is used to locate the transition state.
===MO analysis===

[[file:MG5715_TS_EX1_MO_1.JPG|thumb|550px|center|Fig.6 The molecular orbital of cycloaddition of butadiene with ethylene]]

The MO diagram is shown in Fig.6 and this graph is drawn according to the energy calculated by PM6. The energy of product ({{fontcolor1|black|'''black'''}} line) should be lower than that of the reactants, and the energy of transition state ({{fontcolor1|#fe7af9|'''pink'''}} line) is higher than that of reactants. The HOMO and LUMO are shown in Table 1.

{| class="wikitable" style="margin: auto;"
|
! center; style="background: #0D4F8B; color: white; text-align: center;"| Butadiene
! center; style="background: #0D4F8B; color: white; text-align: center;" | Ethylene
! center; style="background: #0D4F8B; color: white; text-align: center;" colspan="2"| MO of Transition State
|-
| center;| LUMO

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| center;| HOMO
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! center| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_ETHLYENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

! center| <jmol>
<jmolApplet>
<title>HOMO of Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 22; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_TS_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

! center|<jmol>
<jmolApplet>
<title>HOMO-1 of Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 22; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_TS_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ Table 1. The HOMO and LUMO diagram of reactants, product and transition state
|}

For a [p+q]-cycloaddtion reaction, it could be driven either thermally or photochemically. For photochemical reaction, the electrons on HOMO will be excited to LUMO and become two SOMOs.Therefore, the photochemical cycloaddition is a little bit different with the thermal cycloaddition. A general rule called '''''Woodward Hoffmann Rule''''' is used to determine whether the cycloaddition is allowed or forbidden.

*Woodward-Hoffmann Rule for cycloaddition reactions
For a [p+q]-cylcoaddtion reaction, only two components are involved, where one contains p π-electrons and the other one has q π-electrons. s stands for suprafacial and a means antarafacial

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white; text-align: center;"| p+q
! center; style="background: #0D4F8B; color: white; text-align: center;" | Thermally allowed
! center; style="background: #0D4F8B; color: white; text-align: center;" | Photochemically allowed

|-
! center; | 4n
! center| p<sub>s</sub>+q<sub>a</sub> or p<sub>a</sub>+q<sub>s</sub>
! center| p<sub>s</sub>+q<sub>s</sub> or p<sub>a</sub>+q<sub>a</sub>

|-
! center;| 4n+2
! center| p<sub>s</sub>+q<sub>s</sub> or p<sub>a</sub>+q<sub>a</sub>
! center| p<sub>s</sub>+q<sub>a</sub> or p<sub>a</sub>+q<sub>s</sub>
|+ Table 2. Woodward-Hoffman Rule <ref>Semis, K. L., & Rules, B. W. (1965). Woodward-Hoff mann Rules : Electrocyclic Reactions.</ref>
|}

In this reaction, butadiene has 4 π-electrons and ethylene contains 2 π-electrons. The sum of p and q is 6 and they are all suprafacial. Hence, this [4+2] cycloaddition is {{fontcolor1|blue|'''thermally allowed'''}}.

*overlap integral
<center><math>S=\int\psi\psi^*\,d\tau</math></center>
<center><small>Equation 8. Calculation of overlap integral</small></center>

The overlap integral is calculated by equation 8 and it is telling how well two orbitals are overlapped. The value of overlap integral is between 0 and 1. 0 means that the two orbitals do not have any overlap and 1 means that they perfectly overlap with each other. Table 3 is used to determine whether the wavefunction is symmetric or antisymmetric.

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white; text-align: center;"| Symmetric
! center; style="background: #0D4F8B; color: white; text-align: center;" | Antisymmetric
|-
! center;|ψ(r<sub>1</sub>,r<sub>2</sub>)={{fontcolor1|red|'''+'''}}ψ(r<sub>2</sub>,r<sub>1</sub>)
! center;|ψ(r<sub>1</sub>,r<sub>2</sub>)={{fontcolor1|red|'''-'''}}ψ(r<sub>2</sub>,r<sub>1</sub>)
|+Table 3. Symmetric and Antisymetric wavefunction
|}

For two wavefunctions, the overlap integral will be 0 if the product of two wavefunctions is antisymmetric. If the product of two wavefunctions is symmetric, the overlap integral will be 1. Only when '''both of the wavefunctions are antisymmetric''' or '''both are antisymmetric''', the overlap integral will be 1. As shown in MO diagram, the antisymmetric orbital will overlap with the antisymmetric orbital.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Your MO diagram is very nice, but there is some confusion in the discussion of symmetry and orbital overlap. The orbital overlap will only be 1 in case the two functions are exactly the same.)
===Analysis of bond lengths===
{| class="wikitable" style="margin: auto;"
|center; | [[file:MG5715_TS_E1_IRC_DISTANCE.jpg|thumb|none|500px|x500px|center|Fig.7 Disatance VS reaction coordination]]
|center; | [[file:MG5715_TS_E1_LABEL.PNG|thumb|none|500px|x500px|center|Fig.8 Labelled molecule]]
|+ Table 4. IRC bond distance analysis
|}

In Fig.7, it shows that the distances between C atoms change with reaction coordination. and Fig.8 shows the labelled molecule. Initially, the distance between C<sub>14</sub> and C<sub>1</sub> and distance between C<sub>7</sub> and C<sub>11</sub> are around 3.4 Å, which indicates there does not have any bond between those two atoms. The Van der Waal radius of C atom is 1.77Å <ref>Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials Translated from Neorganicheskie Materialy Original Russian Text, 37(9), 871–885. http://doi.org/10.1023/A:1011625728803</ref> 3.4 Å is smaller than twice of Van der Waals radius of C; therefore, C<sub>14</sub> is interacting with C<sub>1</sub> and a bond will be formed between them.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You should have focused your discussion on the length of the bonds at the transition state specifically.)

{| class="wikitable" style="margin: auto;"
|
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>3</sup>)-C(sp<sup>3</sup>)
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>3</sup>)-C(sp<sup>2</sup>)
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>2</sup>)-C(sp<sup>2</sup>)
|-
! center;| Bond length/Å
! center| 1.542
! center| 1.488
! center| 1.459
|+ Table 4. Bond length of C-C bond<ref>Bernstein, H. J. (1961). BOND DISTANCES IN HYDROCARBONS * t. Retrieved from http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649</ref>
|}

Table 4. shows the literature value of C-C bond length with different hybridisation and comparing those with the Fig 7. It suggests C<sub>1</sub>, C<sub>7</sub>,C<sub>11</sub> and C<sub>14</sub> change from sp<sup>2</sup> to sp<sup>3</sup>; C<sub>4</sub> and C<sub>6</sub> remain sp<sup>2</sup>. Besides that, this table also confirms the product is hexene. The distance between C<sub>4</sub> and C<sub>6</sub> is 1.338 Å, which is similar to the bond lenght of C(sp<sup>2</sup>)-C(sp<sup>2</sup>). The rest of bond lengths are around 1.5 Å; so the rest of bonds are C(sp<sup>3</sup>)-C(sp<sup>3</sup>).

===Vibration===
{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Transition State vibration
! center; style="background: #0D4F8B; color: white;" | Inrinsic Reaction Coordinate(IRC)

|-
| center;| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 23; vibration 1;rotate x -20; </script>
<uploadedFileContents>MG5715_TS_E1_TS_VIB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| [[file:MG5715_TS_E1_IRC.gif‎]]

|-
| center;| [[file:MG5715_TS_E1_VF.PNG|thumb|none|500px|x500px|center|Fig 9. Vibration Frequencies of Transition State]]
| [[file:MG5715_TS_E1_IRC_PATH.PNG|thumb|none|500px|x500px|center|Fig 10. summary of IRC plot ]]

|}

As shown in Fig.9, there is only one imaginary frequency (at -948.8 cm<sup>-1</sup>); so it justifies the transition state is right. However, it is not enough for determining the transition state. It is critical to do the IRC calculation. RMS Gradient should be zero in reactants, products and also transition state because they are local minima. However, for transition state, it is saddle point; hence, the second derivative should be negative.

According to the gif shown above, it shows that bonds are formed '''synchronously'''.

===LOG File===
Transition state:[[File:MG5715_TS_E1_TS_MO.LOG]]

Butadiene:[[File:MG5715_TS_E1_BUTADIENE_MO.LOG]]

Ethylene:[[File:MG5715_TS_E1_ETHLYENE_MO.LOG]]

==Excercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

[[File:MG5715_TS_E2_REACTION.jpg|thumb|550px|center|Fig.11 The reaction scheme of Cyclohexadiene and 1,3-Dioxole]]

The reaction of cyclohexadiene and 1,3-Dioxole is also a Diels-Alder reaction, but this reaction will give two products (endo and exo) because of two possible transition states. The reaction scheme is shown in Fig.11 In this exercise, the transition state is opitimised by {{fontcolor1|blue|'''PM6'''}} firstly and then optimised again by {{fontcolor1|blue|'''B3LYP'''}}. Moreover, the transition state is determined by {{fontcolor1|blue|'''method 3'''}} in this exercise.

=== MO analysis of exercise 2===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) This is not the way to draw two separate MO diagrams.)

[[File:MG5715_TS_E2_MO.jpg|thumb|550px|center|Fig.12 MO diagram of Cyclohexadiene and 1,3-Dioxole]]

The MO diagram of this reaction is displayed in Fig.12The energies of product's MO is shown in '''black''' lines and the {{fontcolor1|#fe7af9|'''pink'''}} lines represent the energies of transition states' MO, and all of them are drawn based on the relative energies calculated by '''B3LYP'''. Furthermore, the HOMO and LUMO of reactants are shown in Table 5. and the MOs of transition states are displayed in Table 6.

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white; text-align: center;"| HOMO
! style="background: #0D4F8B; color: white; text-align: center;" | LUMO

|-
| Clycohexadiene

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| 1,3-dioxole
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ Table 5. LUMO and HOMO of reactants
|}

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white; text-align: center;"| ENDO TS
! style="background: #0D4F8B; color: white; text-align: center;" | EXO TS

|-
| LUMO+1
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| HOMO-1
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|+ Table 6. MO of Transition states
|}

====Secondary Orbital Interactions ====
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Endo-TS
! style="background: #0D4F8B; color: white;" | Exo-TS
|-
| Jmol of computed HOMO

|<jmol>
<jmolApplet>
<color>white</color>
<size>225</size>
<script> frame 48; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>225</size>
<script> frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| LCAO diagram of HOMO

| [[File:MG5715_TS_E2_ENDO_TS.jpg|thumb|550px|center]]

| [[File:MG5715_TS_E2_EXO_TS.jpg|thumb|550px|center]]
|+ Table 7. HOMO of Endo-TS and Exo- TS
|}

The computed HOMO and LACO diagram of HOMO are shown in Table 7. Endo-product is more stable than Exo-product due to lack of steric clash with the methyl group in cyclohexadiene. Furthermore, the Endo-TS is lower in energy because of '''Secondary Orbital Interaction'''. The lone pair of oxygen could donate the electron density to the LUMO of cyclohexadiene; hence, the Endo-TS will be stabilised. Both the Endo-TS and Endo-product are lower in energy; so this reaction is endo-selective.

==== Inverse VS Normal Demand Diels-Alder Reaction ====

[[File:MG5715_TS_E2_DA.jpg|thumb|550px|center|Fig.13 two tyes of Diels-Alder reaction]]

For a Diels-Alder reaction, the reactivity is controlled by relative energies of '''Frontier Molecular Orbitals (FMOs)'''. There are two different types as shown in Fig.13:(1) Normal demand and (2) Inverse demand. Usually, the reaction of an all carbon diene with a hetero-dienophile will give a ''normal electron demand'' because the heteroatom in dienophile may withdraw the electron density from dienophile and lower the energy of MOs. The best way to justify whether the reaction is normal demand or inverse demand is to sequence the energy of reactants as shown in Table 8. If the HOMO of dienophile is lower than that of diene, it is normal demand, vice versa. The HOMO of cyclohexadiene is the lowest; hence, this reaction is {{fontcolor1|blue|'''inverse demand'''}} Diels-Alder reaction. The reason is that the two oxygen atom in 1,3-dioxole donate the electron density toward the π-bonding and raise the energy of MOs.

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo-reaction
! style="background: #0D4F8B; color: white;" | Exo-reaction

|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|+ Table 8. Single point energy of reactants
|}

=== Activation Barrier and Energy changed ===
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Energy calculated by B3LYP/kJmol<sup>-1</sup>
|-
! center| Cylcohexadiene
! center| 306.9
! center| -612593

|-
! center| 1,3-dioxole
! center| -137.3
! center| -701189

|-
! center| Endo-product
! center| 99.2
! center| -1313849

|-
! center| Endo-TS
! center| 362.2
! center| -1313622

|-
! center| Exo-product
! center| 99.7
! center| -1313845

|-
! center| Exo-TS
! center| 364.7
! center| -1313614
|+ Table 9. Energies of reactants, products and transition states
|}

According to the energies of reactants, products and transition states (shown in Table 9), the reaction energy and activation energy could be calculated by the following equation:
<pre>
Activation Energy = Transition state energy - Sum of energies of reactants
Reaction Energy = product energy - Sum of energies of reactants
</pre>

{| class="wikitable" style="margin: auto;"
! rowspan="2"|
! style="background: #0D4F8B; color: white;" colspan="2"| Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" colspan="2"| Reaction Energy/kJmol<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
|-
! center| Endo-reaction
! center| +192.6
! center| +159.8
! center| -70.3
! center| -67.4
|-
! center| Exo-reaction
! center| +195.1
! center| +169.7
! center| -69.9
! center| -63.8
|+ Table 10. Reaction energy and activation energy for both Endo and Exo product.
|}

All the energy calculated is shown in Table 10. Both the activation energy and reaction energy for Endo-product are lower than those for Exo-product. A thermodynamically favourable product is more stable, which means it has more negative reaction energy. The kinetically favourable product has lower reaction barrier (activation energy). Hence, the endo-product of this exercise is both '''thermodynamically and kinetically favourable'''.

===LOG File===
1,3-Dioxole:[[File:MG5715_TS_E2_REACTANTS_2.LOG]]

Cyclohexadiene:[[File:MG5715_TS_E2_REACTANTS_1.LOG]]

Exo-Transition State:[[File:MG5715_TS_E2_EXO.LOG]]

Endo-Transition State:[[File:MG5715_TS_E2_ENDO.LOG]]

==Excercise 3 Diels-Alder vs Cheletropic==

[[File:MG5715_TS_E3_REACTION.jpg|thumb|550px|center|Fig.14 Reaction Scheme of o-Xylylene with SO<sub>2</sub>]]

The reaction of o-xylylene with SO<sub>2</sub> could be either Diels-Alder or cheletropic reaction. For Diels-Alder reaction, o-Xylylene acts as diene and SO<sub>2</sub> acts as dienophile to form a six-membered ring and there are two possible products (endo-product and exo-product). As discussed in exercise 2, the Diels-Alder is endo-selective. For the cheletropic reaction, a five-membered ring will be formed and two new bonds are formed with the same atom. The reaction scheme of those reactions is displayed in Fig.14. In this exercise, the reactants, products and transition states were optimised by {{fontcolor1|blue|'''PM6'''}} and {{fontcolor1|blue|'''B3LYP'''}} and {{fontcolor1|blue|'''Method 3'''}} was used to find the transition state. The reaction energy and activation energy were calculated to find out the favourable reaction.

(Endo is only kinetically preferred out of the DA reactions [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== IRC Analysis===
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | IRC
|-
| Cheletropic reaction
| [[File:MG5715_TS_E3_Cheletropic_IRC.gif]]
|-
| Endo Diels-Alder reaction
| [[File:MG5715_TS_E2_ENDO_irc.gif]]
|-
| Exo Diels-Alder reaction
| [[File:MG5715_TS_E3_EXO_irc.gif]]
|+ Table.11 The IRC of three possible reactions
|}

There are two different mechanisms for Diels-Alder reaction:(1)synchronous and symmetrical (concerted) mechanism and (2) multistage (non-concerted) and asynchronous mechanism.

* synchronous and symmetrical (concerted) mechanism
A very typical example of this mechanism is Exercise 1. The two new bonds are formed simultaneously and the two new bonds have the same bond length in the transition state.

* multistage (non-concerted) and asynchronous mechanism
The two bonds could not be formed at the same time because the bond length of them are different at transition state. Therefore, usually, a di-radical will be formed.

For Diels-Alder reaction, the distance between O and C in o-Xylylene is different from the distance between S and C in o-Xylylene at transition state because of distinct Van der Waal radii.
Therefore, the bond does not form synchronously, which could be observed in the IRC in Table 11. However, for cheletropic reaction, the two now bonds are both formed between S atom and C in o-Xylylene; so the two bond are formed synchronously as shown in IRC.

(Be careful: it looks like you're saying the DA reactions are multistage, which involves an intermediate (all positive eigenvalues in Hessian/positive frequencies) [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== Activation Energy and Reaction Energy===
[[File:MG5715_TS_E3_ENERGY.jpg|thumb|550px|center|Fig.15 Energy diagram of o-Xylylene with SO<sub>2</sub>]]

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Energy calculated by B3LYP/kJmol<sup>-1</sup>
|-
! center| O-Xylylene
! center| 469.5
! center| -812604

|-
! center| SO<sub>2</sub>
! center| -311.4
! center| -1440362

|-
! center| Endo-product
! center| 57.0
! center| -2253040

|-
! center| Endo-TS
! center| 237.8
! center| -2252919.7

|-
! center| Exo-product
! center| 56.3
! center| -2253041

|-
! center| Exo-TS
! center| 241.7
! center| -2252919.8

|-
! center| Cheletropic product
! center| -0.005251
! center| -2253024

|-
! center| Cheletropic TS
! center| 260.1
! center| -2252902
|+ Table 12. Energies of reactants, products and transition states
|}

{| class="wikitable" style="margin: auto;"
! rowspan="2"|
! style="background: #0D4F8B; color: white;" colspan="2"| Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" colspan="2"| Reaction Energy/kJmol<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
|-
! center| Endo-reaction
! center| +79.7
! center| +46.2
! center| -101.1
! center| -73.9
|-
! center| Exo-reaction
! center| +83.7
! center| +46.1
! center| -101.8
! center| -73.2
|-
| Cheletropic
! center| +102.0
! center| +63.0
! center| -158.1
! center| -58.8
|+ Table 13. Reaction energy and activation energy for both Endo and Exo product.
|}

The energies of reactants, products and transition states are shown in Table 12 and the calculated reaction energy and activation energy are displayed in Table 13. The energy diagram (Fig.15) is drawn according to the energy calculated by PM6. The product of the cheletropic reaction is the most stable because of aromaticity. However, the activation energy of cheletropic product is quite high. Therefore, at low temperature, a sultine (kinetic product) will be formed but this reaction is reversible. At high temperature, a sulfolene will be formed and this reaction is irreversible.

(Well done doing the B3LYP calculations, but it must have taken a long time. The results are distinctly different to the PM6 calculations, so you could have commented on that [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== Extension===
[[File:MG5715_TS_E3_EXTENSION_SCHEME.jpg|thumb|550px|center|Fig.16 Reaction Scheme of o-Xylylene with SO<sub>2</sub>]]
There are two dienes in o-Xylylene and therefore, it has another possible Diels-Alder reaction as shown in Fig.16. The energy calculated is displayed in Table 14 and they are calculated by PM6.

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
|-
! center| O-Xylylene
! center| 469.5

|-
! center| SO<sub>2</sub>
! center| -311.4

|-
! center| Endo-product
! center| 172.3

|-
! center| Endo-TS
! center| 268.0

|-
! center| Exo-product
! center| 176.7

|-
! center| Exo-TS
! center| 275.8
|+ Table 14. Energy of reactants, products, and transition states
|}

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Reaction Energy/kJmol<sup>-1</sup>
|-
! center| Endo-reaction
! center| +109.9
! center| +14.2

|-
! center| Exo-reaction
! center| +117.7
! center| +18.6

|+ Table 15. Reaction energy and activation energy for both Endo and Exo product.
|}

Compare the energy in Table.15 with the data in Table.13, this reaction is quite unlikely to happen because the activation barrier is higher and the reaction energy is endothermic.

===LOG File===
o-Xylylene:[[File:MG5715_REACTANT_PM6.LOG]]

SO<sub>2</sub>:[[File:MG5715_SO2_PM6.LOG]]

Exo-Transition state:[[File:MG5715_EXO_TS_PM6.LOG]]

Endo-Transition state:[[File:MG5715_ENDO_TS_PM6.LOG]]

Cheletropic Transition state:[[File:MG5715_CHE_TS_PM6.LOG]]

==Conclusion==
In conclusion, Gauss View is a quite efficient way to locate the transition state and to calculate the energy of a reaction. Hence, it could suggest which product is thermodynamically favourable and which one is kinetically favourable. Besides that, it could mimic the reaction pathway by IRC, which can tell us whether the bonds are formed synchronously or not. One of the best way to confirm the transition state is to check the vibration frequency of transition state. For a transition state, it will always have only one imaginary frequency. According to this experiment, it suggests Diels-Alder reaction is endo-selective because of secondary orbital interaction and if the two bonds are formed with same atoms, they will form synchronously.

==Reference==

Rep:Mod:mg5715TS

2018-03-27T15:53:38Z

Fv611: /* Excercise 1: Reaction of Butadiene with Ethylene */

==Introduction==

===Potential energy surface===
[[File:MG5715_TS_INTRO_DIATOMIC.PNG|thumb|500px|x500px|center|Fig.1 The potential energy curve of a diatomic molecule<ref>L., D. J. (1957). Model of a potential energy surface. J. Chem. Educ., 34(5), 215.</ref>]]
The potential energy surface of a diatomic molecule is anharmonic oscillation (as shown in Fig.1). The lowest point in this energy potential is a stationary point, which means it has a zero first derivative:
<center><math>\frac{dE(R)}{dR}=0</math></center>
<small><center>Equation 1. First derivative of 1-D potential energy</center></small>

R stands for the bond length and the physical meaning of the first derivative of potential energy is the force acting on the atoms and the second derivative is the force constant (k). The bond will vibrate; so the vibration wavenumber could be calculated by Equation 2.
<center><math>\tilde{v}=\frac{1}{2c\pi}\sqrt{\frac{k}{\mu}}</math></center>
<small><center>Equation 2. Vibrational wavenumber of a diatomic molecule</center></small>
where <math>\mu</math> is the reduced mass and it could be calculated by Equation 3.
<center><math>\mu=\frac{M_AM_B}{M_A+M_B}</math></center>
<small><center>Equation 3. Reduced mass of a diatomic molecule</center></small>

[[File:MG5715_TS_INTRO_TRIATOMIC.PNG|thumb|500px|x500px|center|Fig.3 Potential energy surface of triatomic molecule<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). http://doi.org/10.1016/0166-1280(90)85035-L</ref>]]
For a triatomic molecule (e.g.H<sub>2</sub>O), the potential energy surface has two coordinates including bond length R and bond angle <math>\theta</math> and the potential energy surface is shown in Fig.3. For a non-linear molecule including N atoms, it will have '''3N-6''' independent geometric variables. For each atom, it will have three variables (bond length, bond angle and torsional angles).The three global rotations and three global translations should be subtracted, so it has 3N-6 degrees of freedom. If it is a linear molecule, there only have two rotation axes, so it has '''3N-5''' independent geometric variables.
A stationary point of the potential energy surface, which has 3N-6 degrees of freedom, could be defined by equation 4.

<center><math>\frac{dE(\mathbf{R})}{dR_i}=0 i=1,2,3,...3N-6</math></center>
<small><center>Equation 4. General equation of a stationary point with 3N-6 variables</center></small>
where '''R''' is the set of all nuclear coordiantes.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). http://doi.org/10.1016/0166-1280(90)85035-L</ref>

[[File:MG5715_TS_INTRO_PES.PNG|thumb|500px|x500px|center|Fig.4 The 1-D potential energy surface of a reaction<ref>L., D. J. (1957). Model of a potential energy surface. J. Chem. Educ., 34(5), 215.</ref>]]
Fig.4 is a 1-D potential energy surface of a reaction. Products and reactants are the minimum points on the lowest energy pathway. For transition state, it is the maximum point on the lowest energy pathway. All of reactants, products and transition state are the stationary points, which means that they satisfy this equation:
(<math>\frac{dE(\mathbf{R})}{dR}=0</math>). The second derivative of potential energy surface, the force constant, is used to distinguish the products and reactants with the transition state. Reactants and products are {{fontcolor1|blue|'''minima'''}}, so the second derivative is positive.(<math>\frac{d^2E(\mathbf{R})}{dR^2}>0</math>) Transition state is the {{fontcolor1|blue|'''saddle point'''}} of the potential energy surface, which means its second derivative is negative.(<math>\frac{d^2E(\mathbf{R})}{dR^2}<0</math>) The force constant of transition state is negative; so, the vibration wavenumber will be imaginary at transition state according to Equation 2.

===Approximations===
The time-independent Schrödinger equation is:
<Center><math>\hat{H}\Psi_A=E\Psi_A </math></center>
<center><small>Equation 5. Time-independent Schrödinger equation</small></center>
where <math>\hat{H}</math> is an operator called Hamiltonian, <math>\Psi_A</math> is the wavefunction of electron A, and E stands for the energy.
Schrödinger equation could be rewritten by Dirac notation (<math>\hat{H}|\Psi =E|\Psi</math>).Premultiply the complex conjugation of the wavefunction and integrate over all variables and then rearrange the equation, an euqation of E will be gained. (<math>E=\frac{<\Psi^*|\hat{H}|\Psi>} {<\Psi^*|\Psi>}</math>) where the denominator is the overlap integer. If the wavefunction is normalised, the overlap integer should be 1; so <math>E=<\Psi^*|\hat{H}|\Psi></math>.

The Hamiltonian operator for a molecule could be separated into kinetic and potential energies of individual particles (<math>\hat{E}=\hat{T}_n+\hat{T}_e+\hat{V}_{ee}+\hat{V}_{en}+\hat{V}_{nn}</math>).T stands for the kinetic energy and V is the potential energy.The {{fontcolor1|blue|'''Born-Oppenheimer approximation'''}} is the first key approximation for Schrödinger equation. Because the motion of electrons is much faster than that of nuclei, the kinetic energy of the nucleus could be ignored and the potential energy of nuclei's interaction will be constant. Hence, the Hamiltonian operator could be rewritten to <math>\hat{E}_{BO}=+\hat{T}_e+\hat{V}_{ee}+\hat{V}_{en}+constant</math>

In quantum chemistry, another very important approximation is that the wavefunction of a molecule is the {{fontcolor1|blue|'''linear combination of atomic orbitals (LCAO)'''}} as shown in Equation 6.
<center><math>\Psi(r)=\sum_{n}^N c_n \phi_n(r)</math></center>
<center><small>Equation 6. linear combination of atomic orbitals</small></center>
where <math>\phi_n(r)</math> is the basis set (atomic orbital). Therefore the hamiltonian could be rewriten as Equation 7.
<center><math>E=<\Psi^*|\hat{H}|\Psi>=\sum_{n}^N \sum_{m}^N c_m <\phi_m(r)|\phi_n(r)> c_n</math></center>
<center><small>Equation 7. linear combination of atomic orbitals</small></center>

The more basis sets are used, the more accurate the molcular orbital is, but increasing the basis sets will increase the cost of computational effort.

===Computational Methods===
Although Gauss View contains lots of different calculation method, only two of them are used in this lab: (1) Semi-empirical method PM6 and (2) Density Functional Theory(DFT) method B3LYP.

The Semi-empirical method is based on the experimental data, which will save time for calculating. The density functional theory is the calculation based on theory and does not include any experimental data. Therefore, this process is slower than semi-empirical method.

===Methods to find Transition State===
* '''Method 1'''
(1) predict and draw a guess transition state structure

(2) optimise the guess transition state structure to TS(Berny) and set ''Calculate force constants'' to '''once''' and the output is the optimised transition state (Only have '''one''' imaginary frequency)

This method is quite easy and it is the fastest method.However, this method is not very reliable and it only works for small systems because it will fail easily if the predicted transition state is not close to the real transition state.

* '''Method 2'''
(1) predict and draw a guess transition state structure

(2) freeze the distance between atoms where the bond will be formed in the reaction

(3) optimise the frozen-bond structure to a minimum

(4) repeat method 1(2)

This method is similar to method 1 but this one is more reliable than method 1 because it freezes the atoms to prevent them from moving. This makes sure the system close to the transition state before calculation. However, this also will fail easily.

* '''Method 3'''
(1) draw the reactant(s) or product(s) and choose the one which has fewer molecules.

(2) optimise the reactant(s) or product(s) to a minimum

(3) break or form the bond and freeze the distance between atoms

(4) repeat method 2 (2)-(4)

This method is much more reliable than the previous two methods and it does not need to predict the possible transition state. However, this method is more complicated and it requires more steps.

==Excercise 1: Reaction of Butadiene with Ethylene==
[[file:MG5715_TS_EX1_REACTION SCHEME.JPG|thumb|550px|center|Fig.5 The reaction scheme of cycloaddition of butadiene and ethylene]]
The reaction of butadiene with ethylene is a traditional '''[4+2] cycloaddition''', which also known as '''Diels-Alder reaction'''.In Diels-Alder reaction, a conjugated diene (butadiene) will react with a dienophile (ethylene) to form a cyclohexene and the reaction scheme is shown in Fig 5. Although the s-''trans'' conformation is more energetically favourable, the conformation of diene should be s-''cis'' because of the interaction between the frontier molecular orbitals(FMO). Moreover, the energy barrier between s-''trans'' and s-''cis'' is not extremely high. In this exercise, all reactants, products and transition state were optimised by {{fontcolor1|blue|'''semi-empirical method PM6 '''}} in Gauss View and {{fontcolor1|blue|'''Method 2'''}} is used to locate the transition state.
===MO analysis===

[[file:MG5715_TS_EX1_MO_1.JPG|thumb|550px|center|Fig.6 The molecular orbital of cycloaddition of butadiene with ethylene]]

The MO diagram is shown in Fig.6 and this graph is drawn according to the energy calculated by PM6. The energy of product ({{fontcolor1|black|'''black'''}} line) should be lower than that of the reactants, and the energy of transition state ({{fontcolor1|#fe7af9|'''pink'''}} line) is higher than that of reactants. The HOMO and LUMO are shown in Table 1.

{| class="wikitable" style="margin: auto;"
|
! center; style="background: #0D4F8B; color: white; text-align: center;"| Butadiene
! center; style="background: #0D4F8B; color: white; text-align: center;" | Ethylene
! center; style="background: #0D4F8B; color: white; text-align: center;" colspan="2"| MO of Transition State
|-
| center;| LUMO

! center| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

! center|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_ETHLYENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

! center| <jmol>
<jmolApplet>
<title>LUMO of Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 22; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_TS_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

! center|<jmol>
<jmolApplet>
<title>LUMO+1 of Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 22; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_TS_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| center;| HOMO
! center| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

! center| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_ETHLYENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

! center| <jmol>
<jmolApplet>
<title>HOMO of Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 22; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_TS_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

! center|<jmol>
<jmolApplet>
<title>HOMO-1 of Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 22; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E1_TS_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ Table 1. The HOMO and LUMO diagram of reactants, product and transition state
|}

For a [p+q]-cycloaddtion reaction, it could be driven either thermally or photochemically. For photochemical reaction, the electrons on HOMO will be excited to LUMO and become two SOMOs.Therefore, the photochemical cycloaddition is a little bit different with the thermal cycloaddition. A general rule called '''''Woodward Hoffmann Rule''''' is used to determine whether the cycloaddition is allowed or forbidden.

*Woodward-Hoffmann Rule for cycloaddition reactions
For a [p+q]-cylcoaddtion reaction, only two components are involved, where one contains p π-electrons and the other one has q π-electrons. s stands for suprafacial and a means antarafacial

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white; text-align: center;"| p+q
! center; style="background: #0D4F8B; color: white; text-align: center;" | Thermally allowed
! center; style="background: #0D4F8B; color: white; text-align: center;" | Photochemically allowed

|-
! center; | 4n
! center| p<sub>s</sub>+q<sub>a</sub> or p<sub>a</sub>+q<sub>s</sub>
! center| p<sub>s</sub>+q<sub>s</sub> or p<sub>a</sub>+q<sub>a</sub>

|-
! center;| 4n+2
! center| p<sub>s</sub>+q<sub>s</sub> or p<sub>a</sub>+q<sub>a</sub>
! center| p<sub>s</sub>+q<sub>a</sub> or p<sub>a</sub>+q<sub>s</sub>
|+ Table 2. Woodward-Hoffman Rule <ref>Semis, K. L., & Rules, B. W. (1965). Woodward-Hoff mann Rules : Electrocyclic Reactions.</ref>
|}

In this reaction, butadiene has 4 π-electrons and ethylene contains 2 π-electrons. The sum of p and q is 6 and they are all suprafacial. Hence, this [4+2] cycloaddition is {{fontcolor1|blue|'''thermally allowed'''}}.

*overlap integral
<center><math>S=\int\psi\psi^*\,d\tau</math></center>
<center><small>Equation 8. Calculation of overlap integral</small></center>

The overlap integral is calculated by equation 8 and it is telling how well two orbitals are overlapped. The value of overlap integral is between 0 and 1. 0 means that the two orbitals do not have any overlap and 1 means that they perfectly overlap with each other. Table 3 is used to determine whether the wavefunction is symmetric or antisymmetric.

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white; text-align: center;"| Symmetric
! center; style="background: #0D4F8B; color: white; text-align: center;" | Antisymmetric
|-
! center;|ψ(r<sub>1</sub>,r<sub>2</sub>)={{fontcolor1|red|'''+'''}}ψ(r<sub>2</sub>,r<sub>1</sub>)
! center;|ψ(r<sub>1</sub>,r<sub>2</sub>)={{fontcolor1|red|'''-'''}}ψ(r<sub>2</sub>,r<sub>1</sub>)
|+Table 3. Symmetric and Antisymetric wavefunction
|}

For two wavefunctions, the overlap integral will be 0 if the product of two wavefunctions is antisymmetric. If the product of two wavefunctions is symmetric, the overlap integral will be 1. Only when '''both of the wavefunctions are antisymmetric''' or '''both are antisymmetric''', the overlap integral will be 1. As shown in MO diagram, the antisymmetric orbital will overlap with the antisymmetric orbital.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Your MO diagram is very nice, but there is some confusion in the discussion of symmetry and orbital overlap. The orbital overlap will only be 1 in case the two functions are exactly the same.)
===Analysis of bond lengths===
{| class="wikitable" style="margin: auto;"
|center; | [[file:MG5715_TS_E1_IRC_DISTANCE.jpg|thumb|none|500px|x500px|center|Fig.7 Disatance VS reaction coordination]]
|center; | [[file:MG5715_TS_E1_LABEL.PNG|thumb|none|500px|x500px|center|Fig.8 Labelled molecule]]
|+ Table 4. IRC bond distance analysis
|}

In Fig.7, it shows that the distances between C atoms change with reaction coordination. and Fig.8 shows the labelled molecule. Initially, the distance between C<sub>14</sub> and C<sub>1</sub> and distance between C<sub>7</sub> and C<sub>11</sub> are around 3.4 Å, which indicates there does not have any bond between those two atoms. The Van der Waal radius of C atom is 1.77Å <ref>Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials Translated from Neorganicheskie Materialy Original Russian Text, 37(9), 871–885. http://doi.org/10.1023/A:1011625728803</ref> 3.4 Å is smaller than twice of Van der Waals radius of C; therefore, C<sub>14</sub> is interacting with C<sub>1</sub> and a bond will be formed between them.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You should have focused your discussion on the length of the bonds at the transition state specifically.)

{| class="wikitable" style="margin: auto;"
|
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>3</sup>)-C(sp<sup>3</sup>)
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>3</sup>)-C(sp<sup>2</sup>)
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>2</sup>)-C(sp<sup>2</sup>)
|-
! center;| Bond length/Å
! center| 1.542
! center| 1.488
! center| 1.459
|+ Table 4. Bond length of C-C bond<ref>Bernstein, H. J. (1961). BOND DISTANCES IN HYDROCARBONS * t. Retrieved from http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649</ref>
|}

Table 4. shows the literature value of C-C bond length with different hybridisation and comparing those with the Fig 7. It suggests C<sub>1</sub>, C<sub>7</sub>,C<sub>11</sub> and C<sub>14</sub> change from sp<sup>2</sup> to sp<sup>3</sup>; C<sub>4</sub> and C<sub>6</sub> remain sp<sup>2</sup>. Besides that, this table also confirms the product is hexene. The distance between C<sub>4</sub> and C<sub>6</sub> is 1.338 Å, which is similar to the bond lenght of C(sp<sup>2</sup>)-C(sp<sup>2</sup>). The rest of bond lengths are around 1.5 Å; so the rest of bonds are C(sp<sup>3</sup>)-C(sp<sup>3</sup>).

===Vibration===
{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Transition State vibration
! center; style="background: #0D4F8B; color: white;" | Inrinsic Reaction Coordinate(IRC)

|-
| center;| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 23; vibration 1;rotate x -20; </script>
<uploadedFileContents>MG5715_TS_E1_TS_VIB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| [[file:MG5715_TS_E1_IRC.gif‎]]

|-
| center;| [[file:MG5715_TS_E1_VF.PNG|thumb|none|500px|x500px|center|Fig 9. Vibration Frequencies of Transition State]]
| [[file:MG5715_TS_E1_IRC_PATH.PNG|thumb|none|500px|x500px|center|Fig 10. summary of IRC plot ]]

|}

As shown in Fig.9, there is only one imaginary frequency (at -948.8 cm<sup>-1</sup>); so it justifies the transition state is right. However, it is not enough for determining the transition state. It is critical to do the IRC calculation. RMS Gradient should be zero in reactants, products and also transition state because they are local minima. However, for transition state, it is saddle point; hence, the second derivative should be negative.

According to the gif shown above, it shows that bonds are formed '''synchronously'''.

===LOG File===
Transition state:[[File:MG5715_TS_E1_TS_MO.LOG]]

Butadiene:[[File:MG5715_TS_E1_BUTADIENE_MO.LOG]]

Ethylene:[[File:MG5715_TS_E1_ETHLYENE_MO.LOG]]

==Excercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

[[File:MG5715_TS_E2_REACTION.jpg|thumb|550px|center|Fig.11 The reaction scheme of Cyclohexadiene and 1,3-Dioxole]]

The reaction of cyclohexadiene and 1,3-Dioxole is also a Diels-Alder reaction, but this reaction will give two products (endo and exo) because of two possible transition states. The reaction scheme is shown in Fig.11 In this exercise, the transition state is opitimised by {{fontcolor1|blue|'''PM6'''}} firstly and then optimised again by {{fontcolor1|blue|'''B3LYP'''}}. Moreover, the transition state is determined by {{fontcolor1|blue|'''method 3'''}} in this exercise.

=== MO analysis of exercise 2===

[[File:MG5715_TS_E2_MO.jpg|thumb|550px|center|Fig.12 MO diagram of Cyclohexadiene and 1,3-Dioxole]]

The MO diagram of this reaction is displayed in Fig.12The energies of product's MO is shown in '''black''' lines and the {{fontcolor1|#fe7af9|'''pink'''}} lines represent the energies of transition states' MO, and all of them are drawn based on the relative energies calculated by '''B3LYP'''. Furthermore, the HOMO and LUMO of reactants are shown in Table 5. and the MOs of transition states are displayed in Table 6.

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white; text-align: center;"| HOMO
! style="background: #0D4F8B; color: white; text-align: center;" | LUMO

|-
| Clycohexadiene

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| 1,3-dioxole
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ Table 5. LUMO and HOMO of reactants
|}

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white; text-align: center;"| ENDO TS
! style="background: #0D4F8B; color: white; text-align: center;" | EXO TS

|-
| LUMO+1
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| HOMO-1
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|+ Table 6. MO of Transition states
|}

====Secondary Orbital Interactions ====
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Endo-TS
! style="background: #0D4F8B; color: white;" | Exo-TS
|-
| Jmol of computed HOMO

|<jmol>
<jmolApplet>
<color>white</color>
<size>225</size>
<script> frame 48; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>225</size>
<script> frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| LCAO diagram of HOMO

| [[File:MG5715_TS_E2_ENDO_TS.jpg|thumb|550px|center]]

| [[File:MG5715_TS_E2_EXO_TS.jpg|thumb|550px|center]]
|+ Table 7. HOMO of Endo-TS and Exo- TS
|}

The computed HOMO and LACO diagram of HOMO are shown in Table 7. Endo-product is more stable than Exo-product due to lack of steric clash with the methyl group in cyclohexadiene. Furthermore, the Endo-TS is lower in energy because of '''Secondary Orbital Interaction'''. The lone pair of oxygen could donate the electron density to the LUMO of cyclohexadiene; hence, the Endo-TS will be stabilised. Both the Endo-TS and Endo-product are lower in energy; so this reaction is endo-selective.

==== Inverse VS Normal Demand Diels-Alder Reaction ====

[[File:MG5715_TS_E2_DA.jpg|thumb|550px|center|Fig.13 two tyes of Diels-Alder reaction]]

For a Diels-Alder reaction, the reactivity is controlled by relative energies of '''Frontier Molecular Orbitals (FMOs)'''. There are two different types as shown in Fig.13:(1) Normal demand and (2) Inverse demand. Usually, the reaction of an all carbon diene with a hetero-dienophile will give a ''normal electron demand'' because the heteroatom in dienophile may withdraw the electron density from dienophile and lower the energy of MOs. The best way to justify whether the reaction is normal demand or inverse demand is to sequence the energy of reactants as shown in Table 8. If the HOMO of dienophile is lower than that of diene, it is normal demand, vice versa. The HOMO of cyclohexadiene is the lowest; hence, this reaction is {{fontcolor1|blue|'''inverse demand'''}} Diels-Alder reaction. The reason is that the two oxygen atom in 1,3-dioxole donate the electron density toward the π-bonding and raise the energy of MOs.

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo-reaction
! style="background: #0D4F8B; color: white;" | Exo-reaction

|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|+ Table 8. Single point energy of reactants
|}

=== Activation Barrier and Energy changed ===
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Energy calculated by B3LYP/kJmol<sup>-1</sup>
|-
! center| Cylcohexadiene
! center| 306.9
! center| -612593

|-
! center| 1,3-dioxole
! center| -137.3
! center| -701189

|-
! center| Endo-product
! center| 99.2
! center| -1313849

|-
! center| Endo-TS
! center| 362.2
! center| -1313622

|-
! center| Exo-product
! center| 99.7
! center| -1313845

|-
! center| Exo-TS
! center| 364.7
! center| -1313614
|+ Table 9. Energies of reactants, products and transition states
|}

According to the energies of reactants, products and transition states (shown in Table 9), the reaction energy and activation energy could be calculated by the following equation:
<pre>
Activation Energy = Transition state energy - Sum of energies of reactants
Reaction Energy = product energy - Sum of energies of reactants
</pre>

{| class="wikitable" style="margin: auto;"
! rowspan="2"|
! style="background: #0D4F8B; color: white;" colspan="2"| Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" colspan="2"| Reaction Energy/kJmol<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
|-
! center| Endo-reaction
! center| +192.6
! center| +159.8
! center| -70.3
! center| -67.4
|-
! center| Exo-reaction
! center| +195.1
! center| +169.7
! center| -69.9
! center| -63.8
|+ Table 10. Reaction energy and activation energy for both Endo and Exo product.
|}

All the energy calculated is shown in Table 10. Both the activation energy and reaction energy for Endo-product are lower than those for Exo-product. A thermodynamically favourable product is more stable, which means it has more negative reaction energy. The kinetically favourable product has lower reaction barrier (activation energy). Hence, the endo-product of this exercise is both '''thermodynamically and kinetically favourable'''.

===LOG File===
1,3-Dioxole:[[File:MG5715_TS_E2_REACTANTS_2.LOG]]

Cyclohexadiene:[[File:MG5715_TS_E2_REACTANTS_1.LOG]]

Exo-Transition State:[[File:MG5715_TS_E2_EXO.LOG]]

Endo-Transition State:[[File:MG5715_TS_E2_ENDO.LOG]]

==Excercise 3 Diels-Alder vs Cheletropic==

[[File:MG5715_TS_E3_REACTION.jpg|thumb|550px|center|Fig.14 Reaction Scheme of o-Xylylene with SO<sub>2</sub>]]

The reaction of o-xylylene with SO<sub>2</sub> could be either Diels-Alder or cheletropic reaction. For Diels-Alder reaction, o-Xylylene acts as diene and SO<sub>2</sub> acts as dienophile to form a six-membered ring and there are two possible products (endo-product and exo-product). As discussed in exercise 2, the Diels-Alder is endo-selective. For the cheletropic reaction, a five-membered ring will be formed and two new bonds are formed with the same atom. The reaction scheme of those reactions is displayed in Fig.14. In this exercise, the reactants, products and transition states were optimised by {{fontcolor1|blue|'''PM6'''}} and {{fontcolor1|blue|'''B3LYP'''}} and {{fontcolor1|blue|'''Method 3'''}} was used to find the transition state. The reaction energy and activation energy were calculated to find out the favourable reaction.

(Endo is only kinetically preferred out of the DA reactions [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== IRC Analysis===
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | IRC
|-
| Cheletropic reaction
| [[File:MG5715_TS_E3_Cheletropic_IRC.gif]]
|-
| Endo Diels-Alder reaction
| [[File:MG5715_TS_E2_ENDO_irc.gif]]
|-
| Exo Diels-Alder reaction
| [[File:MG5715_TS_E3_EXO_irc.gif]]
|+ Table.11 The IRC of three possible reactions
|}

There are two different mechanisms for Diels-Alder reaction:(1)synchronous and symmetrical (concerted) mechanism and (2) multistage (non-concerted) and asynchronous mechanism.

* synchronous and symmetrical (concerted) mechanism
A very typical example of this mechanism is Exercise 1. The two new bonds are formed simultaneously and the two new bonds have the same bond length in the transition state.

* multistage (non-concerted) and asynchronous mechanism
The two bonds could not be formed at the same time because the bond length of them are different at transition state. Therefore, usually, a di-radical will be formed.

For Diels-Alder reaction, the distance between O and C in o-Xylylene is different from the distance between S and C in o-Xylylene at transition state because of distinct Van der Waal radii.
Therefore, the bond does not form synchronously, which could be observed in the IRC in Table 11. However, for cheletropic reaction, the two now bonds are both formed between S atom and C in o-Xylylene; so the two bond are formed synchronously as shown in IRC.

(Be careful: it looks like you're saying the DA reactions are multistage, which involves an intermediate (all positive eigenvalues in Hessian/positive frequencies) [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== Activation Energy and Reaction Energy===
[[File:MG5715_TS_E3_ENERGY.jpg|thumb|550px|center|Fig.15 Energy diagram of o-Xylylene with SO<sub>2</sub>]]

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Energy calculated by B3LYP/kJmol<sup>-1</sup>
|-
! center| O-Xylylene
! center| 469.5
! center| -812604

|-
! center| SO<sub>2</sub>
! center| -311.4
! center| -1440362

|-
! center| Endo-product
! center| 57.0
! center| -2253040

|-
! center| Endo-TS
! center| 237.8
! center| -2252919.7

|-
! center| Exo-product
! center| 56.3
! center| -2253041

|-
! center| Exo-TS
! center| 241.7
! center| -2252919.8

|-
! center| Cheletropic product
! center| -0.005251
! center| -2253024

|-
! center| Cheletropic TS
! center| 260.1
! center| -2252902
|+ Table 12. Energies of reactants, products and transition states
|}

{| class="wikitable" style="margin: auto;"
! rowspan="2"|
! style="background: #0D4F8B; color: white;" colspan="2"| Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" colspan="2"| Reaction Energy/kJmol<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
|-
! center| Endo-reaction
! center| +79.7
! center| +46.2
! center| -101.1
! center| -73.9
|-
! center| Exo-reaction
! center| +83.7
! center| +46.1
! center| -101.8
! center| -73.2
|-
| Cheletropic
! center| +102.0
! center| +63.0
! center| -158.1
! center| -58.8
|+ Table 13. Reaction energy and activation energy for both Endo and Exo product.
|}

The energies of reactants, products and transition states are shown in Table 12 and the calculated reaction energy and activation energy are displayed in Table 13. The energy diagram (Fig.15) is drawn according to the energy calculated by PM6. The product of the cheletropic reaction is the most stable because of aromaticity. However, the activation energy of cheletropic product is quite high. Therefore, at low temperature, a sultine (kinetic product) will be formed but this reaction is reversible. At high temperature, a sulfolene will be formed and this reaction is irreversible.

(Well done doing the B3LYP calculations, but it must have taken a long time. The results are distinctly different to the PM6 calculations, so you could have commented on that [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== Extension===
[[File:MG5715_TS_E3_EXTENSION_SCHEME.jpg|thumb|550px|center|Fig.16 Reaction Scheme of o-Xylylene with SO<sub>2</sub>]]
There are two dienes in o-Xylylene and therefore, it has another possible Diels-Alder reaction as shown in Fig.16. The energy calculated is displayed in Table 14 and they are calculated by PM6.

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
|-
! center| O-Xylylene
! center| 469.5

|-
! center| SO<sub>2</sub>
! center| -311.4

|-
! center| Endo-product
! center| 172.3

|-
! center| Endo-TS
! center| 268.0

|-
! center| Exo-product
! center| 176.7

|-
! center| Exo-TS
! center| 275.8
|+ Table 14. Energy of reactants, products, and transition states
|}

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Reaction Energy/kJmol<sup>-1</sup>
|-
! center| Endo-reaction
! center| +109.9
! center| +14.2

|-
! center| Exo-reaction
! center| +117.7
! center| +18.6

|+ Table 15. Reaction energy and activation energy for both Endo and Exo product.
|}

Compare the energy in Table.15 with the data in Table.13, this reaction is quite unlikely to happen because the activation barrier is higher and the reaction energy is endothermic.

===LOG File===
o-Xylylene:[[File:MG5715_REACTANT_PM6.LOG]]

SO<sub>2</sub>:[[File:MG5715_SO2_PM6.LOG]]

Exo-Transition state:[[File:MG5715_EXO_TS_PM6.LOG]]

Endo-Transition state:[[File:MG5715_ENDO_TS_PM6.LOG]]

Cheletropic Transition state:[[File:MG5715_CHE_TS_PM6.LOG]]

==Conclusion==
In conclusion, Gauss View is a quite efficient way to locate the transition state and to calculate the energy of a reaction. Hence, it could suggest which product is thermodynamically favourable and which one is kinetically favourable. Besides that, it could mimic the reaction pathway by IRC, which can tell us whether the bonds are formed synchronously or not. One of the best way to confirm the transition state is to check the vibration frequency of transition state. For a transition state, it will always have only one imaginary frequency. According to this experiment, it suggests Diels-Alder reaction is endo-selective because of secondary orbital interaction and if the two bonds are formed with same atoms, they will form synchronously.

==Reference==

Rep:XP715TS

2018-03-27T15:41:23Z

Fv611: /* MO Analysis */

='''Transition states and reactivity'''=

==Introduction==

For a potential energy curve with only one variable, the curve is considered to be the energy profile. If more than one geometric coordinates associate with potential energy, the three-dimensional surface is called '''potential energy surface'''. For a nonlinear molecule, there is 3N-6 independent geometric variables.
The transition state is the maximum point on the surface, connecting two minima, reactant and product. These stationary points (transition state, reactant and product) are defined as zero first derivative (<math>\frac{\partial E}{\partial R}</math>= 0), showing that the gradient is zero.

{|class=wikitable
|-
|<math>\frac{\partial E}{\partial R}=-F</math>
|-
|Equation.1, first derivative
|}

The gradient is related to force acts on the atoms, and the negative sign indicates the force is in the direction of lowering potential energy.
In order to distinguish them, curvatures (frequencies) at these points are determined by second derivative.

{|class=wikitable
|-
|<math>\dfrac{\partial ^2 E}{\partial R^2} =k</math>
|-
|Equation.2, second derivative
|}
[[File:XP715 Eqn ferq.PNG|thumb|center|300px|Equation.3, frequency calculation <ref>J. McDouall, Computational Quantum Chemistry: Molecular Structure and Properties in Silico, Royal Society of Chemistry, Cambridge, 2013, ch.1, pp.1-62</ref>]]

Second derivatives are hold in the Hessian matrix, and by diagonalizing the Hessian matrix, force constant k can be determined as well as the frequency by Eqn.3.
The saddle point (transition state) has negative curvature (<math>\dfrac{\partial ^2 E}{\partial R^2} < 0</math>), while the minima have positive curvature (<math>\dfrac{\partial ^2 E}{\partial R^2} > 0</math>).

Energy, electronic structure and properties of molecules can be determined by solving Schrödinger’s equation. The computational method is used to solve the equation by deciding to use different level of theory (Hamiltonian operator) and basis set (mathematical description of wavefunction). In this page, two optimisation methods were adopted, PM6 and B3LYP/6-31G(d). For PM6, it is a semi-empirical method, which is based on Hartree-Fock theory. <ref>C.A. Coulson, B.O’Leary, R.B. Mallion, Hückel theory for organic chemists, Academic Press, London, New York, 1978</ref> It solves the many-electron equation by expanding the coefficient of linear combination of atomic orbitals (LCAO) and simplifies with Born–Oppenheimer approximation. The full HF calculation is too expensive, therefore PM6 is simplified by neglecting two-electron part of Hamiltonian, and further simplification can be applied for π-electron system by Hückel method. It is overall a quick but not reliable method. B3LYP/6-31G(d) is based on density functional theory (DFT), which associates with HF theory and an additional term, exchange-correlation energy.<ref>K. Kim and K. D. Jordan, J. Phys. Chem., 1994, 98, 10089–10094.</ref> B3LYP is the choice of exchange-correlation energy and 6-31G is the basis set. DFT is sufficient accurate but it is an expensive method.

In this page, Gaussian, the computational method, is used to interpret the mechanisms of four pericyclic reactions. This technique is able to identify whether the bond formation is synchronous or asynchronous, formation of kinetic or thermodynamic product and whether the proposed reaction pathway is favourable.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 23:43, 22 March 2018 (UTC) You have clearly read beyond the script here well done. Some equations would have been good. When you diagonalise the hessian your are changing your coordinate basis into the noraml modes. which are then linear combinations of the degrees of freedom.

==Exercise 1: Reaction of Butadiene with Ethylene==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Overall you have done a good job. However you have used your B3LYP optimisation of ethene instead of the PM6 one, which led you to the wrong MO energies.)

[[File:XP715_Scheme_EX1.PNG|thumb|center|500px|Scheme.1, reaction scheme of butadiene and ethylene with annotated bond length]]

The first reaction is the classical [4+2] cycloadditon (Scheme.1), which is also called Diels-Alder reaction. This reaction was investigated by guessing the transition state first and finding the optimised product. Both reactants and TS were optimised at PM6 level, and a frequency calculation and Intrinsic Reaction Coordinate (IRC) were analysed to ensure that a correct TS was obtained. Finally, the product was optimised at PM6 level.

===Optimisation and Calculation===

{| class="wikitable"
| colspan="4" style="text-align: center; background: #3b5998; color: white" | '''Optimised structures of reactants, TS and product at PM6 level'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38 ; </script>
<uploadedFileContents>XP715_DIENE_MINPM6_NEW.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; </script>
<uploadedFileContents>XP715_ETHENE_MINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; </script>
<uploadedFileContents>XP715 2MOL TSPM6 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 42; </script>
<uploadedFileContents>XP715_PROD_MINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene
| Ethene
| TS
| Product
|}

{| class="wikitable"
|[[File:XP715 TS PM6 freq.PNG|thumb|left|700px|Figure.1, Frequency calculation of TS]]
|[[File:XP715 EX1 IRC.png|thumb|center|500px|Figure.2, IRC (total energy and RMS gradient) of TS]]
|}
Fig. 1 shows that only one frequency is negative, indicating the transition state. IRC is the minimum energy pathway on the potential energy surface, starting from the first-derivative stationary point, TS, and calculating in both direction until reaching two minima, reactants and products. Fig. 2 illustrates the total energy and RMS gradient along IRC, and the gradients of reactants, products and TS are all zero, confirming a successful and asymmetric IRC was performed.

=== MO Analysis===
{| class="wikitable"
| colspan="4" style="text-align: center; background: #3b5998; color: white" | '''HOMO and LUMO of reactants and HOMO/-1, LUMO/+1 of transition states'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_DIENE_MINPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_DIENE_MINPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; mo 8; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_ETHENE_MINPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; mo 9; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_ETHENE_MINPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene (HOMO)
| Butadiene (LUMO)
| Ethene (HOMO)
| Ethene (LUMO)
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS (HOMO-1)
| TS (HOMO)
| TS (LUMO)
| TS (LUMO+1)
|}

By visualising MO of reactants and TS, part of the MO was constructed in Fig.3 (MO). The calculated orbital energies at PM6 level are labelled in grey, however, due to the low optimisation level, these energies are only a rough guide to the MO diagram. Although the energies are not accurate, it still provides an evidence of mixing. The dotted orbitals are the MOs without mixing, while the solid-line orbitals are the ones with predicted mixing.
[[File:XP715_MO.PNG|thumb|center|800px|Figure.3, MO diagram]]
[[File:XP715 MO sym.PNG|thumb|center|500px|Figure.4, symmetry label for HOMO and LUMO of diene]]
[[File:XP715 Eqn orbital.PNG|thumb|center|500px|Equation.4, orbital overlap integral]]

The symmetry of each orbital can be identified with its symmetry axis or plane. The HOMO of butadiene is antisymmetric as it has C2 symmetry, while the LUMO is symmetric as it contains σ(v) symmetry plane. (Fig.4) Only the orbitals with same symmetry could combine to form new MOs. The orbital overlap integral is represented by Eqn.4<ref>P. W. Atkins and J. De Paula, Physical Chemistry, 2009.</ref>, and it is zero when the overall interaction is antisymmetric. The symmetric-antisymmetric interaction is '''antisymmetric''', integrating to '''zero''' (forbidden reaction). The symmetric-symmetric and antisymmetric-antisymmetric interaction are '''symmetric''', resulting to '''non-zero''' integral (allowed reaction).
The Woodward-Hoffmann rules states that in a thermally allowed reaction, the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd, where the suffix s stands for suprafacial (forming bond on same face), and a for antarafacial (forming bond on opposite face).
By applying Woodward-Hoffmann rules, this reaction is proved to be '''thermally allowed'''.
<pre>(4q+2)s+(4r)a
=1+0
=1
=thermally allowed reaction
</pre>

===Bond Length Analysis===
{| class="wikitable"
|+ Table 1. Bond length of reactants, transition states and product
''(refer to Scheme.1)''
|-
| style="background: #c8d9ec; color: black;" | '''Structure'''
| style="background: #c8d9ec; color: black;" | '''sp<sup>3</sup>-sp<sup>3</sup> C-C /Å'''
| style="background: #c8d9ec; color: black;" | '''sp<sup>3</sup>-sp<sup>2</sup> C-C /Å'''
| style="background: #c8d9ec; color: black;" | '''sp<sup>2</sup>-sp<sup>2</sup> C=C /Å'''
| style="background: #c8d9ec; color: black;" | '''sp<sup>2</sup>-sp<sup>2</sup> C-C /Å'''
|-
|Butadiene
|n/a
|n/a
|1.34, 1.34
|1.47
|-
| Ethene
| n/a
| n/a
| 1.33
| n/a
|-
| TS
| 2.11, 2.11 (forming single bond)
| n/a
| 1.38, 1.38 (partially double bond);
1.38 (partially double bond)
|1.41 (partially double bond)
|-
|Product
|1.54, 1.54
|1.50, 1.50
|1.34
|n/a
|-
|Typical value
| 1.54
|1.50
|1.34
|1.47
|}

{| class="wikitable"
|+ Table 2. Van der Waals radius of Carbon
| colspan="4" style="text-align: center; background: #3b5998; color: white" |''' Van der Waals radius of Carbon'''
|-
|One carbon atom /Å
|1.70
|Two carbon atoms /Å
|3.40
|}
Comparing the bond length of reactants and TS, the reactants show typical bond length of sp<sup>2</sup>-sp<sup>2</sup> C=C, sp<sup>3</sup>-sp<sup>2</sup> C-C and sp<sup>2</sup>-sp<sup>2</sup> C=C. In the TS, C10-C12 is shortened due the change from sp<sup>3</sup>-sp<sup>3</sup> single bond to sp<sup>2</sup>-sp<sup>2</sup> double bond, while C7-C10 and C12-14 show an elongation because sp<sup>2</sup>-sp<sup>2</sup> double bonds are changed into sp<sup>2</sup>-sp<sup>3</sup> single bonds. C1-C4 becomes longer as it converts from sp<sup>2</sup>-sp<sup>2</sup> double bond to sp<sup>3</sup>-sp<sup>3</sup> single bond. The distance between C4 and C7/ C1 and C14 is both 2.11 Å, which is shorter than sum of Van der Waals radius of two carbon atoms (Table.2), indicating that two molecules are approaching to each other and forming a partial bond. The product shows typical sp<sup>3</sup>-sp<sup>3</sup> C-C, sp<sup>2</sup>-sp<sup>3</sup> C-C and sp<sup>2</sup>-sp<sup>2</sup> C=C bond length.

{| class="wikitable"
| [[File:XP715 EX1 Bond length.png|thumb|center|1000px|a]]
| [[File:XP715 EX1 Prod label.jpg|thumb|center|300px|b]]
|-
| colspan="2" | Figure.5, a) The change of bond length with respect to reaction coordinate. b) Numbering of atoms of the product
|}
Fig.5 illustrated the change of bond length along the reaction coordinate by analysing IRCs of each bond. C1-C4 (purple) and C4-C7 (black) starts from 3.40 Å, where no bond is formed, and then reaching TS at 2.11 Å. The product is formed when the bond length is at 1.54 Å. The rest of the bonds corresponds to the explanation in the previous section.

===Vibration===
{| class="wikitable"
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 7; vibration 2</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
![[File:XP715 EX1 TS formbond.gif|thumb|center|500px|Figure.6, Video of forming and breaking bonds]]
|}
By visualising the vibration of TS and motion picture of Fig.6, the formation of two bonds are '''synchronous'''.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

[[File:XP715 Scheme ex2.JPG|thumb|center|500px|Scheme.2, reaction schemes of Cyclohexadiene and 1,3-Dioxole to form endo and exo products.]]

This Diels-Alder reaction is stereospecific, leading to endo and exo adducts. The more favourable reaction pathway is examined by the calculating activation energy and free energy. Reactants, TS and products were optimised first with PM6 following by using B3LYP/6-31G(d).

===Optimisation and Calculation===
{| class="wikitable"
| colspan="3" style="text-align: center; background: #3b5998; color: white" | '''Optimisation of reactants, TS and products'''
|-
|Cyclohexadiene
|1,3-Dioxole
|Endo TS
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>XP715 DIENE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>XP715 DIOXOLE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|[[File:XP715 Diene freq.PNG|thumb|center|500px]]
|[[File:XP715 Dioxole freq.PNG|thumb|center|500px]]
|[[File:XP715 ENDO TS 631G freq.PNG|thumb|center|500px]]
|-
|Exo TS
|Endo Product
|Exo Product
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>XP715 Endo prod 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8</script>
<uploadedFileContents>XP715 EXO 631G jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|[[File:XP715 EXO TS 631G freq.PNG|thumb|center|500px]]
|[[File:XP715_ENDO_prod_freq.PNG|thumb|center|500px]]
|[[File:XP715_EXO_prod_freq.PNG|thumb|center|500px]]
|}
There is no imaginary frequency for all the reactants and products, and there is only one negative frequency for each TS, confirming that all of them were well optimised.

===MO Analysis===
{| class="wikitable"
| colspan="4" style="text-align: center; background: #3b5998; color: white" | '''HOMO and LUMO of reactants and HOMO/-1, LUMO/+1 of ENDO/EXO transition states'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 DIENE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 DIENE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 DIOXOLE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 DIOXOLE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Cyclohexadiene (HOMO)
| Cyclohexadiene (LUMO)
| 1,3-Dioxole (HOMO)
| 1,3-Dioxole (LUMO)
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO TS (HOMO-1)
| ENDO TS (HOMO)
| ENDO TS (LUMO)
| ENDO TS (LUMO+1)
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| EXO TS (HOMO-1)
| EXO TS (HOMO)
| EXO TS (LUMO)
| EXO TS (LUMO+1)
|}

{| class="wikitable"
| colspan="2" style="text-align: center; background: #3b5998; color: white" | '''MOs of reactants and transition states'''
|-
|[[File:XP715_Endo_MO.png|thumb|center|700px|Figure.7, MO diagram of Endo TS]]
|[[File:XP715Exo MO.png|thumb|center|700px|Figure.8, MO diagram of Exo TS]]
|}
By visualising MOs of reactants and TSs, the MO diagrams of endo and exo TSs were constructed. The calculated orbital energies (in grey) gave a rough guide to the energy difference between orbitals. The orbital energies of HOMO/HOMO-1 and LUMO/LUMO+1 of two TSs are similar, but the actual shapes shown in jmol are different (in later section). The HOMO of endo TS is slightly more stabilised than that of exo TS.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good MO diagrams. Could have discussed more the differences between exo and endo conformations in terms of relative MO energies.)

====Inverse Demand DA Reaction====
For a standard DA reaction, the electron rich component is diene and the electron poor component is dienophile. The HOMO of diene and the LUMO of dienophile are similar in energy and interact strongly. However, for a DA reaction with inverse electron demand, the electron rich component is dienophile and the electron poor component is diene.<ref>A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236</ref> Then the more strongly interacting frontier orbitals are the HOMO of dienophile and the LUMO of diene. In this reaction, the dienophile is 1,3-dioxole, and the electron donation from lone pair of oxygen atoms results in more electron rich dienophile. The single point energy calculation confirms this suggestion.

{| class="wikitable"
|+ Table.3, Single point energy of HOMO/LUMO of reactants
|-
| style="background: #c8d9ec; color: black;" | '''Molecule'''
| style="background: #c8d9ec; color: black;" | '''Energy of HOMO/a.u.'''
| style="background: #c8d9ec; color: black;" | '''Energy of LUMO/a.u.'''
| style="background: #c8d9ec; color: black;" | '''Difference of LUMO<sub>diene</sub> and HOMO<sub>dienophile</sub>'''
| style="background: #c8d9ec; color: black;" | '''Difference of HOMO<sub>diene</sub> and LUMO<sub>dienophile</sub>'''
|-
|Cyclohexadiene
|style="text-align: center;"| -0.20601
|style="text-align: center;"|-0.01800
|rowspan="2" style="text-align: center;"| 0.17815
|rowspan="2" style="text-align: center;"| 0.24265
|-
|1,3-Dioxole
|style="text-align: center;"|-0.19615
|style="text-align: center;"| 0.03664
|}

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 23:49, 22 March 2018 (UTC) Nice this is well done and clear.

===Energy Analysis===

{| class="wikitable"
|+ Table.4, Gibbs free energies of reactants, TSs and products using B3LYP/6-31G(d)
|-
| style="background: #c8d9ec; color: black;" | '''Molecule'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/Hartrees'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/kJmol<sup>-1</sup>'''
|-
|Cyclohexadiene
|style="text-align: center;" |-233.324375
|style="text-align: center;" |-612593.193227
|-
|1,3-Dioxole
|style="text-align: center;" |-267.068644
|style="text-align: center;" |-701188.778236
|-
|Reactants (total)
|style="text-align: center;" |-500.393019
|style="text-align: center;" |-1313781.971463
|-
|Endo TS
|style="text-align: center;" |-500.332149
|style="text-align: center;" |-1313622.15727
|-
|Exo TS
|style="text-align: center;" |-500.329163
|style="text-align: center;" |-1313614.31752
|-
|Endo Product
|style="text-align: center;" |-500.418694
|style="text-align: center;" |-1313849.381181
|-
|Exo Product
|style="text-align: center;" |-500.417319
|style="text-align: center;" |-1313845.77112
|}

{| class="wikitable"
|+ Table.5, Activation energies and ΔG of two reactions using B3LYP/6-31G(d)
|-
| style="background: #c8d9ec; color: black;" | '''State'''
| style="background: #c8d9ec; color: black;" | '''Activation energy /kJmol<sup>-1</sup>'''
| style="background: #c8d9ec; color: black;" | '''ΔG /kJmol<sup>-1</sup>'''
|-
|Endo
|style="text-align: center;" |159.8
|style="text-align: center;" |-67.4
|-
|Exo
|style="text-align: center;" |167.7
|style="text-align: center;" |-63.8
|}

The kinetic product is the one with lower activation energy, leading to faster reaction, and the thermodynamic product is the one with more negative ΔG, which forms more stable product. The calculation of energies in Table.5 illustrates that the endo product has lower activation energy and more negative ΔG, indicating that '''endo product''' is the '''kinetic''' product as well as '''thermodynamic''' product

{| class="wikitable"
| colspan="3" style="text-align: center; background: #3b5998; color: white" | '''HOMOs of endo and exo TSs'''
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
![[File:XP715 Secondary interaction.PNG]]
|-
|Endo TS
|Exo TS
|Figure.9, graphic illustration of primary/secondary interactions of HOMOs.
|}

There is only primary interaction in exo TS, while the secondary interaction is also observed in endo TS. The secondary interaction stabilises the endo TS (Fig.9), resulting in faster formation of endo TS and confirming that the endo product is more kinetically favourable.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 23:53, 22 March 2018 (UTC) Good section, you could have gone into more detail about the thermo and kenetic theory. But otherwise a very good section.

==Exercise 3: Diels-Alder vs Cheletropic==

[[File:XP715 Scheme ex3.JPG|thumb|center|700px|Scheme.3, reaction schemes between Xylylene and SO<sub>2</sub> through Diels-Alder reaction and Cheletropic reaction]]

For this reaction, three products were examined, including endo and exo products of DA reactions and cheletropic product. Energy calculations were carried out to identify the most favourable reaction pathway. All the reaction species were optimised at PM6 level. The extension investigated the possibility of DA reaction of a second cis-butadiene in o-xylylene. The activation energies and Gibbs free energies were calculated to suggest the viability of the reactions.

===Optimisation and Calculation===
{| class="wikitable"
| colspan="3" style="text-align: center; background: #3b5998; color: white" | '''Optimisation of three TSs'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715 M3 MOL1 SPLIT TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715 DA ENDO SPLIT TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715_CHE_SPLIT_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|DA-Exo
|DA-Endo
|Cheletropic
|-
|[[File:XP715 DA ENDO freq.PNG|thumb|center|500px]]
|[[File:XP715_DA_EXO_freq.PNG|thumb|center|500px]]
|[[File:XP715_CHE_freq.PNG|thumb|center|500px]]
|}

{| class="wikitable"
| colspan="3" style="text-align: center; background: #3b5998; color: white" | '''IRC of three TSs'''
|-
|DA-Endo TS
|[[File:XP715_DA_ENDO_TS_IRC.png|thumb|center|900px]]
|[[File:XP715 DA ENDO TS.gif|thumb|center|500px]]
|-
|DA-Exo TS
|[[File:XP715_DA_EXO_TS_IRC.png|thumb|center|900px]]
|[[File:XP715_DA_EXO_TS.gif|thumb|center|500px]]
|-
|Cheletropic TS
|[[File:XP715_Che_TS_IRC.png|thumb|center|900px]]
|[[File:XP715_CHE_TS.gif|thumb|center|500px]]
|-
|colspan="3"|Figure.10, IRCs of three TSs
|}

All IRCs were successful asymmetric graphs. The endo and exo DA TS starts from product to reactant and the cheletropic TS starts from reactant to product. The approach trajectories are shown as motion pictures on the right.

===Energy Analysis===

{| class="wikitable"
|+ Table.6, Gibbs free energies of reactants, TSs and products at PM6
|-
| style="background: #c8d9ec; color: black;" | '''Molecule'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/Hartrees'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/kJmol<sup>-1</sup>'''
|-
|o-Xylylene
|style="text-align: center;" |0.178816
|style="text-align: center;" |469.481444
|-
|SO<sub>2</sub>
|style="text-align: center;" |-0.119268
|style="text-align: center;" |-313.1381579
|-
|Reactants (total)
|style="text-align: center;" |0.059548
|style="text-align: center;" |156.343286
|-
|Endo TS
|style="text-align: center;" |0.090559
|style="text-align: center;" |237.762673
|-
|Exo TS
|style="text-align: center;" |0.092077
|style="text-align: center;" |241.748182
|-
|Cheletropic TS
|style="text-align: center;" |0.099059
|style="text-align: center;" |260.079424
|-
|Endo Product
|style="text-align: center;" |0.021697
|style="text-align: center;" |56.9654778
|-
|Exo Product
|style="text-align: center;" |0.021452
|style="text-align: center;" |56.3222303
|-
|Cheletropic product
|style="text-align: center;" |0.000007
|style="text-align: center;" |0.0183785014
|}

{| class="wikitable"
|+ Table.7, Activation energies and ΔG of two reactions at PM6
|-
| style="background: #c8d9ec; color: black;" | '''State'''
| style="background: #c8d9ec; color: black;" | '''Activation energy /kJmol<sup>-1</sup>'''
| style="background: #c8d9ec; color: black;" | '''ΔG /kJmol<sup>-1</sup>'''
|-
|Endo
|style="text-align: center;" |81.4
|style="text-align: center;" |-99.4
|-
|Exo
|style="text-align: center;" |85.4
|style="text-align: center;" |-100.0
|-
|Cheletropic
|style="text-align: center;" |103.7
|style="text-align: center;" |-156.3
|}

[[File:XP715_Energy_profile.png|thumb|center|700px|Figure.11, reaction profile of three reactions]]

By plotting the energy profile (Fig.11), the '''endo''' product is the '''kinetic product''' as the activation barrier is the lowest. The ΔG of exo product is similar to endo product, indicating that endo and exo products have same thermodynamic stability. The '''thermodynamic product''' is the '''cheletropic''' product as the ΔG is the most negative one. The energy of o-xylylene is very high, indicating that it is highly unstable. Therefore, by examining IRCs, the 6-membered ring is converted from 8π electrons (4n, '''antiaromatic''') to 6π electrons (4n+2, '''aromatic'''), resulting in more stable structures. The required cis-butadiene structure is already present in the o-xylylene, so it accelerates the DA reactions.

===Extension===

[[File:XP715_Scheme_ext.PNG|thumb|center|500px|Scheme.4, reaction scheme of o-Xylylene with a second cis-butadiene fragment and SO<sub>2</sub>]]

====Optimisation====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #3b5998; color: white" | '''Optimisation of Endo and Exo TSs and products'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715_EXT_ENDO_SPLIT_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715_EXT_EXO_SPLIT_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715 EXT ENDO MINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715 EXT EXO MINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|Endo TS
|Exo TS
|Endo Product
|Exo Product
|}

====Energy Analysis====

{| class="wikitable"
|+ Table.8, Gibbs free energies of reactants, TSs and products at PM6
|-
| style="background: #c8d9ec; color: black;" | '''Molecule'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/Hartrees'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/kJmol<sup>-1</sup>'''
|-
|Endo TS
|style="text-align: center;" |0.102071
|style="text-align: center;" |267.987431
|-
|Exo TS
|style="text-align: center;" |0.105053
|style="text-align: center;" |275.816673
|-
|Endo Product
|style="text-align: center;" |0.065611
|style="text-align: center;" |172.261694
|-
|Exo Product
|style="text-align: center;" |0.067306
|style="text-align: center;" |176.711916
|}

{| class="wikitable"
|+ Table.9, Activation energies and ΔG of two reactions at PM6
|-
| style="background: #c8d9ec; color: black;" | '''State'''
| style="background: #c8d9ec; color: black;" | '''Activation energy /kJmol<sup>-1</sup>'''
| style="background: #c8d9ec; color: black;" | '''ΔG /kJmol<sup>-1</sup>'''
|-
|Endo
|style="text-align: center;" |111.6
|style="text-align: center;" |15.9
|-
|Exo
|style="text-align: center;" |119.5
|style="text-align: center;" |20.4
|}

Both of the reactions has positive ΔG, which requires energy from the environment to proceed the reaction, and the activation energies are much higher than previous DA reactions, suggesting that the DA reaction of cis-butadiene within the ring is '''kinetically and thermodynamically unfavourable'''.

==Conclusion==

Gaussian is powerful in applying the computational method to carry out pericyclic reactions. Different optimisation methods (PM6 and B3LYP) can be adopted to optimise reactants, TSs and products to the required level of precision. The structures can be checked by frequency calculation, as one imaginary frequency appears in TS. The IRC shows the energy profile, and the activation energy and Gibbs free energy can be calculated to predict the most favourable reaction pathway. Information including shape of MOs and bond length is also available, so a MO diagram is constructed easily.

In exercise 1, Woodward-Hoffmann rules and Frontier molecular orbital theory are confirmed experimentally. The reactions in exercise 2 concludes that the endo product is the kinetic and thermodynamic product, and the DA reaction is with inverse electron demand. The reactions in exercise 3 infer that the endo product is the kinetic product and the cheletropic product is the thermodynamic product. Due to the high activation energy barrier of cheletropic TS, the endo product is more likely to form. The cis-butadiene fragment within the ring is too steric to perform DA reactions.

Gaussian is also viable for other pericyclic reactions such as electrocyclic reactions.

==Reference==

<references/>

==Appendix==

===Exercise 1===
Butadiene: [[File:XP715_DIENE_MINPM6_NEW.LOG]]

Ethene: [[File:XP715_ETHENE_MINPM6.LOG]]

TS: [[File:XP715 2MOL TSPM6 JMOL.LOG]]

Product:[[File:XP715_PROD_MINPM6.LOG]]

IRC: [[File:XP715 2mol IRC.log]]

===Exercise 2===
Cyclohexadiene:[[File:XP715 DIENE 631G JMOL.LOG]]

1,3-Dioxole:[[File:XP715 DIOXOLE 631G JMOL.LOG]]

Endo TS:[[File:XP715 ENDO TSPM6 631G 3 JMOL.LOG]]

Exo TS:[[File:XP715_EXO_TS_jmol.log]]

Endo Product:[[File:XP715 Endo prod 631G.log]]

Exo product: [[File:XP715 EXO 631G jmol.log]]

IRC (Endo):[[File:ENDO TSPM6 IRC.log]]

IRC (Exo):[[File:XP715 EXO SPLIT TSPM6 IRC.log]]

===Exercise 3===
Exo TS:[[File:XP715 M3 MOL1 SPLIT TSPM6.LOG]]

Endo TS: [[File:XP715 DA ENDO SPLIT TSPM6.LOG]]

Cheletropic TS: [[File:XP715_CHE_SPLIT_TSPM6.LOG]]

IRC (Exo):[[File:XP715 M3 mol1 IRC.log]]

IRC (Endo):[[File:XP715 DA ENDO SPLIT TSPM6 IRC.LOG]]

IRC (Cheletropic):[[File:XP715 CHE SPLIT TSPM6 IRC protal.log]]

====Extension====
Endo TS:[[File:XP715_EXT_ENDO_SPLIT_TSPM6.LOG]]

Exo TS:[[File:XP715_EXT_EXO_SPLIT_TSPM6.LOG]]

Endo Product: [[File:XP715 EXT ENDO MINPM6.LOG]]

Exo Product: [[File:XP715 EXT EXO MINPM6.LOG]]

IRC (Endo): [[File:XP715 EXT ENDO SPLIT TSPM6 IRC.LOG]]

IRC (Exo): [[File:XP715 EXT EXO SPLIT TSPM6 IRC.LOG]]

Rep:XP715TS

2018-03-27T15:38:22Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene */

='''Transition states and reactivity'''=

==Introduction==

For a potential energy curve with only one variable, the curve is considered to be the energy profile. If more than one geometric coordinates associate with potential energy, the three-dimensional surface is called '''potential energy surface'''. For a nonlinear molecule, there is 3N-6 independent geometric variables.
The transition state is the maximum point on the surface, connecting two minima, reactant and product. These stationary points (transition state, reactant and product) are defined as zero first derivative (<math>\frac{\partial E}{\partial R}</math>= 0), showing that the gradient is zero.

{|class=wikitable
|-
|<math>\frac{\partial E}{\partial R}=-F</math>
|-
|Equation.1, first derivative
|}

The gradient is related to force acts on the atoms, and the negative sign indicates the force is in the direction of lowering potential energy.
In order to distinguish them, curvatures (frequencies) at these points are determined by second derivative.

{|class=wikitable
|-
|<math>\dfrac{\partial ^2 E}{\partial R^2} =k</math>
|-
|Equation.2, second derivative
|}
[[File:XP715 Eqn ferq.PNG|thumb|center|300px|Equation.3, frequency calculation <ref>J. McDouall, Computational Quantum Chemistry: Molecular Structure and Properties in Silico, Royal Society of Chemistry, Cambridge, 2013, ch.1, pp.1-62</ref>]]

Second derivatives are hold in the Hessian matrix, and by diagonalizing the Hessian matrix, force constant k can be determined as well as the frequency by Eqn.3.
The saddle point (transition state) has negative curvature (<math>\dfrac{\partial ^2 E}{\partial R^2} < 0</math>), while the minima have positive curvature (<math>\dfrac{\partial ^2 E}{\partial R^2} > 0</math>).

Energy, electronic structure and properties of molecules can be determined by solving Schrödinger’s equation. The computational method is used to solve the equation by deciding to use different level of theory (Hamiltonian operator) and basis set (mathematical description of wavefunction). In this page, two optimisation methods were adopted, PM6 and B3LYP/6-31G(d). For PM6, it is a semi-empirical method, which is based on Hartree-Fock theory. <ref>C.A. Coulson, B.O’Leary, R.B. Mallion, Hückel theory for organic chemists, Academic Press, London, New York, 1978</ref> It solves the many-electron equation by expanding the coefficient of linear combination of atomic orbitals (LCAO) and simplifies with Born–Oppenheimer approximation. The full HF calculation is too expensive, therefore PM6 is simplified by neglecting two-electron part of Hamiltonian, and further simplification can be applied for π-electron system by Hückel method. It is overall a quick but not reliable method. B3LYP/6-31G(d) is based on density functional theory (DFT), which associates with HF theory and an additional term, exchange-correlation energy.<ref>K. Kim and K. D. Jordan, J. Phys. Chem., 1994, 98, 10089–10094.</ref> B3LYP is the choice of exchange-correlation energy and 6-31G is the basis set. DFT is sufficient accurate but it is an expensive method.

In this page, Gaussian, the computational method, is used to interpret the mechanisms of four pericyclic reactions. This technique is able to identify whether the bond formation is synchronous or asynchronous, formation of kinetic or thermodynamic product and whether the proposed reaction pathway is favourable.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 23:43, 22 March 2018 (UTC) You have clearly read beyond the script here well done. Some equations would have been good. When you diagonalise the hessian your are changing your coordinate basis into the noraml modes. which are then linear combinations of the degrees of freedom.

==Exercise 1: Reaction of Butadiene with Ethylene==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Overall you have done a good job. However you have used your B3LYP optimisation of ethene instead of the PM6 one, which led you to the wrong MO energies.)

[[File:XP715_Scheme_EX1.PNG|thumb|center|500px|Scheme.1, reaction scheme of butadiene and ethylene with annotated bond length]]

The first reaction is the classical [4+2] cycloadditon (Scheme.1), which is also called Diels-Alder reaction. This reaction was investigated by guessing the transition state first and finding the optimised product. Both reactants and TS were optimised at PM6 level, and a frequency calculation and Intrinsic Reaction Coordinate (IRC) were analysed to ensure that a correct TS was obtained. Finally, the product was optimised at PM6 level.

===Optimisation and Calculation===

{| class="wikitable"
| colspan="4" style="text-align: center; background: #3b5998; color: white" | '''Optimised structures of reactants, TS and product at PM6 level'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38 ; </script>
<uploadedFileContents>XP715_DIENE_MINPM6_NEW.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; </script>
<uploadedFileContents>XP715_ETHENE_MINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; </script>
<uploadedFileContents>XP715 2MOL TSPM6 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 42; </script>
<uploadedFileContents>XP715_PROD_MINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene
| Ethene
| TS
| Product
|}

{| class="wikitable"
|[[File:XP715 TS PM6 freq.PNG|thumb|left|700px|Figure.1, Frequency calculation of TS]]
|[[File:XP715 EX1 IRC.png|thumb|center|500px|Figure.2, IRC (total energy and RMS gradient) of TS]]
|}
Fig. 1 shows that only one frequency is negative, indicating the transition state. IRC is the minimum energy pathway on the potential energy surface, starting from the first-derivative stationary point, TS, and calculating in both direction until reaching two minima, reactants and products. Fig. 2 illustrates the total energy and RMS gradient along IRC, and the gradients of reactants, products and TS are all zero, confirming a successful and asymmetric IRC was performed.

=== MO Analysis===
{| class="wikitable"
| colspan="4" style="text-align: center; background: #3b5998; color: white" | '''HOMO and LUMO of reactants and HOMO/-1, LUMO/+1 of transition states'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_DIENE_MINPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_DIENE_MINPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; mo 8; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_ETHENE_MINPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; mo 9; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_ETHENE_MINPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene (HOMO)
| Butadiene (LUMO)
| Ethene (HOMO)
| Ethene (LUMO)
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS (HOMO-1)
| TS (HOMO)
| TS (LUMO)
| TS (LUMO+1)
|}

By visualising MO of reactants and TS, part of the MO was constructed in Fig.3 (MO). The calculated orbital energies at PM6 level are labelled in grey, however, due to the low optimisation level, these energies are only a rough guide to the MO diagram. Although the energies are not accurate, it still provides an evidence of mixing. The dotted orbitals are the MOs without mixing, while the solid-line orbitals are the ones with predicted mixing.
[[File:XP715_MO.PNG|thumb|center|800px|Figure.3, MO diagram]]
[[File:XP715 MO sym.PNG|thumb|center|500px|Figure.4, symmetry label for HOMO and LUMO of diene]]
[[File:XP715 Eqn orbital.PNG|thumb|center|500px|Equation.4, orbital overlap integral]]

The symmetry of each orbital can be identified with its symmetry axis or plane. The HOMO of butadiene is antisymmetric as it has C2 symmetry, while the LUMO is symmetric as it contains σ(v) symmetry plane. (Fig.4) Only the orbitals with same symmetry could combine to form new MOs. The orbital overlap integral is represented by Eqn.4<ref>P. W. Atkins and J. De Paula, Physical Chemistry, 2009.</ref>, and it is zero when the overall interaction is antisymmetric. The symmetric-antisymmetric interaction is '''antisymmetric''', integrating to '''zero''' (forbidden reaction). The symmetric-symmetric and antisymmetric-antisymmetric interaction are '''symmetric''', resulting to '''non-zero''' integral (allowed reaction).
The Woodward-Hoffmann rules states that in a thermally allowed reaction, the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd, where the suffix s stands for suprafacial (forming bond on same face), and a for antarafacial (forming bond on opposite face).
By applying Woodward-Hoffmann rules, this reaction is proved to be '''thermally allowed'''.
<pre>(4q+2)s+(4r)a
=1+0
=1
=thermally allowed reaction
</pre>

===Bond Length Analysis===
{| class="wikitable"
|+ Table 1. Bond length of reactants, transition states and product
''(refer to Scheme.1)''
|-
| style="background: #c8d9ec; color: black;" | '''Structure'''
| style="background: #c8d9ec; color: black;" | '''sp<sup>3</sup>-sp<sup>3</sup> C-C /Å'''
| style="background: #c8d9ec; color: black;" | '''sp<sup>3</sup>-sp<sup>2</sup> C-C /Å'''
| style="background: #c8d9ec; color: black;" | '''sp<sup>2</sup>-sp<sup>2</sup> C=C /Å'''
| style="background: #c8d9ec; color: black;" | '''sp<sup>2</sup>-sp<sup>2</sup> C-C /Å'''
|-
|Butadiene
|n/a
|n/a
|1.34, 1.34
|1.47
|-
| Ethene
| n/a
| n/a
| 1.33
| n/a
|-
| TS
| 2.11, 2.11 (forming single bond)
| n/a
| 1.38, 1.38 (partially double bond);
1.38 (partially double bond)
|1.41 (partially double bond)
|-
|Product
|1.54, 1.54
|1.50, 1.50
|1.34
|n/a
|-
|Typical value
| 1.54
|1.50
|1.34
|1.47
|}

{| class="wikitable"
|+ Table 2. Van der Waals radius of Carbon
| colspan="4" style="text-align: center; background: #3b5998; color: white" |''' Van der Waals radius of Carbon'''
|-
|One carbon atom /Å
|1.70
|Two carbon atoms /Å
|3.40
|}
Comparing the bond length of reactants and TS, the reactants show typical bond length of sp<sup>2</sup>-sp<sup>2</sup> C=C, sp<sup>3</sup>-sp<sup>2</sup> C-C and sp<sup>2</sup>-sp<sup>2</sup> C=C. In the TS, C10-C12 is shortened due the change from sp<sup>3</sup>-sp<sup>3</sup> single bond to sp<sup>2</sup>-sp<sup>2</sup> double bond, while C7-C10 and C12-14 show an elongation because sp<sup>2</sup>-sp<sup>2</sup> double bonds are changed into sp<sup>2</sup>-sp<sup>3</sup> single bonds. C1-C4 becomes longer as it converts from sp<sup>2</sup>-sp<sup>2</sup> double bond to sp<sup>3</sup>-sp<sup>3</sup> single bond. The distance between C4 and C7/ C1 and C14 is both 2.11 Å, which is shorter than sum of Van der Waals radius of two carbon atoms (Table.2), indicating that two molecules are approaching to each other and forming a partial bond. The product shows typical sp<sup>3</sup>-sp<sup>3</sup> C-C, sp<sup>2</sup>-sp<sup>3</sup> C-C and sp<sup>2</sup>-sp<sup>2</sup> C=C bond length.

{| class="wikitable"
| [[File:XP715 EX1 Bond length.png|thumb|center|1000px|a]]
| [[File:XP715 EX1 Prod label.jpg|thumb|center|300px|b]]
|-
| colspan="2" | Figure.5, a) The change of bond length with respect to reaction coordinate. b) Numbering of atoms of the product
|}
Fig.5 illustrated the change of bond length along the reaction coordinate by analysing IRCs of each bond. C1-C4 (purple) and C4-C7 (black) starts from 3.40 Å, where no bond is formed, and then reaching TS at 2.11 Å. The product is formed when the bond length is at 1.54 Å. The rest of the bonds corresponds to the explanation in the previous section.

===Vibration===
{| class="wikitable"
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 7; vibration 2</script>
<uploadedFileContents>XP715_2MOL_TSPM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
![[File:XP715 EX1 TS formbond.gif|thumb|center|500px|Figure.6, Video of forming and breaking bonds]]
|}
By visualising the vibration of TS and motion picture of Fig.6, the formation of two bonds are '''synchronous'''.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

[[File:XP715 Scheme ex2.JPG|thumb|center|500px|Scheme.2, reaction schemes of Cyclohexadiene and 1,3-Dioxole to form endo and exo products.]]

This Diels-Alder reaction is stereospecific, leading to endo and exo adducts. The more favourable reaction pathway is examined by the calculating activation energy and free energy. Reactants, TS and products were optimised first with PM6 following by using B3LYP/6-31G(d).

===Optimisation and Calculation===
{| class="wikitable"
| colspan="3" style="text-align: center; background: #3b5998; color: white" | '''Optimisation of reactants, TS and products'''
|-
|Cyclohexadiene
|1,3-Dioxole
|Endo TS
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>XP715 DIENE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>XP715 DIOXOLE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|[[File:XP715 Diene freq.PNG|thumb|center|500px]]
|[[File:XP715 Dioxole freq.PNG|thumb|center|500px]]
|[[File:XP715 ENDO TS 631G freq.PNG|thumb|center|500px]]
|-
|Exo TS
|Endo Product
|Exo Product
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>XP715 Endo prod 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8</script>
<uploadedFileContents>XP715 EXO 631G jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|[[File:XP715 EXO TS 631G freq.PNG|thumb|center|500px]]
|[[File:XP715_ENDO_prod_freq.PNG|thumb|center|500px]]
|[[File:XP715_EXO_prod_freq.PNG|thumb|center|500px]]
|}
There is no imaginary frequency for all the reactants and products, and there is only one negative frequency for each TS, confirming that all of them were well optimised.

===MO Analysis===
{| class="wikitable"
| colspan="4" style="text-align: center; background: #3b5998; color: white" | '''HOMO and LUMO of reactants and HOMO/-1, LUMO/+1 of ENDO/EXO transition states'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 DIENE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 DIENE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 DIOXOLE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 DIOXOLE 631G JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Cyclohexadiene (HOMO)
| Cyclohexadiene (LUMO)
| 1,3-Dioxole (HOMO)
| 1,3-Dioxole (LUMO)
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO TS (HOMO-1)
| ENDO TS (HOMO)
| ENDO TS (LUMO)
| ENDO TS (LUMO+1)
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| EXO TS (HOMO-1)
| EXO TS (HOMO)
| EXO TS (LUMO)
| EXO TS (LUMO+1)
|}

{| class="wikitable"
| colspan="2" style="text-align: center; background: #3b5998; color: white" | '''MOs of reactants and transition states'''
|-
|[[File:XP715_Endo_MO.png|thumb|center|700px|Figure.7, MO diagram of Endo TS]]
|[[File:XP715Exo MO.png|thumb|center|700px|Figure.8, MO diagram of Exo TS]]
|}
By visualising MOs of reactants and TSs, the MO diagrams of endo and exo TSs were constructed. The calculated orbital energies (in grey) gave a rough guide to the energy difference between orbitals. The orbital energies of HOMO/HOMO-1 and LUMO/LUMO+1 of two TSs are similar, but the actual shapes shown in jmol are different (in later section). The HOMO of endo TS is slightly more stabilised than that of exo TS.

====Inverse Demand DA Reaction====
For a standard DA reaction, the electron rich component is diene and the electron poor component is dienophile. The HOMO of diene and the LUMO of dienophile are similar in energy and interact strongly. However, for a DA reaction with inverse electron demand, the electron rich component is dienophile and the electron poor component is diene.<ref>A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236</ref> Then the more strongly interacting frontier orbitals are the HOMO of dienophile and the LUMO of diene. In this reaction, the dienophile is 1,3-dioxole, and the electron donation from lone pair of oxygen atoms results in more electron rich dienophile. The single point energy calculation confirms this suggestion.

{| class="wikitable"
|+ Table.3, Single point energy of HOMO/LUMO of reactants
|-
| style="background: #c8d9ec; color: black;" | '''Molecule'''
| style="background: #c8d9ec; color: black;" | '''Energy of HOMO/a.u.'''
| style="background: #c8d9ec; color: black;" | '''Energy of LUMO/a.u.'''
| style="background: #c8d9ec; color: black;" | '''Difference of LUMO<sub>diene</sub> and HOMO<sub>dienophile</sub>'''
| style="background: #c8d9ec; color: black;" | '''Difference of HOMO<sub>diene</sub> and LUMO<sub>dienophile</sub>'''
|-
|Cyclohexadiene
|style="text-align: center;"| -0.20601
|style="text-align: center;"|-0.01800
|rowspan="2" style="text-align: center;"| 0.17815
|rowspan="2" style="text-align: center;"| 0.24265
|-
|1,3-Dioxole
|style="text-align: center;"|-0.19615
|style="text-align: center;"| 0.03664
|}

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 23:49, 22 March 2018 (UTC) Nice this is well done and clear.

===Energy Analysis===

{| class="wikitable"
|+ Table.4, Gibbs free energies of reactants, TSs and products using B3LYP/6-31G(d)
|-
| style="background: #c8d9ec; color: black;" | '''Molecule'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/Hartrees'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/kJmol<sup>-1</sup>'''
|-
|Cyclohexadiene
|style="text-align: center;" |-233.324375
|style="text-align: center;" |-612593.193227
|-
|1,3-Dioxole
|style="text-align: center;" |-267.068644
|style="text-align: center;" |-701188.778236
|-
|Reactants (total)
|style="text-align: center;" |-500.393019
|style="text-align: center;" |-1313781.971463
|-
|Endo TS
|style="text-align: center;" |-500.332149
|style="text-align: center;" |-1313622.15727
|-
|Exo TS
|style="text-align: center;" |-500.329163
|style="text-align: center;" |-1313614.31752
|-
|Endo Product
|style="text-align: center;" |-500.418694
|style="text-align: center;" |-1313849.381181
|-
|Exo Product
|style="text-align: center;" |-500.417319
|style="text-align: center;" |-1313845.77112
|}

{| class="wikitable"
|+ Table.5, Activation energies and ΔG of two reactions using B3LYP/6-31G(d)
|-
| style="background: #c8d9ec; color: black;" | '''State'''
| style="background: #c8d9ec; color: black;" | '''Activation energy /kJmol<sup>-1</sup>'''
| style="background: #c8d9ec; color: black;" | '''ΔG /kJmol<sup>-1</sup>'''
|-
|Endo
|style="text-align: center;" |159.8
|style="text-align: center;" |-67.4
|-
|Exo
|style="text-align: center;" |167.7
|style="text-align: center;" |-63.8
|}

The kinetic product is the one with lower activation energy, leading to faster reaction, and the thermodynamic product is the one with more negative ΔG, which forms more stable product. The calculation of energies in Table.5 illustrates that the endo product has lower activation energy and more negative ΔG, indicating that '''endo product''' is the '''kinetic''' product as well as '''thermodynamic''' product

{| class="wikitable"
| colspan="3" style="text-align: center; background: #3b5998; color: white" | '''HOMOs of endo and exo TSs'''
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715 ENDO TSPM6 631G 3 JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 102; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>XP715_EXO_TS_jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
![[File:XP715 Secondary interaction.PNG]]
|-
|Endo TS
|Exo TS
|Figure.9, graphic illustration of primary/secondary interactions of HOMOs.
|}

There is only primary interaction in exo TS, while the secondary interaction is also observed in endo TS. The secondary interaction stabilises the endo TS (Fig.9), resulting in faster formation of endo TS and confirming that the endo product is more kinetically favourable.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 23:53, 22 March 2018 (UTC) Good section, you could have gone into more detail about the thermo and kenetic theory. But otherwise a very good section.

==Exercise 3: Diels-Alder vs Cheletropic==

[[File:XP715 Scheme ex3.JPG|thumb|center|700px|Scheme.3, reaction schemes between Xylylene and SO<sub>2</sub> through Diels-Alder reaction and Cheletropic reaction]]

For this reaction, three products were examined, including endo and exo products of DA reactions and cheletropic product. Energy calculations were carried out to identify the most favourable reaction pathway. All the reaction species were optimised at PM6 level. The extension investigated the possibility of DA reaction of a second cis-butadiene in o-xylylene. The activation energies and Gibbs free energies were calculated to suggest the viability of the reactions.

===Optimisation and Calculation===
{| class="wikitable"
| colspan="3" style="text-align: center; background: #3b5998; color: white" | '''Optimisation of three TSs'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715 M3 MOL1 SPLIT TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715 DA ENDO SPLIT TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715_CHE_SPLIT_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|DA-Exo
|DA-Endo
|Cheletropic
|-
|[[File:XP715 DA ENDO freq.PNG|thumb|center|500px]]
|[[File:XP715_DA_EXO_freq.PNG|thumb|center|500px]]
|[[File:XP715_CHE_freq.PNG|thumb|center|500px]]
|}

{| class="wikitable"
| colspan="3" style="text-align: center; background: #3b5998; color: white" | '''IRC of three TSs'''
|-
|DA-Endo TS
|[[File:XP715_DA_ENDO_TS_IRC.png|thumb|center|900px]]
|[[File:XP715 DA ENDO TS.gif|thumb|center|500px]]
|-
|DA-Exo TS
|[[File:XP715_DA_EXO_TS_IRC.png|thumb|center|900px]]
|[[File:XP715_DA_EXO_TS.gif|thumb|center|500px]]
|-
|Cheletropic TS
|[[File:XP715_Che_TS_IRC.png|thumb|center|900px]]
|[[File:XP715_CHE_TS.gif|thumb|center|500px]]
|-
|colspan="3"|Figure.10, IRCs of three TSs
|}

All IRCs were successful asymmetric graphs. The endo and exo DA TS starts from product to reactant and the cheletropic TS starts from reactant to product. The approach trajectories are shown as motion pictures on the right.

===Energy Analysis===

{| class="wikitable"
|+ Table.6, Gibbs free energies of reactants, TSs and products at PM6
|-
| style="background: #c8d9ec; color: black;" | '''Molecule'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/Hartrees'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/kJmol<sup>-1</sup>'''
|-
|o-Xylylene
|style="text-align: center;" |0.178816
|style="text-align: center;" |469.481444
|-
|SO<sub>2</sub>
|style="text-align: center;" |-0.119268
|style="text-align: center;" |-313.1381579
|-
|Reactants (total)
|style="text-align: center;" |0.059548
|style="text-align: center;" |156.343286
|-
|Endo TS
|style="text-align: center;" |0.090559
|style="text-align: center;" |237.762673
|-
|Exo TS
|style="text-align: center;" |0.092077
|style="text-align: center;" |241.748182
|-
|Cheletropic TS
|style="text-align: center;" |0.099059
|style="text-align: center;" |260.079424
|-
|Endo Product
|style="text-align: center;" |0.021697
|style="text-align: center;" |56.9654778
|-
|Exo Product
|style="text-align: center;" |0.021452
|style="text-align: center;" |56.3222303
|-
|Cheletropic product
|style="text-align: center;" |0.000007
|style="text-align: center;" |0.0183785014
|}

{| class="wikitable"
|+ Table.7, Activation energies and ΔG of two reactions at PM6
|-
| style="background: #c8d9ec; color: black;" | '''State'''
| style="background: #c8d9ec; color: black;" | '''Activation energy /kJmol<sup>-1</sup>'''
| style="background: #c8d9ec; color: black;" | '''ΔG /kJmol<sup>-1</sup>'''
|-
|Endo
|style="text-align: center;" |81.4
|style="text-align: center;" |-99.4
|-
|Exo
|style="text-align: center;" |85.4
|style="text-align: center;" |-100.0
|-
|Cheletropic
|style="text-align: center;" |103.7
|style="text-align: center;" |-156.3
|}

[[File:XP715_Energy_profile.png|thumb|center|700px|Figure.11, reaction profile of three reactions]]

By plotting the energy profile (Fig.11), the '''endo''' product is the '''kinetic product''' as the activation barrier is the lowest. The ΔG of exo product is similar to endo product, indicating that endo and exo products have same thermodynamic stability. The '''thermodynamic product''' is the '''cheletropic''' product as the ΔG is the most negative one. The energy of o-xylylene is very high, indicating that it is highly unstable. Therefore, by examining IRCs, the 6-membered ring is converted from 8π electrons (4n, '''antiaromatic''') to 6π electrons (4n+2, '''aromatic'''), resulting in more stable structures. The required cis-butadiene structure is already present in the o-xylylene, so it accelerates the DA reactions.

===Extension===

[[File:XP715_Scheme_ext.PNG|thumb|center|500px|Scheme.4, reaction scheme of o-Xylylene with a second cis-butadiene fragment and SO<sub>2</sub>]]

====Optimisation====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #3b5998; color: white" | '''Optimisation of Endo and Exo TSs and products'''
|-
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715_EXT_ENDO_SPLIT_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715_EXT_EXO_SPLIT_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715 EXT ENDO MINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
! <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>XP715 EXT EXO MINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|Endo TS
|Exo TS
|Endo Product
|Exo Product
|}

====Energy Analysis====

{| class="wikitable"
|+ Table.8, Gibbs free energies of reactants, TSs and products at PM6
|-
| style="background: #c8d9ec; color: black;" | '''Molecule'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/Hartrees'''
| style="background: #c8d9ec; color: black;" | '''Gibbs free energy/kJmol<sup>-1</sup>'''
|-
|Endo TS
|style="text-align: center;" |0.102071
|style="text-align: center;" |267.987431
|-
|Exo TS
|style="text-align: center;" |0.105053
|style="text-align: center;" |275.816673
|-
|Endo Product
|style="text-align: center;" |0.065611
|style="text-align: center;" |172.261694
|-
|Exo Product
|style="text-align: center;" |0.067306
|style="text-align: center;" |176.711916
|}

{| class="wikitable"
|+ Table.9, Activation energies and ΔG of two reactions at PM6
|-
| style="background: #c8d9ec; color: black;" | '''State'''
| style="background: #c8d9ec; color: black;" | '''Activation energy /kJmol<sup>-1</sup>'''
| style="background: #c8d9ec; color: black;" | '''ΔG /kJmol<sup>-1</sup>'''
|-
|Endo
|style="text-align: center;" |111.6
|style="text-align: center;" |15.9
|-
|Exo
|style="text-align: center;" |119.5
|style="text-align: center;" |20.4
|}

Both of the reactions has positive ΔG, which requires energy from the environment to proceed the reaction, and the activation energies are much higher than previous DA reactions, suggesting that the DA reaction of cis-butadiene within the ring is '''kinetically and thermodynamically unfavourable'''.

==Conclusion==

Gaussian is powerful in applying the computational method to carry out pericyclic reactions. Different optimisation methods (PM6 and B3LYP) can be adopted to optimise reactants, TSs and products to the required level of precision. The structures can be checked by frequency calculation, as one imaginary frequency appears in TS. The IRC shows the energy profile, and the activation energy and Gibbs free energy can be calculated to predict the most favourable reaction pathway. Information including shape of MOs and bond length is also available, so a MO diagram is constructed easily.

In exercise 1, Woodward-Hoffmann rules and Frontier molecular orbital theory are confirmed experimentally. The reactions in exercise 2 concludes that the endo product is the kinetic and thermodynamic product, and the DA reaction is with inverse electron demand. The reactions in exercise 3 infer that the endo product is the kinetic product and the cheletropic product is the thermodynamic product. Due to the high activation energy barrier of cheletropic TS, the endo product is more likely to form. The cis-butadiene fragment within the ring is too steric to perform DA reactions.

Gaussian is also viable for other pericyclic reactions such as electrocyclic reactions.

==Reference==

<references/>

==Appendix==

===Exercise 1===
Butadiene: [[File:XP715_DIENE_MINPM6_NEW.LOG]]

Ethene: [[File:XP715_ETHENE_MINPM6.LOG]]

TS: [[File:XP715 2MOL TSPM6 JMOL.LOG]]

Product:[[File:XP715_PROD_MINPM6.LOG]]

IRC: [[File:XP715 2mol IRC.log]]

===Exercise 2===
Cyclohexadiene:[[File:XP715 DIENE 631G JMOL.LOG]]

1,3-Dioxole:[[File:XP715 DIOXOLE 631G JMOL.LOG]]

Endo TS:[[File:XP715 ENDO TSPM6 631G 3 JMOL.LOG]]

Exo TS:[[File:XP715_EXO_TS_jmol.log]]

Endo Product:[[File:XP715 Endo prod 631G.log]]

Exo product: [[File:XP715 EXO 631G jmol.log]]

IRC (Endo):[[File:ENDO TSPM6 IRC.log]]

IRC (Exo):[[File:XP715 EXO SPLIT TSPM6 IRC.log]]

===Exercise 3===
Exo TS:[[File:XP715 M3 MOL1 SPLIT TSPM6.LOG]]

Endo TS: [[File:XP715 DA ENDO SPLIT TSPM6.LOG]]

Cheletropic TS: [[File:XP715_CHE_SPLIT_TSPM6.LOG]]

IRC (Exo):[[File:XP715 M3 mol1 IRC.log]]

IRC (Endo):[[File:XP715 DA ENDO SPLIT TSPM6 IRC.LOG]]

IRC (Cheletropic):[[File:XP715 CHE SPLIT TSPM6 IRC protal.log]]

====Extension====
Endo TS:[[File:XP715_EXT_ENDO_SPLIT_TSPM6.LOG]]

Exo TS:[[File:XP715_EXT_EXO_SPLIT_TSPM6.LOG]]

Endo Product: [[File:XP715 EXT ENDO MINPM6.LOG]]

Exo Product: [[File:XP715 EXT EXO MINPM6.LOG]]

IRC (Endo): [[File:XP715 EXT ENDO SPLIT TSPM6 IRC.LOG]]

IRC (Exo): [[File:XP715 EXT EXO SPLIT TSPM6 IRC.LOG]]

Rep:MOD:JDN15Y3lab

2018-03-27T15:30:30Z

Fv611: /* Molecular Orbitals */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 22:15, 22 March 2018 (UTC) Correct you get this info by diaginalising the hessian in the basis of the normal modes. which are linear combinations of the degrees of freedom. These are the vibrations that you see , when you move along the normal mode vector.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate. DFT calculations define the energy of a system as a sum of 6 components, E<sub>DFT</sub> = E<sub>NN</sub> + E<sub>T</sub> + E<sub>V</sub> + E<sub>Coul</sub> + E<sub>Exchange</sub> + E<sub>Corr</sub>.

E<sub>NN</sub> = nuclear-nuclear repulsion, E<sub>V</sub> = nuclear-electron attraction, E<sub>Coul</sub> = electron-electron Coloumb repulsion.

These terms above are the same used in the Hartree-Fock theory. The energies below are different from the terms used in the Hartree-Fock theory as E<sub>Corr</sub> is not accounted for in the theory.

E<sub>T</sub> = kinetic energy of the electrons, E<sub>Exchange</sub> = electron-electron exchange energies, E<sub>Corr</sub> = correlated movement of electrons of different spin.

B3LYP (Becke-3-LFP) is a hybrid method, which mixing exchange energies calculated in an exact manner with those obtained from DFT methods to improve performance.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 22:17, 22 March 2018 (UTC) This is correct however in DFT the exchange and correlation terms are put together into the exchange correlation term, which is unknown and we use different functionals to model it. B3LYP uses HF to get the exact static correlation.

== Exercise 1: Reaction between Butadiene and Ethene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job across the whole exercise. Well done!)
=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===

The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You have presented the same MO diagram with different TS schemes. You should have shows or discussed the differences between exo and endo conformations in terms of their relative MO energies.)

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy. <br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

[[File:JDN15EXOClash.png| centre |300px]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 22:33, 22 March 2018 (UTC) Nice diagram of the sterics. Your energies are correct. But you have only stated that the reaction in inverse with no proof. You can do this quantitatively. There were parts that you could have gone into more detail in.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}
By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

(The carbon atoms are all sp2-hybridised in xylylene. The structure forms a resonance with the diradical form (aromatic but still unstable) [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15RP2.png|centre|600px]]

(Use straight lines for reaction profiles [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

Based on the data from the table, we can calculate that the Cheletropic product has the lowest energy and hence is thermodynamically favoured. As sulfur is larger than C, the resulting twist in the 6 membered ring in the Diels-Alder products have a ring strain due to inefficient sp<sup>3</sup> hybridisation, resulting in a highly distorted structure. This is in comparison to the Cheletropic product, which is able to adopt a planar configuration that maximises the distance between the O and the neighbouring H atoms. However, the Cheletropic reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

From the transition state HOMO, we can observe that both the endo and exo TS have stabilising secondary orbital interactions, therefore reducing the reaction barrier in these reactions. This also explains why the energy of the exo and endo TS are relatively close in energy. We can also see that the Cheletropic TS has no stabilising secondary interactions and is highly antisymmetric with many nodes, resulting a higher energy TS.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!rowspan="2" style="text-align: center;"|
! colspan="2" style="text-align: center;"| Diels-Alder Reaction
!rowspan="2" style="text-align: center;"| Cheletropic Reaction
|-
!style="text-align: center;"| ENDO
!style="text-align: center;"| EXO
|-
|style="text-align: center;"|Transition State
HOMO
| [[File:JDN15EXOHOMO.png]]
| [[File:JDN15ENDOHOMO.png]]
| [[File:JDN15CHEHOMO.png]]
|}

(It's pretty hard to see what's going on in these MO pictures. Perhaps use transparent surfaces? [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)
!File Logs

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.105054
|style="text-align: center;" | 0.067300
|style="text-align: center;" | 119.8
|style="text-align: center;" | 20.7
|style="text-align: center;" | [[File:JDN15_EXO2_Product.LOG]]
[[File:JDN15_EXO_TS2.LOG]]
|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" | 0.102070
|style="text-align: center;" | 0.065612
|style="text-align: center;" | 112.0
|style="text-align: center;" | 16.3
|style="text-align: center;" | [[File:JDN15_ENDO2_Product.LOG]]
[[File:JDN15_ENDO2_TS.LOG]]
|}

Comparing the values from the table, we can see that both exo and endo for this Diels-Alder reaction has a much higher reaction barrier than the previous reactions (discussed earlier). Hence the secondary Diels-Alder reactions are the least kinetically favourable. We can also see that the reaction energies of the secondary Diels-Alder reactions are positive, indicating that the reaction is highly thermodynamically unfavourable as ΔG>0 and hence the reaction is not spontaneous.

==Conclusion==
Gaussian is a useful method to carry out molecular geometry optimisations and calculations. By investigating the free energies of the transition states and products, we can determine the reaction energies and reaction barriers of the reaction. We can then determine which reactions are kinetically or thermodynamically favoured. This computational method is a powerful tool that can be used for preliminary research before testing out the reactions experimentally. It also provides a visual representation that allows better understanding on the interactions between the MOs of the molecules before, during and after the reaction.

Rep:MOD:JDN15Y3lab

2018-03-27T15:26:49Z

Fv611: /* Exercise 1: Reaction between Butadiene and Ethene */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 22:15, 22 March 2018 (UTC) Correct you get this info by diaginalising the hessian in the basis of the normal modes. which are linear combinations of the degrees of freedom. These are the vibrations that you see , when you move along the normal mode vector.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate. DFT calculations define the energy of a system as a sum of 6 components, E<sub>DFT</sub> = E<sub>NN</sub> + E<sub>T</sub> + E<sub>V</sub> + E<sub>Coul</sub> + E<sub>Exchange</sub> + E<sub>Corr</sub>.

E<sub>NN</sub> = nuclear-nuclear repulsion, E<sub>V</sub> = nuclear-electron attraction, E<sub>Coul</sub> = electron-electron Coloumb repulsion.

These terms above are the same used in the Hartree-Fock theory. The energies below are different from the terms used in the Hartree-Fock theory as E<sub>Corr</sub> is not accounted for in the theory.

E<sub>T</sub> = kinetic energy of the electrons, E<sub>Exchange</sub> = electron-electron exchange energies, E<sub>Corr</sub> = correlated movement of electrons of different spin.

B3LYP (Becke-3-LFP) is a hybrid method, which mixing exchange energies calculated in an exact manner with those obtained from DFT methods to improve performance.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 22:17, 22 March 2018 (UTC) This is correct however in DFT the exchange and correlation terms are put together into the exchange correlation term, which is unknown and we use different functionals to model it. B3LYP uses HF to get the exact static correlation.

== Exercise 1: Reaction between Butadiene and Ethene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job across the whole exercise. Well done!)
=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy. <br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

[[File:JDN15EXOClash.png| centre |300px]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 22:33, 22 March 2018 (UTC) Nice diagram of the sterics. Your energies are correct. But you have only stated that the reaction in inverse with no proof. You can do this quantitatively. There were parts that you could have gone into more detail in.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}
By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

(The carbon atoms are all sp2-hybridised in xylylene. The structure forms a resonance with the diradical form (aromatic but still unstable) [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15RP2.png|centre|600px]]

(Use straight lines for reaction profiles [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

Based on the data from the table, we can calculate that the Cheletropic product has the lowest energy and hence is thermodynamically favoured. As sulfur is larger than C, the resulting twist in the 6 membered ring in the Diels-Alder products have a ring strain due to inefficient sp<sup>3</sup> hybridisation, resulting in a highly distorted structure. This is in comparison to the Cheletropic product, which is able to adopt a planar configuration that maximises the distance between the O and the neighbouring H atoms. However, the Cheletropic reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

From the transition state HOMO, we can observe that both the endo and exo TS have stabilising secondary orbital interactions, therefore reducing the reaction barrier in these reactions. This also explains why the energy of the exo and endo TS are relatively close in energy. We can also see that the Cheletropic TS has no stabilising secondary interactions and is highly antisymmetric with many nodes, resulting a higher energy TS.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!rowspan="2" style="text-align: center;"|
! colspan="2" style="text-align: center;"| Diels-Alder Reaction
!rowspan="2" style="text-align: center;"| Cheletropic Reaction
|-
!style="text-align: center;"| ENDO
!style="text-align: center;"| EXO
|-
|style="text-align: center;"|Transition State
HOMO
| [[File:JDN15EXOHOMO.png]]
| [[File:JDN15ENDOHOMO.png]]
| [[File:JDN15CHEHOMO.png]]
|}

(It's pretty hard to see what's going on in these MO pictures. Perhaps use transparent surfaces? [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)
!File Logs

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.105054
|style="text-align: center;" | 0.067300
|style="text-align: center;" | 119.8
|style="text-align: center;" | 20.7
|style="text-align: center;" | [[File:JDN15_EXO2_Product.LOG]]
[[File:JDN15_EXO_TS2.LOG]]
|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" | 0.102070
|style="text-align: center;" | 0.065612
|style="text-align: center;" | 112.0
|style="text-align: center;" | 16.3
|style="text-align: center;" | [[File:JDN15_ENDO2_Product.LOG]]
[[File:JDN15_ENDO2_TS.LOG]]
|}

Comparing the values from the table, we can see that both exo and endo for this Diels-Alder reaction has a much higher reaction barrier than the previous reactions (discussed earlier). Hence the secondary Diels-Alder reactions are the least kinetically favourable. We can also see that the reaction energies of the secondary Diels-Alder reactions are positive, indicating that the reaction is highly thermodynamically unfavourable as ΔG>0 and hence the reaction is not spontaneous.

==Conclusion==
Gaussian is a useful method to carry out molecular geometry optimisations and calculations. By investigating the free energies of the transition states and products, we can determine the reaction energies and reaction barriers of the reaction. We can then determine which reactions are kinetically or thermodynamically favoured. This computational method is a powerful tool that can be used for preliminary research before testing out the reactions experimentally. It also provides a visual representation that allows better understanding on the interactions between the MOs of the molecules before, during and after the reaction.

Rep:Mod:pk1615Yr3

2018-03-27T15:23:05Z

Fv611: /* Molecular orbital analysis */

=Transition states and reactivity=

==Introduction==
This experiment involves using computational quantum chemistry methods to analyse molecular structures, their molecular orbitals (MO's) and energetics. Providing information about reaction pathways, activation energies and transition state (TS) intermediates. The transition state structures that are investigated are based on the shape of the potential energy surface; these are found through computational molecular-orbital based methods by solving the Schrödinger equation. The computational methods used to optimise and run frequency calculations on molecular structures are the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP.
<br>
===Computational methods used===
The semi-empirical PM6 method is based on the Hartree–Fock (HF) formalism, in which the wavefunction of a system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The PM6 method differs with the HF method as it makes many approximations and obtains some parameters from empirical data. This method is used for molecules where the full HF method of optimisation without any approximations is too expensive. The fact that the PM6 method incorporates empirical data as approximations allows for optimisation to be fast as less calculations need to be made. However, these approximations mean that results are less accurate. On the other hand, the B3LYP method is a DFT-hybrid method which is based on electron density in antithesis to the PM6 which is based on wavefunctions. The B3LYP method, which incorporates both the HF and DFT methods, uses less approximations making it a more accurate but more computationally expensive optimisation method compared to the PM6 method.
<br>
[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:19, 22 March 2018 (UTC) This is good you have clearly shown some understanding here and you are correct. However it would have been good to show some equations here to help back up your discussion.

===The Potential Energy Surface of a system===
The Potential Energy Surface (PES) describes the energy of a system in terms of parameters such as the positions of atoms in a structure. For a molecule with N<sub>atoms</sub> there are 3N<sub>atoms</sub>-6 independent geometric variables that are determined; including bond lengths, bond angles and torsional angles. Using computational methods the points of a potential energy curve can be determined and analysis of its first and second derivatives yields important information about the systems reaction energetics. The first derivatives give the gradient and the second derivatives give the curvature of the (PES). Points with zero gradient are minima which correspond to products, or can be saddle points, energy maxima, that represent transition state species. The transition state is an intermediate structure between reactants and products in the reaction pathway; it is a maximum in the potential energy curve that requires maximum energy to be overcome to result in products.
<br>

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:22, 22 March 2018 (UTC) IT is only a maximum in the reaction coordinate.

The PES curve's first derivative can be related to the force acting on atoms which acts in the direction that will lower potential energy, giving it a negative value. At bond length distances above the equilibrium bond length the potential energy curve gradient is positive and the force acting upon it to reach the minimum equilibrium length point on the curve is negative. At bond length distances below the equilibrium bond length the potential energy curve gradient is negative and the force acting on it to increase the bond length is positive<ref name="intro" />. Since the TS is at the maxima the force acts on it in the direction to minimise bond length to reach products indicating it has a negative force constant. A TS can therefore be identified by an imaginary frequency in its first vibrational mode since calculating the frequency of a harmonic oscillator with a negative force constant yields an imaginary frequency. This frequency calculation was a method to confirm if a TS structure was created after optimisation.
<br>

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:22, 22 March 2018 (UTC) Technically the force constant comes from diagonalisation of the hessian matrix, which bring the coordingates into the basis of the normal modes which is a linear combination of the degrees of freedom. Hence when you move back an forth along this vector you ae changing them all at the same time. hence why it looks like a vibration.

The reactions that will be studied using these computational methods are pericyclic reactions which occur through a cyclic TS in a concerted fashion. More specifically Diels-Alder cycloadditions will be looked into where a [4+2] cycloaddition occurs to form a 6-membered ring system.

==Exercise 1==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job across the whole exercise. Well done!)

[[File:Overall reaction pk1615.PNG|thumb|400px|centre|Scheme 1:Diels-Alder reaction of butadiene and ethene]]

The transition state of the Diels-Alder reaction between butadiene and ethene, shown above in scheme 1, will be studied. This reaction involves a [4+2] cycloaddition between the two reactant molecules resulting in a ring product. The PM6 optimisation method was used in this exercise to optimise the reaction molecules.
<br>

===Molecular orbital analysis===

Optimising the reactants, transition state and product molecules revealed the energies and shape of the molecular orbitals for each structure. This then helped to identify the reactant HOMO and LUMO MO's that reacted to form the transition state, leading to the construction of the molecular orbital diagram for the transition state, figure 2.
{|style="margin: 0 auto;"
| [[File:Mos of butadiene ethene word pk1615.PNG|thumb|upright|344x344px|Figure 1:Molecular orbital energy levels of butadiene and ethene.]]
| [[File:Mo diagram butadiene pk1615.PNG|thumb|upright|500x500px|Figure 2:Molecular orbital diagram of the Diels-Alder transition state.]]
|}
<br>

{| class="wikitable"
! Ethene MO's
! Butadiene MO's
! Transition state Mo's
|-
| Ethene-φ1 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ2 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene-φ2 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ3 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The Jmols of the MO's of the reactants and TS have been displayed above. It is observed that for a molecular orbital to react successfully and produce a product they need to be of the same symmetry. In the MO diagram it can be seen that symmetric reacts with symmetric and anti-symmetric reacts with anti-symmetric orbitals to product a TS HOMO or LUMO of the same symmetry.If they are of different symmetry the reaction is disallowed. This is seen where the butadiene HOMO which is asymmetric reacts with the ethene LUMO, also asymmetric, to product TS HOMO 1 and LUMO 2 which are both asymmetric.

The overlap integral for a symmetric-antisymmetric interaction is zero, whereas for a symmetric-symmetric or antisymmetric-antisymmetric interaction a non-zero value is obtained. The transition state MO diagram reveals that the transition state orbitals produced arise from s-s or a-a interactions, these inteaction contain non-zero overlap integrals, yielding true MO's.

===Carbon-Carbon bond length analysis===

{| class="wikitable"
|+ Table 1-Carbon-Carbon bond lengths of the reactants, TS and products.
! Carbon bonds
! Ethene bond lengths (Å)
[[File:Ethene pk1615.PNG]]
! Butadiene bond lengths (Å)
[[File:Butadiene pk1615.PNG]]
! Transition state bond lengths (Å)
[[File:Ts pk1615.PNG]]
! Cyclohexene bond lengths (Å)
[[File:Product pk1615.PNG]]
! Bond length change
|-
| C<sub>1</sub>-C<sub>2</sub>
| 1.327
| -
| 1.380
| 1.538
|Increase
|-
| C<sub>2</sub>-C<sub>3</sub>
| -
| -
| 2.115
| 1.536
|Decrease
|-
| C<sub>3</sub>-C<sub>4</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>4</sub>-C<sub>5</sub>
| -
| 1.471
| 1.411
| 1.333
|Decrease
|-
| C<sub>5</sub>-C<sub>6</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>6</sub>-C<sub>1</sub>
| -
| -
| 2.114
| 1.536
|Decrease
|}

The typical length for a C-C sp<sup>3</sup> bond is 1.54 Å, whereas the length of a C-C sp<sup>2</sup> bond is 1.34 Å <ref name="C length" />. In table 1 it can be seen that single and double bond values are approximately the same length as the typical values expected, confirming the structures obtained through optimisation. For example the bond between C<sub>1</sub>-C<sub>2</sub> is seen to increase as the bond becomes sp<sup>3</sup> hybridised from sp<sup>2</sup>.
<br>
The Van der Waals radius of a carbon atom is 1.7 Å <ref name="C radius" />. In the Diels-Alder transition state is can be seen that the bonds that form between C<sub>6</sub>-C<sub>1</sub> and C<sub>2</sub>-C<sub>3</sub>, 2.1 Å, are shorter than two carbon Van der Waals radii values, 3.4 Å. This confirms that in the TS the molecules, that were far apart, gradually come closer; when they are found within less than two carbon Van der Waals radii they are able to approach the formation of a single bond that is found in the products.
<br>

===Transition state vibration===
The vibration that corresponds to the reaction path at the transition state is identified as the one with a negative frequency, known as the imaginary frequency stated above. The Diels-Alder transition state at this vibration is displayed below. It can be seen that at this transition state vibration the bonds between the two reactants form in a synchronous manner, this is seen by the movement of the displacement vectors that move towards each other at the same time. This synchronous bond formation is further confirmed by the analysis of the IRC that shows the reactions proceeds through a concerted mechanism. This is the typical mechanism pathway found for Diels-Alder cycloadditions.

<jmol>
<jmolApplet>
<title>Transition state vibration</title>
<color>white</color>
<size>300</size>
<script>frame 17; vibration 1;rotate x -20; </script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The IRC for the Diels-Alder transition state can be found [[Media:CH IRC PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene TS can be found [[Media:CH OPT TS PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene product can be found [[Media:CH OPT MIN PRODUCTS pk1615.LOG|here]]

==Exercise 2==
[[File:Exercise 2 overall reactionpk1615.PNG|thumb|400px|centre|Scheme 2:Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole]]
In this exercise the [4+2] cycloaddition reaction between cyclohexadiene and 1,3-dioxole is investigated. This Diels-Alder reaction yields two products, the exo and endo products, due to the different symmetries of the transition state.
<br>
===Molecular orbital analysis===
Using the B3LYP optimisation method the TS for both the exo and endo molecules was determined. This yielded the occupied, HOMO, and unoccupied, LUMO, orbitals and their energies for each TS. The HOMO and LUMO orbitals for both symmetries are displayed below. These were then used to construct an MO diagram for this Diels-Alder reaction, figure 3, which was based on the MO diagram of the butadiene and ethene TS as these reacting molecules are symmetrically similar.

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>EXO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>EXO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>ENDO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
[[File:Exercise 2 mo edited pk1615.PNG|thumb|400px|centre|Figure 3:Molecular orbital diagram of Cyclohexadiene and 1,3-Dioxole TS (the exo TS has been draw, however, the same orbitals apply for the endo TS)]]

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) The MO diagrams of endo and exo are different and you should have discussed the reasons why that might be. Addiyionally your MO diagram is missing symmetry labels.)

According to symmetry the cyclohexadiene and 1,3-dioxole MO's can be considered as the butadiene and ethene MO's from figure 2 respectively. The energy levels of the reactant and TS orbitals has been determined from their B3LYP/6-31G(d) optimised .chk file MO's, and have been positioned accordingly. It is observed that the energy level of these MO's is slightly shifted compared to the butadiene ethene MO's. The cyclohexadiene HOMO is lower in energy than the 1,3-dioxole HOMO, whereas, in figure 2, the butadiene HOMO is higher in energy compared to the ethene HOMO. It is to be noted that both the exo and endo TS have different geometries and their MO's differ slightly in energy, however,they both contain the same molecular orbital combinations and their MO's are found in similar energetic regions compared to reactant MO's, therefore, one molecular orbital diagram has been drawn for both.
<br>
The .log files for the B3LYP/6-31G(d) optimised molecules can be found here:[[Media:CYCLOHEXANE OPT FREQ MIN B pk1615.LOG|Cyclohexadiene]], [[Media:CYCLOPENTADIENE OPT FREQ MIN B pk1615.LOG|1,3-dioxole]], [[Media:EXO TS OPT FREQ B pk1615.LOG |Exo TS]], [[Media:ENDO_TS_OPT_FREQ_TS_B pk1615.LOG|Endo TS]], [[Media:EXO PRODUCT OPT FREQ MIN B. pk1615LOG|Exo product]], [[Media:ENDO PRODUCT OPT FREQ MIN B pk1615.LOG|Endo product]].

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:40, 22 March 2018 (UTC) You shouldnt comapre the MOs energies of things on different PESs because they experience different potentials and therefore it is meaningless to compare them

===Normal and Inverse demand Diels-Alder reaction analysis===
In a normal demand Diels-Alder reaction the HOMO of the electron rich diene reacts with the LUMO, π<sup>*</sup> bond, of the electron deficient dienophile ( the substituted alkene). In a normal demand reaction the HOMO of the diene reacts with the LUMO of the dienophile to form the HOMO and LUMO of the TS, this is seen in the reaction between butadiene (diene) and ethene (dienophile), figure 2, which produces HOMO 2 and LUMO 1.
<br>
In an inverse demand reaction, an electron deficient diene's LUMO now reacts with an electron rich dienophile's HOMO. This occurs due to a switch in energies of the diene's and dienophile's orbitals which occurs when an electron withdrawing group is attached to the diene, lowering its HOMO, and/or an electron donating group is attached to the dienophile, raising its π orbital's energy making it's HOMO higher in energy. This leads to the dienophile HOMO being high enough in energy to react with the diene's LUMO. This case is seen in the reaction between cyclohexadiene and 1,3-dioxole, figure 3, in which the dienophile, 1,3-dioxole, has electron donating oxygen atoms attached to it, raising its HOMO and allowing the TS HOMO 2 and LUMO 1 to be reached in an inverse demand reaction.
[[File:Inverse demand pk1615 .PNG|thumb|400px|centre|Figure 4:Diels-Alder normal and inverse reaction molecular orbital analysis]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:43, 22 March 2018 (UTC) Nicely explained well done.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:45, 22 March 2018 (UTC) However you have only explained this qualitatively and not quantitatively. you can do this by lookng at the energy of the reactant MOs on the same PES (first point on IRC).

==Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the B3LYP/6-31G(d) optimised .log files
{| class="wikitable"
|+ Table 2-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| Cyclohexadiene
| -233.324374
| -612593.1906
|-
| 1,3-dioxole
| -267.068642
| -701188.773
|-
| Reactants combined
| -500.393016
| -1313781.964
|-
| Endo TS
| -500.332146
| -1313622.149
|-
| Exo TS
| -500.329167
| -1313614.328
|-
| Endo product
| -500.418692
| -1313849.376
|-
| Exo product
| -500.417319
| -1313845.771
|}

{| class="wikitable"
|+ Table 3-Endo and Exo reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 159.8142
| -67.41234
|-
| Exo
| 167.63557
| -63.80753
|}

Table 2 gives energy values of reactants, TS's and products for both the exo and endo geometries. These energy values were used to obtain calculations of the reaction barriers, also known as the activation energies, and the reaction energies for the endo and exo reaction pathways, table 3. The reaction barrier is the maximum energy in the reaction pathway which needs to be overcome for a reaction to proceed to its product. The reaction barrier energy is calculated as the TS minus the reactants and is the energy value needed to reach the maximum in the potential energy surface of the system. Furthermore, the reaction energy is calculated as the reactant minus the products and is the energy obtained when the minimum of the potential energy surface is reached. The results of the energy barriers and energies shown that the endo product is both the kinetically and thermodynamically stable product. This is explained through secondary orbital interactions that occur in the endo product between the ring π bond and the oxygen p-orbitals displayed in figure 5.
<br>
[[File:Endo stabilisation pk1615.PNG|thumb|400px|centre|Figure 5:Endo product secondary orbital stabilisation interaction]]
<br>
These secondary orbital interactions stabilise the product, making the endo product the lowest energy product, the thermodynamic one. Additionally, through stabilising the product these secondary orbital interactions lower the energy barrier of the endo reaction making it the more kinetically stable one as well. The kinetic product has the lower energy barrier i.e less energy is needed to overcome its activation energy. Moreover, steric reasons that may affect the exo product, making it both thermodynamically and kinetically less stable, are the repulsive interactions that could occur between the bridgehead carbons of the ring and the 1,3-dioxole oxygens that are closer in the exo geometry. This could lead to destabilisation of the exo product molecule.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:46, 22 March 2018 (UTC) Good section, but you could have gone into more detail in parts. But your energies were correct and you have come to the correct conclusions.

==Exercise 3==
[[File:Diels alder cheletropic pk1615.PNG|thumb|400px|centre|Scheme 3:Diels-Alder/Cheletropic reaction of o-Xylylene and SO<sub>2</sub>]]
This exercise involves studying the Diels-Alder and Cheletropic reactions between o-Xylylene- and SO<sub>2</sub>, dispayed in scheme 3.
<br>
The IRC for the three reaction pathways can be found here: [[Media:XYLENE ENDO IRC pk1615.LOG|Diels-Alder endo]], [[Media:XYLENE EXO IRC PM6 pk1615.LOG|Diels-Alder exo]], [[Media:ISO-INDENE IRC PM6 pk1615.LOG|Cheletropic]].
<br>
The PM6 optimised .log files for the reaction molecules can be found here: [[Media:XYLYLENE REACTANT OPT MIN PM6 pk1615.LOG|o-Xylylene]], [[Media:SO2 OPT MIN PM6 pk1615.LOG|SO<sub>2</sub>]], [[Media:XYLENE OPT TS PM6 ENDO pk1615.LOG|Endo TS]], [[Media:XYLENE OPT TS PM6 exo pk1615.LOG|Exo TS]], [[Media:ISO-INDENE OPT TS PM6 pk1615.LOG|Cheletropic TS]], [[Media:XYLENE OPT MIN PM6 ENDO pk1615.LOG|Endo product]], [[Media:XYLENE OPT MIN PM6 pk1615 exo.LOG|Exo product]], [[Media:ISO-INDENE OPT MIN PM6 pk1615.LOG|Cheletropic product]].
===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the PM6 optimised .log files.
{| class="wikitable"
|+ Table 4-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| ortho-Xylylene
| 0.177678
| 466.493625
|-
| SO<sub>2</sub>
| -0.119269
| -313.1407834
|-
| Reactants
| 0.058409
| 153.352841
|-
| DA Endo TS
| 0.090560
| 237.765298
|-
| DA Exo TS
| 0.092077
| 241.748182
|-
| Cheletropic TS
| 0.099061
| 260.084675
|-
| DA Endo product
| 0.021705
| 56.9864818
|-
| DA Exo product
| 0.021454
| 56.3274813
|-
| Cheletropic Product
| 0.000005
| 0.013127501
|}

{| class="wikitable"
|+ Table 5-Reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 84.4124569
| -96.3663593
|-
| Exo
| 88.3953407
| -97.0253599
|-
| Cheletropic
| 106.731834
| -153.339714
|}
<br>
The most favourable route in this reaction is the endo route. As seen in table 5 the endo TS has the lowest reaction barrier energy, therefore, it is easier to overcome this reaction barrier to reach the TS and get a product. This lower energy barrier value is due to the endo TS and product having the secondary orbital interactions stated above; now between the oxygen p orbital and the pi orbitals of the conjugated benzene ring. These secondary orbital interactions stabilise the molecule, lowering its reaction energy barrier. It is to be noted that the cheletropic product is the more thermodynamically stable one but has a very high energy barrier which is unfavourable to reach as a lot of energy is needed to overcome it; this is an undesirable route. The endo product is the kinetically stable one and is the route that is preferred. A reaction profile diagram for the three pathways has been constructed in figure 6, enabling their energetics to be compared.

(You should show this secondary orbital overlap too [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 16 March 2018 (UTC))

<br>
[[File:Exercise 3 reaction coordinate 3.PNG|thumb|400px|centre|Figure 6:Reaction profile diagram]]
<br>
Observing the IRC paths for the three reaction TS's, it can be seen that the xylylene 6-membered ring bonds change in length as the reaction proceeds from reactants to products through the TS. The xylylene ring obtains aromaticity as the bond length changes, this could be considered a driving force for the reaction and proves the molecule's instability as it readily rearranges as the reaction proceeds to the product.

===An alternative reaction route===
An alternative reaction route can occur in the Diels-Alder reaction between o-Xylylene and SO<sub>2</sub>, where the SO<sub>2</sub> molecule reacts with the diene inside the six-membered ring of the xylylene molecule. This approach is displayed in scheme 4.
[[File:Alternative route pk1615.PNG|thumb|400px|centre|Scheme 4:Diels-Alder alternative reaction of o-Xylylene and SO<sub>2</sub>]]
{| class="wikitable"
|+ Table 6-Reaction barriers and energies.
! Reaction
! Energy barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 114.631969
| -18.906229
|-
| Exo
| 122.469083
| -23.353824
|}

(The reaction energies are not negative by my calculations [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 16 March 2018 (UTC))

<br>
This endo and exo route are neither thermodynamically or kinetically stable since they have low reaction energy values (are not stable) and have high energy barriers. These high energy barriers require large amounts of energy to be overcome which is undesirable and would lead to products that are not very thermodynamically stable.
<br>
The IRC for the the alternative reaction pathways can be found here: [[Media:ENDO TS IRC pk1615.LOG|Alternative Diels-Alder endo]], [[Media:EXO TS IRC pk1615.LOG|Alternative Diels-Alder exo]].

==Further work==
An electrocyclic reaction is a pericyclic reaction that involves a rearrangement of a pi to a sigma bond to form a ring product, such as the one displayed in scheme 5.
[[File:Electrocyclic pk1615.PNG|thumb|400px|centre|Scheme 5: Electrocyclic reaction.]]
<br>
[[File:Further work disrotation pk1615.PNG|thumb|400px|centre|Figure 7: Electrocyclic reaction orbital alignment.]]
<br>
This reaction is photochemically allowed to occur in a 4π disrotatory mechanism according to the Woodward-Hoffmann rules. The molecular orbital interactions that yield the ring product are shown in figure 7. It can be seen that the orbitals move in a disrotatory fashion. The TS of the molecule was optimised to the PM6 level and the MO's where identified in order to confirm their movement.

(It's true that it would undergo disrotation under photochemical conditions, but you are running these calculations on the ground state ie thermal. Your IRC actually goes via conrotation (HOMO) if you observe it [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:37, 16 March 2018 (UTC))

<br>
{|style="margin: 0 auto;"
| [[File:Further work reactant MO pk1615.PNG|thumb|upright|344x344px|Figure 8: Reactant MO (1).]]
| [[File:Further work TS MO pk1615.PNG|thumb|upright|344x344px|Figure 9: TS MO (3).]]
|}
<br>
Even though the PM6 level of optimisation is not the most accurate for viewing the correct symmetry of the MO's; it is concluded through the MO's that this electrocyclic reaction proceeds with disrotatory motion, as the orbitals allign as expected in the TS LUMO of the molecule leading to the formation of the sigma bond. A higher level of optimisation would be more suitable to determine the direction of orbital movement.
<br>
The IRC for the TS can be found [[Media:TS IRC pk1615.LOG|here]].
<br>
The PM6 optimised .log files can be found here: [[Media:REACTANTS OPT MIN PM6 pk1615.LOG|Reactant]], [[Media:PRODUCT OPT TS PM6 pk1615.LOG|TS]], [[Media:PRODUCT OPT MIN PM6 pk1615.LOG|Product]].

==Conclusion==
Over the years computational chemistry has been and is still being widely developed. It provides the opportunity to optimise structures; revealing information about their bond lengths, bond angles, MO's and their energetics. These optimised structures can then be used for comparison to synthetically formed structures in the lab. Optimisation methods such as the PM6 and B3LYP methods have proven to yield accurate results for molecules and TS's that can be used to further analyse and compare the thermochemistry of reactions. A huge advantage of quantum computational chemistry is that it allows for the prediction and analysis of a TS that cannot be isolated as an individual structure in the physical world, as in the case of the pericyclic reactions that have been investigated in this experiment.

==References==
<references>
<ref name="intro">Computational Quantum Chemistry. Chapter 1, 2013, Pages 1-62.</ref>
<ref name="C length">B.P. Stoicheff. "The variation of carbon-carbon bond lengths with environment as determined by spectroscopic studies of simple polyatomic molecules". Tetrahedron, Vol 17, Issues 3–4, 1962, Pages 135-145.</ref>
<ref name="C radius">A Bondi. "Van der Waals Volumes and Radii". J. Phys. Chem., 68 (3), 1964, Pages 441–451.</ref>
</references>

Rep:Mod:pk1615Yr3

2018-03-27T15:19:19Z

Fv611: /* Exercise 1 */

=Transition states and reactivity=

==Introduction==
This experiment involves using computational quantum chemistry methods to analyse molecular structures, their molecular orbitals (MO's) and energetics. Providing information about reaction pathways, activation energies and transition state (TS) intermediates. The transition state structures that are investigated are based on the shape of the potential energy surface; these are found through computational molecular-orbital based methods by solving the Schrödinger equation. The computational methods used to optimise and run frequency calculations on molecular structures are the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP.
<br>
===Computational methods used===
The semi-empirical PM6 method is based on the Hartree–Fock (HF) formalism, in which the wavefunction of a system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The PM6 method differs with the HF method as it makes many approximations and obtains some parameters from empirical data. This method is used for molecules where the full HF method of optimisation without any approximations is too expensive. The fact that the PM6 method incorporates empirical data as approximations allows for optimisation to be fast as less calculations need to be made. However, these approximations mean that results are less accurate. On the other hand, the B3LYP method is a DFT-hybrid method which is based on electron density in antithesis to the PM6 which is based on wavefunctions. The B3LYP method, which incorporates both the HF and DFT methods, uses less approximations making it a more accurate but more computationally expensive optimisation method compared to the PM6 method.
<br>
[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:19, 22 March 2018 (UTC) This is good you have clearly shown some understanding here and you are correct. However it would have been good to show some equations here to help back up your discussion.

===The Potential Energy Surface of a system===
The Potential Energy Surface (PES) describes the energy of a system in terms of parameters such as the positions of atoms in a structure. For a molecule with N<sub>atoms</sub> there are 3N<sub>atoms</sub>-6 independent geometric variables that are determined; including bond lengths, bond angles and torsional angles. Using computational methods the points of a potential energy curve can be determined and analysis of its first and second derivatives yields important information about the systems reaction energetics. The first derivatives give the gradient and the second derivatives give the curvature of the (PES). Points with zero gradient are minima which correspond to products, or can be saddle points, energy maxima, that represent transition state species. The transition state is an intermediate structure between reactants and products in the reaction pathway; it is a maximum in the potential energy curve that requires maximum energy to be overcome to result in products.
<br>

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:22, 22 March 2018 (UTC) IT is only a maximum in the reaction coordinate.

The PES curve's first derivative can be related to the force acting on atoms which acts in the direction that will lower potential energy, giving it a negative value. At bond length distances above the equilibrium bond length the potential energy curve gradient is positive and the force acting upon it to reach the minimum equilibrium length point on the curve is negative. At bond length distances below the equilibrium bond length the potential energy curve gradient is negative and the force acting on it to increase the bond length is positive<ref name="intro" />. Since the TS is at the maxima the force acts on it in the direction to minimise bond length to reach products indicating it has a negative force constant. A TS can therefore be identified by an imaginary frequency in its first vibrational mode since calculating the frequency of a harmonic oscillator with a negative force constant yields an imaginary frequency. This frequency calculation was a method to confirm if a TS structure was created after optimisation.
<br>

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:22, 22 March 2018 (UTC) Technically the force constant comes from diagonalisation of the hessian matrix, which bring the coordingates into the basis of the normal modes which is a linear combination of the degrees of freedom. Hence when you move back an forth along this vector you ae changing them all at the same time. hence why it looks like a vibration.

The reactions that will be studied using these computational methods are pericyclic reactions which occur through a cyclic TS in a concerted fashion. More specifically Diels-Alder cycloadditions will be looked into where a [4+2] cycloaddition occurs to form a 6-membered ring system.

==Exercise 1==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job across the whole exercise. Well done!)

[[File:Overall reaction pk1615.PNG|thumb|400px|centre|Scheme 1:Diels-Alder reaction of butadiene and ethene]]

The transition state of the Diels-Alder reaction between butadiene and ethene, shown above in scheme 1, will be studied. This reaction involves a [4+2] cycloaddition between the two reactant molecules resulting in a ring product. The PM6 optimisation method was used in this exercise to optimise the reaction molecules.
<br>

===Molecular orbital analysis===

Optimising the reactants, transition state and product molecules revealed the energies and shape of the molecular orbitals for each structure. This then helped to identify the reactant HOMO and LUMO MO's that reacted to form the transition state, leading to the construction of the molecular orbital diagram for the transition state, figure 2.
{|style="margin: 0 auto;"
| [[File:Mos of butadiene ethene word pk1615.PNG|thumb|upright|344x344px|Figure 1:Molecular orbital energy levels of butadiene and ethene.]]
| [[File:Mo diagram butadiene pk1615.PNG|thumb|upright|500x500px|Figure 2:Molecular orbital diagram of the Diels-Alder transition state.]]
|}
<br>

{| class="wikitable"
! Ethene MO's
! Butadiene MO's
! Transition state Mo's
|-
| Ethene-φ1 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ2 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene-φ2 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ3 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The Jmols of the MO's of the reactants and TS have been displayed above. It is observed that for a molecular orbital to react successfully and produce a product they need to be of the same symmetry. In the MO diagram it can be seen that symmetric reacts with symmetric and anti-symmetric reacts with anti-symmetric orbitals to product a TS HOMO or LUMO of the same symmetry.If they are of different symmetry the reaction is disallowed. This is seen where the butadiene HOMO which is asymmetric reacts with the ethene LUMO, also asymmetric, to product TS HOMO 1 and LUMO 2 which are both asymmetric.

The overlap integral for a symmetric-antisymmetric interaction is zero, whereas for a symmetric-symmetric or antisymmetric-antisymmetric interaction a non-zero value is obtained. The transition state MO diagram reveals that the transition state orbitals produced arise from s-s or a-a interactions, these inteaction contain non-zero overlap integrals, yielding true MO's.

===Carbon-Carbon bond length analysis===

{| class="wikitable"
|+ Table 1-Carbon-Carbon bond lengths of the reactants, TS and products.
! Carbon bonds
! Ethene bond lengths (Å)
[[File:Ethene pk1615.PNG]]
! Butadiene bond lengths (Å)
[[File:Butadiene pk1615.PNG]]
! Transition state bond lengths (Å)
[[File:Ts pk1615.PNG]]
! Cyclohexene bond lengths (Å)
[[File:Product pk1615.PNG]]
! Bond length change
|-
| C<sub>1</sub>-C<sub>2</sub>
| 1.327
| -
| 1.380
| 1.538
|Increase
|-
| C<sub>2</sub>-C<sub>3</sub>
| -
| -
| 2.115
| 1.536
|Decrease
|-
| C<sub>3</sub>-C<sub>4</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>4</sub>-C<sub>5</sub>
| -
| 1.471
| 1.411
| 1.333
|Decrease
|-
| C<sub>5</sub>-C<sub>6</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>6</sub>-C<sub>1</sub>
| -
| -
| 2.114
| 1.536
|Decrease
|}

The typical length for a C-C sp<sup>3</sup> bond is 1.54 Å, whereas the length of a C-C sp<sup>2</sup> bond is 1.34 Å <ref name="C length" />. In table 1 it can be seen that single and double bond values are approximately the same length as the typical values expected, confirming the structures obtained through optimisation. For example the bond between C<sub>1</sub>-C<sub>2</sub> is seen to increase as the bond becomes sp<sup>3</sup> hybridised from sp<sup>2</sup>.
<br>
The Van der Waals radius of a carbon atom is 1.7 Å <ref name="C radius" />. In the Diels-Alder transition state is can be seen that the bonds that form between C<sub>6</sub>-C<sub>1</sub> and C<sub>2</sub>-C<sub>3</sub>, 2.1 Å, are shorter than two carbon Van der Waals radii values, 3.4 Å. This confirms that in the TS the molecules, that were far apart, gradually come closer; when they are found within less than two carbon Van der Waals radii they are able to approach the formation of a single bond that is found in the products.
<br>

===Transition state vibration===
The vibration that corresponds to the reaction path at the transition state is identified as the one with a negative frequency, known as the imaginary frequency stated above. The Diels-Alder transition state at this vibration is displayed below. It can be seen that at this transition state vibration the bonds between the two reactants form in a synchronous manner, this is seen by the movement of the displacement vectors that move towards each other at the same time. This synchronous bond formation is further confirmed by the analysis of the IRC that shows the reactions proceeds through a concerted mechanism. This is the typical mechanism pathway found for Diels-Alder cycloadditions.

<jmol>
<jmolApplet>
<title>Transition state vibration</title>
<color>white</color>
<size>300</size>
<script>frame 17; vibration 1;rotate x -20; </script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The IRC for the Diels-Alder transition state can be found [[Media:CH IRC PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene TS can be found [[Media:CH OPT TS PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene product can be found [[Media:CH OPT MIN PRODUCTS pk1615.LOG|here]]

==Exercise 2==
[[File:Exercise 2 overall reactionpk1615.PNG|thumb|400px|centre|Scheme 2:Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole]]
In this exercise the [4+2] cycloaddition reaction between cyclohexadiene and 1,3-dioxole is investigated. This Diels-Alder reaction yields two products, the exo and endo products, due to the different symmetries of the transition state.
<br>
===Molecular orbital analysis===
Using the B3LYP optimisation method the TS for both the exo and endo molecules was determined. This yielded the occupied, HOMO, and unoccupied, LUMO, orbitals and their energies for each TS. The HOMO and LUMO orbitals for both symmetries are displayed below. These were then used to construct an MO diagram for this Diels-Alder reaction, figure 3, which was based on the MO diagram of the butadiene and ethene TS as these reacting molecules are symmetrically similar.

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>EXO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>EXO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>ENDO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
[[File:Exercise 2 mo edited pk1615.PNG|thumb|400px|centre|Figure 3:Molecular orbital diagram of Cyclohexadiene and 1,3-Dioxole TS (the exo TS has been draw, however, the same orbitals apply for the endo TS)]]

According to symmetry the cyclohexadiene and 1,3-dioxole MO's can be considered as the butadiene and ethene MO's from figure 2 respectively. The energy levels of the reactant and TS orbitals has been determined from their B3LYP/6-31G(d) optimised .chk file MO's, and have been positioned accordingly. It is observed that the energy level of these MO's is slightly shifted compared to the butadiene ethene MO's. The cyclohexadiene HOMO is lower in energy than the 1,3-dioxole HOMO, whereas, in figure 2, the butadiene HOMO is higher in energy compared to the ethene HOMO. It is to be noted that both the exo and endo TS have different geometries and their MO's differ slightly in energy, however,they both contain the same molecular orbital combinations and their MO's are found in similar energetic regions compared to reactant MO's, therefore, one molecular orbital diagram has been drawn for both.
<br>
The .log files for the B3LYP/6-31G(d) optimised molecules can be found here:[[Media:CYCLOHEXANE OPT FREQ MIN B pk1615.LOG|Cyclohexadiene]], [[Media:CYCLOPENTADIENE OPT FREQ MIN B pk1615.LOG|1,3-dioxole]], [[Media:EXO TS OPT FREQ B pk1615.LOG |Exo TS]], [[Media:ENDO_TS_OPT_FREQ_TS_B pk1615.LOG|Endo TS]], [[Media:EXO PRODUCT OPT FREQ MIN B. pk1615LOG|Exo product]], [[Media:ENDO PRODUCT OPT FREQ MIN B pk1615.LOG|Endo product]].

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:40, 22 March 2018 (UTC) You shouldnt comapre the MOs energies of things on different PESs because they experience different potentials and therefore it is meaningless to compare them

===Normal and Inverse demand Diels-Alder reaction analysis===
In a normal demand Diels-Alder reaction the HOMO of the electron rich diene reacts with the LUMO, π<sup>*</sup> bond, of the electron deficient dienophile ( the substituted alkene). In a normal demand reaction the HOMO of the diene reacts with the LUMO of the dienophile to form the HOMO and LUMO of the TS, this is seen in the reaction between butadiene (diene) and ethene (dienophile), figure 2, which produces HOMO 2 and LUMO 1.
<br>
In an inverse demand reaction, an electron deficient diene's LUMO now reacts with an electron rich dienophile's HOMO. This occurs due to a switch in energies of the diene's and dienophile's orbitals which occurs when an electron withdrawing group is attached to the diene, lowering its HOMO, and/or an electron donating group is attached to the dienophile, raising its π orbital's energy making it's HOMO higher in energy. This leads to the dienophile HOMO being high enough in energy to react with the diene's LUMO. This case is seen in the reaction between cyclohexadiene and 1,3-dioxole, figure 3, in which the dienophile, 1,3-dioxole, has electron donating oxygen atoms attached to it, raising its HOMO and allowing the TS HOMO 2 and LUMO 1 to be reached in an inverse demand reaction.
[[File:Inverse demand pk1615 .PNG|thumb|400px|centre|Figure 4:Diels-Alder normal and inverse reaction molecular orbital analysis]]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:43, 22 March 2018 (UTC) Nicely explained well done.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:45, 22 March 2018 (UTC) However you have only explained this qualitatively and not quantitatively. you can do this by lookng at the energy of the reactant MOs on the same PES (first point on IRC).

==Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the B3LYP/6-31G(d) optimised .log files
{| class="wikitable"
|+ Table 2-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| Cyclohexadiene
| -233.324374
| -612593.1906
|-
| 1,3-dioxole
| -267.068642
| -701188.773
|-
| Reactants combined
| -500.393016
| -1313781.964
|-
| Endo TS
| -500.332146
| -1313622.149
|-
| Exo TS
| -500.329167
| -1313614.328
|-
| Endo product
| -500.418692
| -1313849.376
|-
| Exo product
| -500.417319
| -1313845.771
|}

{| class="wikitable"
|+ Table 3-Endo and Exo reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 159.8142
| -67.41234
|-
| Exo
| 167.63557
| -63.80753
|}

Table 2 gives energy values of reactants, TS's and products for both the exo and endo geometries. These energy values were used to obtain calculations of the reaction barriers, also known as the activation energies, and the reaction energies for the endo and exo reaction pathways, table 3. The reaction barrier is the maximum energy in the reaction pathway which needs to be overcome for a reaction to proceed to its product. The reaction barrier energy is calculated as the TS minus the reactants and is the energy value needed to reach the maximum in the potential energy surface of the system. Furthermore, the reaction energy is calculated as the reactant minus the products and is the energy obtained when the minimum of the potential energy surface is reached. The results of the energy barriers and energies shown that the endo product is both the kinetically and thermodynamically stable product. This is explained through secondary orbital interactions that occur in the endo product between the ring π bond and the oxygen p-orbitals displayed in figure 5.
<br>
[[File:Endo stabilisation pk1615.PNG|thumb|400px|centre|Figure 5:Endo product secondary orbital stabilisation interaction]]
<br>
These secondary orbital interactions stabilise the product, making the endo product the lowest energy product, the thermodynamic one. Additionally, through stabilising the product these secondary orbital interactions lower the energy barrier of the endo reaction making it the more kinetically stable one as well. The kinetic product has the lower energy barrier i.e less energy is needed to overcome its activation energy. Moreover, steric reasons that may affect the exo product, making it both thermodynamically and kinetically less stable, are the repulsive interactions that could occur between the bridgehead carbons of the ring and the 1,3-dioxole oxygens that are closer in the exo geometry. This could lead to destabilisation of the exo product molecule.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:46, 22 March 2018 (UTC) Good section, but you could have gone into more detail in parts. But your energies were correct and you have come to the correct conclusions.

==Exercise 3==
[[File:Diels alder cheletropic pk1615.PNG|thumb|400px|centre|Scheme 3:Diels-Alder/Cheletropic reaction of o-Xylylene and SO<sub>2</sub>]]
This exercise involves studying the Diels-Alder and Cheletropic reactions between o-Xylylene- and SO<sub>2</sub>, dispayed in scheme 3.
<br>
The IRC for the three reaction pathways can be found here: [[Media:XYLENE ENDO IRC pk1615.LOG|Diels-Alder endo]], [[Media:XYLENE EXO IRC PM6 pk1615.LOG|Diels-Alder exo]], [[Media:ISO-INDENE IRC PM6 pk1615.LOG|Cheletropic]].
<br>
The PM6 optimised .log files for the reaction molecules can be found here: [[Media:XYLYLENE REACTANT OPT MIN PM6 pk1615.LOG|o-Xylylene]], [[Media:SO2 OPT MIN PM6 pk1615.LOG|SO<sub>2</sub>]], [[Media:XYLENE OPT TS PM6 ENDO pk1615.LOG|Endo TS]], [[Media:XYLENE OPT TS PM6 exo pk1615.LOG|Exo TS]], [[Media:ISO-INDENE OPT TS PM6 pk1615.LOG|Cheletropic TS]], [[Media:XYLENE OPT MIN PM6 ENDO pk1615.LOG|Endo product]], [[Media:XYLENE OPT MIN PM6 pk1615 exo.LOG|Exo product]], [[Media:ISO-INDENE OPT MIN PM6 pk1615.LOG|Cheletropic product]].
===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the PM6 optimised .log files.
{| class="wikitable"
|+ Table 4-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| ortho-Xylylene
| 0.177678
| 466.493625
|-
| SO<sub>2</sub>
| -0.119269
| -313.1407834
|-
| Reactants
| 0.058409
| 153.352841
|-
| DA Endo TS
| 0.090560
| 237.765298
|-
| DA Exo TS
| 0.092077
| 241.748182
|-
| Cheletropic TS
| 0.099061
| 260.084675
|-
| DA Endo product
| 0.021705
| 56.9864818
|-
| DA Exo product
| 0.021454
| 56.3274813
|-
| Cheletropic Product
| 0.000005
| 0.013127501
|}

{| class="wikitable"
|+ Table 5-Reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 84.4124569
| -96.3663593
|-
| Exo
| 88.3953407
| -97.0253599
|-
| Cheletropic
| 106.731834
| -153.339714
|}
<br>
The most favourable route in this reaction is the endo route. As seen in table 5 the endo TS has the lowest reaction barrier energy, therefore, it is easier to overcome this reaction barrier to reach the TS and get a product. This lower energy barrier value is due to the endo TS and product having the secondary orbital interactions stated above; now between the oxygen p orbital and the pi orbitals of the conjugated benzene ring. These secondary orbital interactions stabilise the molecule, lowering its reaction energy barrier. It is to be noted that the cheletropic product is the more thermodynamically stable one but has a very high energy barrier which is unfavourable to reach as a lot of energy is needed to overcome it; this is an undesirable route. The endo product is the kinetically stable one and is the route that is preferred. A reaction profile diagram for the three pathways has been constructed in figure 6, enabling their energetics to be compared.

(You should show this secondary orbital overlap too [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 16 March 2018 (UTC))

<br>
[[File:Exercise 3 reaction coordinate 3.PNG|thumb|400px|centre|Figure 6:Reaction profile diagram]]
<br>
Observing the IRC paths for the three reaction TS's, it can be seen that the xylylene 6-membered ring bonds change in length as the reaction proceeds from reactants to products through the TS. The xylylene ring obtains aromaticity as the bond length changes, this could be considered a driving force for the reaction and proves the molecule's instability as it readily rearranges as the reaction proceeds to the product.

===An alternative reaction route===
An alternative reaction route can occur in the Diels-Alder reaction between o-Xylylene and SO<sub>2</sub>, where the SO<sub>2</sub> molecule reacts with the diene inside the six-membered ring of the xylylene molecule. This approach is displayed in scheme 4.
[[File:Alternative route pk1615.PNG|thumb|400px|centre|Scheme 4:Diels-Alder alternative reaction of o-Xylylene and SO<sub>2</sub>]]
{| class="wikitable"
|+ Table 6-Reaction barriers and energies.
! Reaction
! Energy barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 114.631969
| -18.906229
|-
| Exo
| 122.469083
| -23.353824
|}

(The reaction energies are not negative by my calculations [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 16 March 2018 (UTC))

<br>
This endo and exo route are neither thermodynamically or kinetically stable since they have low reaction energy values (are not stable) and have high energy barriers. These high energy barriers require large amounts of energy to be overcome which is undesirable and would lead to products that are not very thermodynamically stable.
<br>
The IRC for the the alternative reaction pathways can be found here: [[Media:ENDO TS IRC pk1615.LOG|Alternative Diels-Alder endo]], [[Media:EXO TS IRC pk1615.LOG|Alternative Diels-Alder exo]].

==Further work==
An electrocyclic reaction is a pericyclic reaction that involves a rearrangement of a pi to a sigma bond to form a ring product, such as the one displayed in scheme 5.
[[File:Electrocyclic pk1615.PNG|thumb|400px|centre|Scheme 5: Electrocyclic reaction.]]
<br>
[[File:Further work disrotation pk1615.PNG|thumb|400px|centre|Figure 7: Electrocyclic reaction orbital alignment.]]
<br>
This reaction is photochemically allowed to occur in a 4π disrotatory mechanism according to the Woodward-Hoffmann rules. The molecular orbital interactions that yield the ring product are shown in figure 7. It can be seen that the orbitals move in a disrotatory fashion. The TS of the molecule was optimised to the PM6 level and the MO's where identified in order to confirm their movement.

(It's true that it would undergo disrotation under photochemical conditions, but you are running these calculations on the ground state ie thermal. Your IRC actually goes via conrotation (HOMO) if you observe it [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:37, 16 March 2018 (UTC))

<br>
{|style="margin: 0 auto;"
| [[File:Further work reactant MO pk1615.PNG|thumb|upright|344x344px|Figure 8: Reactant MO (1).]]
| [[File:Further work TS MO pk1615.PNG|thumb|upright|344x344px|Figure 9: TS MO (3).]]
|}
<br>
Even though the PM6 level of optimisation is not the most accurate for viewing the correct symmetry of the MO's; it is concluded through the MO's that this electrocyclic reaction proceeds with disrotatory motion, as the orbitals allign as expected in the TS LUMO of the molecule leading to the formation of the sigma bond. A higher level of optimisation would be more suitable to determine the direction of orbital movement.
<br>
The IRC for the TS can be found [[Media:TS IRC pk1615.LOG|here]].
<br>
The PM6 optimised .log files can be found here: [[Media:REACTANTS OPT MIN PM6 pk1615.LOG|Reactant]], [[Media:PRODUCT OPT TS PM6 pk1615.LOG|TS]], [[Media:PRODUCT OPT MIN PM6 pk1615.LOG|Product]].

==Conclusion==
Over the years computational chemistry has been and is still being widely developed. It provides the opportunity to optimise structures; revealing information about their bond lengths, bond angles, MO's and their energetics. These optimised structures can then be used for comparison to synthetically formed structures in the lab. Optimisation methods such as the PM6 and B3LYP methods have proven to yield accurate results for molecules and TS's that can be used to further analyse and compare the thermochemistry of reactions. A huge advantage of quantum computational chemistry is that it allows for the prediction and analysis of a TS that cannot be isolated as an individual structure in the physical world, as in the case of the pericyclic reactions that have been investigated in this experiment.

==References==
<references>
<ref name="intro">Computational Quantum Chemistry. Chapter 1, 2013, Pages 1-62.</ref>
<ref name="C length">B.P. Stoicheff. "The variation of carbon-carbon bond lengths with environment as determined by spectroscopic studies of simple polyatomic molecules". Tetrahedron, Vol 17, Issues 3–4, 1962, Pages 135-145.</ref>
<ref name="C radius">A Bondi. "Van der Waals Volumes and Radii". J. Phys. Chem., 68 (3), 1964, Pages 441–451.</ref>
</references>

Rep:Mod:cjc415 TS

2018-03-27T14:21:57Z

Fv611: /* Molecular orbitals */

==Introduction==
This wiki explores a variety of pericyclic reactions, namely Diels-Alders and Cheletropic reactions and their transitions states.

===Potential energy surfaces (PES)===
A potential energy surface gives the energy of a molecule as a function of its geometry. It serves as a tool to help in the analysis of reaction dynamics and molecular geometry. The PES has a total of 3N-6 degrees of freedom.

At the stationary points, the gradient is equal to zero. These energy minima correspond to the physically stable species, such as reactants and products while transition states correspond to saddle points. When the second derivative is calculated, the energy minima and transition states can be differentiated. If a positive value is obtained, it suggests that an energy minima is obtained. Conversely, a negative value corresponds to a transition state.

This is also reflected in Gaussview. A transition state would produce one negative frequency while minima points will not reflect negative values, hence no imaginary frequencies are present.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:28, 21 March 2018 (UTC) what you are actually doing is finding the eigenvalues of the hessian which relate to the force constants. each one relates to a dimension of the PES. a TS only has 1 negative force constant.

===What is a transition state?===
A transition state (TS) is usually defined as a structure along the reaction coordinate which corresponds to the highest potential energy along this coordinate. In terms of mathematics, the TS of a chemical reaction represents a Saddle Point on the Potential Energy Surface (PES).

A transition state of a reactive pathway is the one with lowest energy compared to other paths perpendicular to it. It is also the highest energy point of that reactive pathway.

===Diels Alders reaction===
Otherwise known as a [4+2] cycloaddition, the Diels-Alder reaction involves a conjugated diene and an alkene, known as the dienophile. The reaction is concerted and occurs via a single, cyclic transition state.

Usually, the diene is electron-rich while the dienophile is electron poor. The HOMO of the diene would interact with the LUMO of the dienophile. However, there is also a possibility of an inverse electron demand Diels-Alder reaction, whereby it is the LUMO of the diene interacting with the HOMO of the dienophile. This can occur if electron withdrawing substituents are added to the diene and electron donating substituents are added to the dienophile. There are other types of Diels-Alder reactions, such as Hetero-Diels-Alder, which involves at least one heteroatom and lewis acid activation Diels-Alder reactions, which involves the use of lewis acids such as zinc chloride to act as catalysts of normal-demand Diels-Alder reactions by coordinating to the dienophile.

When selectivity issues arise, in the case of example 2, where the dienophile is substituted, this would give rise to the possibility of either the endo or exo product. The kinetic endo product is favoured in irreversible reactions due to the stabilisation of the endo transition state by dipolar, orbital and van der waals interactions. The exo product is considered the thermodynamic product due better sterics.

===Cheletropic reactions===
Cheletropic reactions are pericyclic reactions involving a transition state with a cyclic array of atoms and interacting orbitals. It would involve a reorganisation of sigma and pi bonds in the cyclic array. A key feature of these reactions are that in one of the reagents, both new bonds are being made on the same atom. In the case of example 3, both new bonds are made on the sulfur atom.

===Studying Transition States using Gaussview===
When more than one product can be formed, it is important to study the transition state. In the formation of kinetic products, the pathway which involves the lower activation energy and hence more stable transition state, is favoured. Should thermodynamic products be favoured, the more stable thermodynamic product is favoured.

Gaussview is being used to study these transition states. By optimising the structures in their transition states, the MOs and their respective energies can be analysed and extracted.

In this lab, semi-empirical PM6 and Density Function Theory (DFT) methods are being used to optimise the structures. PM6 is a faster but less accurate method. It replaces the two electron integrals, exchange and Coulomb integrals, which are challenging to determine.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:36, 21 March 2018 (UTC) Some equations would have been nice in this section, but good understanding.

DFT optimisations defines the energy of the system as a summation of 6 individual components, namely: nuclear-nuclear repulsion, nuclear-electron attraction, electron-electron coloumb repulsion, kinetic energy of electrons, electron-electron exchange energies and correlated movement of electrons of different spins.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:36, 21 March 2018 (UTC) All quantum chem methods split up the hamiltonian into these parts. DFT is only different because you have the exchange correlation term

==Exercise 1: Reaction of Butadiene with Ethylene==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job overall.)

===Overall reaction scheme===
[[Image:CJC Ex1 Rxn scheme.jpg |300px]]

It is to be noted that the trans-butadiene form is the lowest global energy minimum. However, it is the cis conformation that is reacting with ethene.

===Molecular orbitals===
The three tables below show the jmols of the optimised reactants (butadiene and ethene) as well as MO 16, 17, 18 and 19 of the transition state.

{| class="wikitable"
|-
| colspan="3"|'''Butadiene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
It is to be noted that the trans-butadiene form is the lowest global energy minimum. However, it is the cis conformation that is reacting with ethene.

{| class="wikitable"
|-
| colspan="3"|'''Ethene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You added the wrong JMol as an optimised structure (this is not a cope rearrangement).)
{| class="wikitable"
|-
| colspan="5"|'''Transition state'''
|-
! Optimised TS
! MO 16
! MO 17 (HOMO)
! MO 18 (LUMO)
! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The MO diagram for the transition state is shown below, with S representing 'Symmetric' and AS representing 'Asymmetric'.

It is assumed based on prior knowledge that only orbitals of the same symmetry combine.

It is to be noted that the MO for a TS is very much different compared to a reactant-product MO diagram. For a transition state MO, the resulting orbitals which the electrons occupy are destabilised and at a higher energy level with respect to the original orbitals in the reactants.

[[Image:CJC415 Ex1 MO.jpg |500px]]

The antisymmetric HOMO of butadiene (MO 11) reacts with the antisymmetric LUMO of ethene (MO 7) to give two antisymmetric MOs (MO 16 and 19).
Similarly, the symmetric LUMO of butadiene (MO 12) reacts with the symmetric HOMO of ethene (MO 6) to give two symmetric MOs (MO 17 and 18).

When symmetric and asymmetric orbitals overlap, the orbital overlap integral is zero, hence causing them to be unable to overlap, even if they are of similar energies. On the other hand, when two symmetric orbitals or two asymmetric orbitals overlap, the orbital overlap integral is non zero, allowing interaction to occur.

To determine the energy levels of the respective MOs in the TS with respect to the original MOs in butadiene and ethene, the energy levels of the MOs were compared. It was found that MO 16 and 17 were very similar in energy, at -0.32536 and -0.32531 respectively.

===Bond lengths===
{| class="wikitable"
|-
! Butadiene
! Ethene
! Cyclohexene
! Transition state
|-
|[[Image:CJC415 Ex1 Butadiene.bmp |80px]]
|[[Image:CJC415 Ex1 Ethene.bmp |50px]]
|[[Image:CJC415 Ex1 Cyclohexene.jpg |150px]]
|[[Image:CJC415 Ex1 TS.bmp |150px]]
|}

Going from reactants to TS and to products, the shortening of the C5-C6 bond, going from single to double bond was observed. Distances between C1-C2 and C3-C4 were also reduced as bonds were formed. Conversely, lengthening of C1-C6 and C4-C5 bonds were observed, going from double to single bonds.

The typical sp3 and sp2 C-C bond lengths are 1.54 Å and 1.34 Å respectively and the Van der Waals radius of the C atom is 1.70 Å. It can be noted that the partly formed C-C bonds (C1-C2 and C3-C4), which were at lengths 2.11Å in the TS, are longer than the typical sp3 bond, but also shorter than twice the radius of the carbon atom. This would suggest that the orbitals are sufficiently close to interact but the formation of a full C-C bond has yet to be completed.

===Reaction pathway===
From the jmol file shown below, formation of bonds between diene and dienophile took place simultaneously, hence bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 109; vibration 1</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Molecular orbitals===
The jmols of the optimised reactants and products are shown in the tables below. They were optimized using the B3LYP 6-31G(d) level.

{| class="wikitable"
|-
| colspan="3"|'''Cyclohexadiene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="3"|'''1,3 dioxole'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="2"|'''Optimised products'''
|-
! Exo product
! Endo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 EXO PRODUCT MINIMISED B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 ENDO PRODUCT MINIMISED B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

At the transition state, the interactions between the 4 MOs (shown above) produced the following 4 MOs for the endo and exo products accordingly.

{| class="wikitable"
|-
| colspan="5"|'''Transition State MOs - Exo product'''
|-
! Optimised molecule
! MO 40
! MO 41 (HOMO)
! MO 42 (LUMO)
! MO 43
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="5"|'''Transition State MOs - Endo product'''
|-
! Optimised molecule
! MO 40
! MO 41 (HOMO)
! MO 42 (LUMO)
! MO 43
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the energy levels obtained from the log files of the optimised structures, the MO diagram shown below was drawn. For a normal Diels-Alder reaction, where the diene is electron rich and the dienophile is electron poor, the diene has a higher HOMO than the dienophile. However, from the MO diagram in this example, dioxole, which acts as the dienophile, has a higher energy HOMO than cyclohexadiene. This would imply that it is an inverse demand Diels-Alder reaction.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:39, 21 March 2018 (UTC) You havent shown that you have done this quantitatively. you have just said that you have have looked at the MOs. You need to look at the reactant MO energies on the same PES (the first step on the irc)

The dienophile is electron rich due to the presence of two oxygen atoms adjacent to the C=C bond, donating electron density to the double bond, hence resulting in a higher energy HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:CJC415 Ex2 Exo MO.jpg|frameless|658x658px]]
|[[File:CJC415 Ex2 Endo MO.jpg|frameless|678x678px]]
|}

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) This is the same MO diagram twice, just with different TS drawn in. You should have shown or discussed the differences between the endo and exo conformations in term of their relative MO energies.)

===Calculating Energies===
The energies extracted from the log files of the molecules are from optimisations using the B3LYP/6-31G(d) method at 298K.

{| class="wikitable"
|-
! Structure
! Energy (hartree/particle)
|-
|Cyclohexadiene
| -233.324375
|-
|1,3 dioxole
| -267.068132
|-
|Endo product
| -500.418692
|-
|Endo TS
| -500.332149
|-
|Exo product
| -500.417323
|-
|Exo TS
| -500.329166
|}

To calculate the activation and reaction energies for the products formed, the following calculations were made:

1) Activation energy = Energy of TS - sum of energy of reactants

2) Reaction energy = Energy of product - sum of energy of reactants

The conversion between hartree and KJ/mol is: 1 hartree = 2625.4976 KJ/mol

Combined energies of reactants = -1.313779 x 10<sup>6</sup> KJ/mol

The reaction barriers and reaction energies of the products formed are shown below.

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo
| 166.3
| -65.5
|-
|Endo
| 158.1
| -69.1
|}

===Kinetic and thermodynamic products===

From the calculated reaction energies, it can observed that the endo product is both the kinetic and thermodynamic product. It has a smaller reaction barrier and hence a lower activation energy, making it the kinetic product. Moreover, it also has a lower reaction energy and is more stable than the exo product, hence making it the thermodynamic product.

This is different from the large majority of Diels-Alders reactions, whereby the exo product is more thermodynamically favoured as it has lower steric interactions. The endo product is then the kinetic product due to the presence of stabilising secondary orbital interactions.

The reason for this is as follows. As seen from the 3D chemdraw diagram of the product below, the endo product experiences additional secondary non bonding interactions. It is also slightly less hindered compared to the exo product which experiences a greater steric clash between the two hydrogens (circled in red) which are pointing towards each other in space. The endo product experiences less steric clashes as seen from the fact that the hydrogens are further apart.

[[File:CJC415 Ex2 Steric clashes.jpg|frameless|658x658px]]

Moreover, from the jmols above, the endo TS experiences stabilising secondary orbital interactions between the p orbitals of oxygen in 1,3-dioxole and the p orbitals of carbon in cyclohexadiene. These interactions are not present in the exo product. Hence the TS of the endo product would be lower in energy.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:42, 21 March 2018 (UTC) Your energies are correct and you have come to the correct conclusions. you could have gone into some more detail in certain areas. The diagram of sterics is really nice.

==Exercise 3: Diels-Alder vs Cheletropic==
Unlike the previous two examples, which are purely Diels-Alder reactions, this final example involves a competing cheletropic reaction in addition to the Diels-Alder reaction pathways.

It is common for cheletropic reactions to involve SO<sub>2</sub>. Such a competing reaction arises due to the competing thermodynamic and kinetic products. Experimental work has found that Diels-Alder product is the kinetic product of SO<sub>2</sub> with conjugated dienes. However, this product is thermally unstable and undergoes a retro-Diels-Alder reaction. A thermodynamic product then forms, producing a stable five membered ring. Hence, the dominance of cheletropic products arises not from reactivity but from product instability. <ref>[http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852]</ref>

The optimised structures of the reactants, transition states and products that have been optimized at PM6 level of the 3 different reaction routes are shown below:

{| class="wikitable"
|-
| colspan="8"|'''Optimised structures at 298K'''
|-
! Xylylene
! SO2
! Endo TS
! Exo TS
! Cheletropic TS
! Endo Product
! Exo Product
! Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 XYLYLENE REACTANT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 SO2 REACTANT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 ENDO TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 EXO TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 CHELETROPIC TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 ENDO PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 EXO PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 CHELETROPIC PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(It seems that you've read in the wrong file for the Endo TS (it has frozen bonds). It's also missing 2 hydrogens. For all your JMols you must make sure you select the correct frame [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

===IRC paths===
The IRC paths for these 3 reactions as well as the log file links are shown below.
{| class="wikitable"
|-
|Endo DA reaction
| [[Image:CJC415 Ex3 Endo IRC movie.gif]]
| [[File:CJC415 Ex3 ENDO PRODUCT.LOG]]
[[File:CJC415 Ex3 ENDO TS.LOG]]
|-
|Exo DA reaction
| [[Image:CJC415 Ex3 Exo IRC movie.gif]]
| [[File:CJC415 Ex3 EXO PRODUCT.LOG]]
[[File:CJC415 Ex3 EXO TS.LOG]]
|-
|Cheletropic reaction
| [[Image:CJC415 Ex3 Cheletropic IRC movie.gif]]
| [[File:CJC415 Ex3 CHELETROPIC PRODUCT.LOG]]
[[File:CJC415 Ex3 CHELETROPIC TS.LOG]]
|}

===Energy calculations===

The optimized energies of the structures in hartrees obtained from their log files are tabulated below.
{| class="wikitable"
|-
! Structure
! Energy at RT (hartree/particle)
|-
|Xylylene
| 0.178764
|-
|SO2
| -0.118614
|-
|Exo DA TS
| 0.092077
|-
|Exo DA Product
| 0.021451
|-
|Endo DA TS
| 0.090559
|-
|Endo DA Product
| 0.021697
|-
|Cheletropic TS
| 0.099062
|-
|Cheletropic Product
| 0.000005
|}

(Your xylylene energy is a bit high [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

Similar as the previous calculations:

1) Activation energy = Energy of TS - sum of energy of reactants

2) Reaction energy = Energy of product - sum of energy of reactants

The conversion between hartree and KJ/mol is: 1 hartree = 2625.4976 KJ/mol

Combined energies of reactants = 157.9236 KJ/mol

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo DA
| 83.8
| -101.6
|-
|Endo DA
| 79.8
| -100.9
|-
|Cheletropic
| 102.2
| -157.9
|}

Using the values calculated from above, the following reaction coordinate was drawn.

[[Image:CJC415 Ex3 Reaction coordinate.jpg |frameless|800x800px]]

(Please use straight lines for reaction profiles. But the data is clear [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

From the reaction profile and calculations above, it can be seen that the activation energy of both endo and exo reactions are similar in energy, at +79.8KJ/mol and +83.8KJ/mol respectively. It is much lower than the cheletropic reaction which has an activation of +102.2KJ/mol. This is because both the transition states of the endo and exo pathways experience stabilising secondary interactions while the cheletropic TS, which also has numerous nodes, does not.

(Numerous nodes in the HOMO? It would be good to show this [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

It can be easily seen that the thermodynamic product is the cheletropic product due to the fact that the product is of the lowest energy. However, the amount of activation energy required is the largest. Hence, this pathway is likely to be reactive only under thermodynamic conditions, such as at high temperature and under equilibrating conditions.

Favouring the cheletropic product which is the most stable could be because the product is able to adopt a planar geometry, allowing the distance between the oxygen and neighbouring hydrogen atoms to be maximised.

Based on the activation energy values, it can be deduced that the endo Diels-Alders product is the kinetic product as that reaction pathway has the lowest energy barrier. This is because the endo product has secondary stabilising interactions between the oxygen on sulfur dioxide and the pi system of xylylene. Hence, this route would be favoured when the reaction is irreversible, under low temperatures and non equilibrating conditions.

===Extension: Reaction at second cis-butadiene fragment of xylylene===

One of the key reasons why the cheletropic and Diels-Alders reactions occur (shown above) is due to the reactivity of xylylene. Though it has a conjugated pi system and is planar, it is not aromatic. This is because the π electrons are not in a cyclic arrangement and since xylylene contains 8 π electrons, it does not fulfill Hückel's rule which states that a cyclic, planar molecule with 4n+2 π electrons are required for the molecule to be aromatic. Hence, xylylene is anti-aromatic. The formation of a stable aromatic benzene ring in the above 3 reactions would drive product formation, since the products are more stable than the reactants.

Apart from the outer cis-butadiene, there is another inner cis-butadiene fragment present that can participate in a Diels-Alders reaction. However, this site is not favoured due to the presence of steric hinderance and the formation of a strained bicyclic ring in the product as shown in the reaction scheme below.

[[Image:CJC415 Ex3 Extension rxn scheme.jpg |frameless|800x800px]]

It is important to note that in the cheletropic and Diels-Alders reactions involving the outer cis-butadiene, a stable benzene ring is formed in the product. However, this stabilising aromaticity is not found when the inner cis-butadiene reacts, causing it to be unfavoured.

{| class="wikitable"
|-
!
! Log file
! Energy (hartress)
|-
|Exo TS
| [[File:CJC415 Extension EXO TS.LOG]]
| 0.105054
|-
|Exo Product
| [[File:CJC415 Extension EXO PRODUCT.LOG]]
| 0.067301
|-
|Endo TS
| [[File:CJC415 Extension ENDO TS.LOG]]
| 0.102070
|-
|Endo Product
| [[File:CJC415 Extension ENDO PRODUCT.LOG]]
| 0.065607
|}

Similar to the previous section, the combined energies of reactants = 157.9236 KJ/mol. Hence, using the same formulas to calculate the activation and reaction energies, the following values were obtained:

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo DA
| 117.9
| 18.8
|-
|Endo DA
| 110.1
| 14.3
|}

==Conclusion==
Different pericyclic reactions were studied in this lab using Gaussian to optimize the products, reactants and transition states as well as study their optimized geometry. This has allowed us to rationalize and explain the reasoning behind why certain products were favoured over others as well as calculate the activation and reaction energies of these pathways. Doing so has allowed us to draw out the MOs to see the orbital interactions as well as predict product formation, something extremely useful that can be done before experiments are being carried out.

==References==

Rep:Mod:cjc415 TS

2018-03-27T09:28:12Z

Fv611: /* Molecular orbitals */

==Introduction==
This wiki explores a variety of pericyclic reactions, namely Diels-Alders and Cheletropic reactions and their transitions states.

===Potential energy surfaces (PES)===
A potential energy surface gives the energy of a molecule as a function of its geometry. It serves as a tool to help in the analysis of reaction dynamics and molecular geometry. The PES has a total of 3N-6 degrees of freedom.

At the stationary points, the gradient is equal to zero. These energy minima correspond to the physically stable species, such as reactants and products while transition states correspond to saddle points. When the second derivative is calculated, the energy minima and transition states can be differentiated. If a positive value is obtained, it suggests that an energy minima is obtained. Conversely, a negative value corresponds to a transition state.

This is also reflected in Gaussview. A transition state would produce one negative frequency while minima points will not reflect negative values, hence no imaginary frequencies are present.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:28, 21 March 2018 (UTC) what you are actually doing is finding the eigenvalues of the hessian which relate to the force constants. each one relates to a dimension of the PES. a TS only has 1 negative force constant.

===What is a transition state?===
A transition state (TS) is usually defined as a structure along the reaction coordinate which corresponds to the highest potential energy along this coordinate. In terms of mathematics, the TS of a chemical reaction represents a Saddle Point on the Potential Energy Surface (PES).

A transition state of a reactive pathway is the one with lowest energy compared to other paths perpendicular to it. It is also the highest energy point of that reactive pathway.

===Diels Alders reaction===
Otherwise known as a [4+2] cycloaddition, the Diels-Alder reaction involves a conjugated diene and an alkene, known as the dienophile. The reaction is concerted and occurs via a single, cyclic transition state.

Usually, the diene is electron-rich while the dienophile is electron poor. The HOMO of the diene would interact with the LUMO of the dienophile. However, there is also a possibility of an inverse electron demand Diels-Alder reaction, whereby it is the LUMO of the diene interacting with the HOMO of the dienophile. This can occur if electron withdrawing substituents are added to the diene and electron donating substituents are added to the dienophile. There are other types of Diels-Alder reactions, such as Hetero-Diels-Alder, which involves at least one heteroatom and lewis acid activation Diels-Alder reactions, which involves the use of lewis acids such as zinc chloride to act as catalysts of normal-demand Diels-Alder reactions by coordinating to the dienophile.

When selectivity issues arise, in the case of example 2, where the dienophile is substituted, this would give rise to the possibility of either the endo or exo product. The kinetic endo product is favoured in irreversible reactions due to the stabilisation of the endo transition state by dipolar, orbital and van der waals interactions. The exo product is considered the thermodynamic product due better sterics.

===Cheletropic reactions===
Cheletropic reactions are pericyclic reactions involving a transition state with a cyclic array of atoms and interacting orbitals. It would involve a reorganisation of sigma and pi bonds in the cyclic array. A key feature of these reactions are that in one of the reagents, both new bonds are being made on the same atom. In the case of example 3, both new bonds are made on the sulfur atom.

===Studying Transition States using Gaussview===
When more than one product can be formed, it is important to study the transition state. In the formation of kinetic products, the pathway which involves the lower activation energy and hence more stable transition state, is favoured. Should thermodynamic products be favoured, the more stable thermodynamic product is favoured.

Gaussview is being used to study these transition states. By optimising the structures in their transition states, the MOs and their respective energies can be analysed and extracted.

In this lab, semi-empirical PM6 and Density Function Theory (DFT) methods are being used to optimise the structures. PM6 is a faster but less accurate method. It replaces the two electron integrals, exchange and Coulomb integrals, which are challenging to determine.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:36, 21 March 2018 (UTC) Some equations would have been nice in this section, but good understanding.

DFT optimisations defines the energy of the system as a summation of 6 individual components, namely: nuclear-nuclear repulsion, nuclear-electron attraction, electron-electron coloumb repulsion, kinetic energy of electrons, electron-electron exchange energies and correlated movement of electrons of different spins.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:36, 21 March 2018 (UTC) All quantum chem methods split up the hamiltonian into these parts. DFT is only different because you have the exchange correlation term

==Exercise 1: Reaction of Butadiene with Ethylene==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job overall.)

===Overall reaction scheme===
[[Image:CJC Ex1 Rxn scheme.jpg |300px]]

It is to be noted that the trans-butadiene form is the lowest global energy minimum. However, it is the cis conformation that is reacting with ethene.

===Molecular orbitals===
The three tables below show the jmols of the optimised reactants (butadiene and ethene) as well as MO 16, 17, 18 and 19 of the transition state.

{| class="wikitable"
|-
| colspan="3"|'''Butadiene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
It is to be noted that the trans-butadiene form is the lowest global energy minimum. However, it is the cis conformation that is reacting with ethene.

{| class="wikitable"
|-
| colspan="3"|'''Ethene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You added the wrong JMol as an optimised structure (this is not a cope rearrangement).)
{| class="wikitable"
|-
| colspan="5"|'''Transition state'''
|-
! Optimised TS
! MO 16
! MO 17 (HOMO)
! MO 18 (LUMO)
! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The MO diagram for the transition state is shown below, with S representing 'Symmetric' and AS representing 'Asymmetric'.

It is assumed based on prior knowledge that only orbitals of the same symmetry combine.

It is to be noted that the MO for a TS is very much different compared to a reactant-product MO diagram. For a transition state MO, the resulting orbitals which the electrons occupy are destabilised and at a higher energy level with respect to the original orbitals in the reactants.

[[Image:CJC415 Ex1 MO.jpg |500px]]

The antisymmetric HOMO of butadiene (MO 11) reacts with the antisymmetric LUMO of ethene (MO 7) to give two antisymmetric MOs (MO 16 and 19).
Similarly, the symmetric LUMO of butadiene (MO 12) reacts with the symmetric HOMO of ethene (MO 6) to give two symmetric MOs (MO 17 and 18).

When symmetric and asymmetric orbitals overlap, the orbital overlap integral is zero, hence causing them to be unable to overlap, even if they are of similar energies. On the other hand, when two symmetric orbitals or two asymmetric orbitals overlap, the orbital overlap integral is non zero, allowing interaction to occur.

To determine the energy levels of the respective MOs in the TS with respect to the original MOs in butadiene and ethene, the energy levels of the MOs were compared. It was found that MO 16 and 17 were very similar in energy, at -0.32536 and -0.32531 respectively.

===Bond lengths===
{| class="wikitable"
|-
! Butadiene
! Ethene
! Cyclohexene
! Transition state
|-
|[[Image:CJC415 Ex1 Butadiene.bmp |80px]]
|[[Image:CJC415 Ex1 Ethene.bmp |50px]]
|[[Image:CJC415 Ex1 Cyclohexene.jpg |150px]]
|[[Image:CJC415 Ex1 TS.bmp |150px]]
|}

Going from reactants to TS and to products, the shortening of the C5-C6 bond, going from single to double bond was observed. Distances between C1-C2 and C3-C4 were also reduced as bonds were formed. Conversely, lengthening of C1-C6 and C4-C5 bonds were observed, going from double to single bonds.

The typical sp3 and sp2 C-C bond lengths are 1.54 Å and 1.34 Å respectively and the Van der Waals radius of the C atom is 1.70 Å. It can be noted that the partly formed C-C bonds (C1-C2 and C3-C4), which were at lengths 2.11Å in the TS, are longer than the typical sp3 bond, but also shorter than twice the radius of the carbon atom. This would suggest that the orbitals are sufficiently close to interact but the formation of a full C-C bond has yet to be completed.

===Reaction pathway===
From the jmol file shown below, formation of bonds between diene and dienophile took place simultaneously, hence bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 109; vibration 1</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Molecular orbitals===
The jmols of the optimised reactants and products are shown in the tables below. They were optimized using the B3LYP 6-31G(d) level.

{| class="wikitable"
|-
| colspan="3"|'''Cyclohexadiene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="3"|'''1,3 dioxole'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="2"|'''Optimised products'''
|-
! Exo product
! Endo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 EXO PRODUCT MINIMISED B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 ENDO PRODUCT MINIMISED B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

At the transition state, the interactions between the 4 MOs (shown above) produced the following 4 MOs for the endo and exo products accordingly.

{| class="wikitable"
|-
| colspan="5"|'''Transition State MOs - Exo product'''
|-
! Optimised molecule
! MO 40
! MO 41 (HOMO)
! MO 42 (LUMO)
! MO 43
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="5"|'''Transition State MOs - Endo product'''
|-
! Optimised molecule
! MO 40
! MO 41 (HOMO)
! MO 42 (LUMO)
! MO 43
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the energy levels obtained from the log files of the optimised structures, the MO diagram shown below was drawn. For a normal Diels-Alder reaction, where the diene is electron rich and the dienophile is electron poor, the diene has a higher HOMO than the dienophile. However, from the MO diagram in this example, dioxole, which acts as the dienophile, has a higher energy HOMO than cyclohexadiene. This would imply that it is an inverse demand Diels-Alder reaction.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:39, 21 March 2018 (UTC) You havent shown that you have done this quantitatively. you have just said that you have have looked at the MOs. You need to look at the reactant MO energies on the same PES (the first step on the irc)

The dienophile is electron rich due to the presence of two oxygen atoms adjacent to the C=C bond, donating electron density to the double bond, hence resulting in a higher energy HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:CJC415 Ex2 Exo MO.jpg|frameless|658x658px]]
|[[File:CJC415 Ex2 Endo MO.jpg|frameless|678x678px]]
|}

===Calculating Energies===
The energies extracted from the log files of the molecules are from optimisations using the B3LYP/6-31G(d) method at 298K.

{| class="wikitable"
|-
! Structure
! Energy (hartree/particle)
|-
|Cyclohexadiene
| -233.324375
|-
|1,3 dioxole
| -267.068132
|-
|Endo product
| -500.418692
|-
|Endo TS
| -500.332149
|-
|Exo product
| -500.417323
|-
|Exo TS
| -500.329166
|}

To calculate the activation and reaction energies for the products formed, the following calculations were made:

1) Activation energy = Energy of TS - sum of energy of reactants

2) Reaction energy = Energy of product - sum of energy of reactants

The conversion between hartree and KJ/mol is: 1 hartree = 2625.4976 KJ/mol

Combined energies of reactants = -1.313779 x 10<sup>6</sup> KJ/mol

The reaction barriers and reaction energies of the products formed are shown below.

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo
| 166.3
| -65.5
|-
|Endo
| 158.1
| -69.1
|}

===Kinetic and thermodynamic products===

From the calculated reaction energies, it can observed that the endo product is both the kinetic and thermodynamic product. It has a smaller reaction barrier and hence a lower activation energy, making it the kinetic product. Moreover, it also has a lower reaction energy and is more stable than the exo product, hence making it the thermodynamic product.

This is different from the large majority of Diels-Alders reactions, whereby the exo product is more thermodynamically favoured as it has lower steric interactions. The endo product is then the kinetic product due to the presence of stabilising secondary orbital interactions.

The reason for this is as follows. As seen from the 3D chemdraw diagram of the product below, the endo product experiences additional secondary non bonding interactions. It is also slightly less hindered compared to the exo product which experiences a greater steric clash between the two hydrogens (circled in red) which are pointing towards each other in space. The endo product experiences less steric clashes as seen from the fact that the hydrogens are further apart.

[[File:CJC415 Ex2 Steric clashes.jpg|frameless|658x658px]]

Moreover, from the jmols above, the endo TS experiences stabilising secondary orbital interactions between the p orbitals of oxygen in 1,3-dioxole and the p orbitals of carbon in cyclohexadiene. These interactions are not present in the exo product. Hence the TS of the endo product would be lower in energy.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:42, 21 March 2018 (UTC) Your energies are correct and you have come to the correct conclusions. you could have gone into some more detail in certain areas. The diagram of sterics is really nice.

==Exercise 3: Diels-Alder vs Cheletropic==
Unlike the previous two examples, which are purely Diels-Alder reactions, this final example involves a competing cheletropic reaction in addition to the Diels-Alder reaction pathways.

It is common for cheletropic reactions to involve SO<sub>2</sub>. Such a competing reaction arises due to the competing thermodynamic and kinetic products. Experimental work has found that Diels-Alder product is the kinetic product of SO<sub>2</sub> with conjugated dienes. However, this product is thermally unstable and undergoes a retro-Diels-Alder reaction. A thermodynamic product then forms, producing a stable five membered ring. Hence, the dominance of cheletropic products arises not from reactivity but from product instability. <ref>[http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852]</ref>

The optimised structures of the reactants, transition states and products that have been optimized at PM6 level of the 3 different reaction routes are shown below:

{| class="wikitable"
|-
| colspan="8"|'''Optimised structures at 298K'''
|-
! Xylylene
! SO2
! Endo TS
! Exo TS
! Cheletropic TS
! Endo Product
! Exo Product
! Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 XYLYLENE REACTANT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 SO2 REACTANT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 ENDO TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 EXO TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 CHELETROPIC TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 ENDO PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 EXO PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 CHELETROPIC PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(It seems that you've read in the wrong file for the Endo TS (it has frozen bonds). It's also missing 2 hydrogens. For all your JMols you must make sure you select the correct frame [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

===IRC paths===
The IRC paths for these 3 reactions as well as the log file links are shown below.
{| class="wikitable"
|-
|Endo DA reaction
| [[Image:CJC415 Ex3 Endo IRC movie.gif]]
| [[File:CJC415 Ex3 ENDO PRODUCT.LOG]]
[[File:CJC415 Ex3 ENDO TS.LOG]]
|-
|Exo DA reaction
| [[Image:CJC415 Ex3 Exo IRC movie.gif]]
| [[File:CJC415 Ex3 EXO PRODUCT.LOG]]
[[File:CJC415 Ex3 EXO TS.LOG]]
|-
|Cheletropic reaction
| [[Image:CJC415 Ex3 Cheletropic IRC movie.gif]]
| [[File:CJC415 Ex3 CHELETROPIC PRODUCT.LOG]]
[[File:CJC415 Ex3 CHELETROPIC TS.LOG]]
|}

===Energy calculations===

The optimized energies of the structures in hartrees obtained from their log files are tabulated below.
{| class="wikitable"
|-
! Structure
! Energy at RT (hartree/particle)
|-
|Xylylene
| 0.178764
|-
|SO2
| -0.118614
|-
|Exo DA TS
| 0.092077
|-
|Exo DA Product
| 0.021451
|-
|Endo DA TS
| 0.090559
|-
|Endo DA Product
| 0.021697
|-
|Cheletropic TS
| 0.099062
|-
|Cheletropic Product
| 0.000005
|}

(Your xylylene energy is a bit high [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

Similar as the previous calculations:

1) Activation energy = Energy of TS - sum of energy of reactants

2) Reaction energy = Energy of product - sum of energy of reactants

The conversion between hartree and KJ/mol is: 1 hartree = 2625.4976 KJ/mol

Combined energies of reactants = 157.9236 KJ/mol

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo DA
| 83.8
| -101.6
|-
|Endo DA
| 79.8
| -100.9
|-
|Cheletropic
| 102.2
| -157.9
|}

Using the values calculated from above, the following reaction coordinate was drawn.

[[Image:CJC415 Ex3 Reaction coordinate.jpg |frameless|800x800px]]

(Please use straight lines for reaction profiles. But the data is clear [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

From the reaction profile and calculations above, it can be seen that the activation energy of both endo and exo reactions are similar in energy, at +79.8KJ/mol and +83.8KJ/mol respectively. It is much lower than the cheletropic reaction which has an activation of +102.2KJ/mol. This is because both the transition states of the endo and exo pathways experience stabilising secondary interactions while the cheletropic TS, which also has numerous nodes, does not.

(Numerous nodes in the HOMO? It would be good to show this [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

It can be easily seen that the thermodynamic product is the cheletropic product due to the fact that the product is of the lowest energy. However, the amount of activation energy required is the largest. Hence, this pathway is likely to be reactive only under thermodynamic conditions, such as at high temperature and under equilibrating conditions.

Favouring the cheletropic product which is the most stable could be because the product is able to adopt a planar geometry, allowing the distance between the oxygen and neighbouring hydrogen atoms to be maximised.

Based on the activation energy values, it can be deduced that the endo Diels-Alders product is the kinetic product as that reaction pathway has the lowest energy barrier. This is because the endo product has secondary stabilising interactions between the oxygen on sulfur dioxide and the pi system of xylylene. Hence, this route would be favoured when the reaction is irreversible, under low temperatures and non equilibrating conditions.

===Extension: Reaction at second cis-butadiene fragment of xylylene===

One of the key reasons why the cheletropic and Diels-Alders reactions occur (shown above) is due to the reactivity of xylylene. Though it has a conjugated pi system and is planar, it is not aromatic. This is because the π electrons are not in a cyclic arrangement and since xylylene contains 8 π electrons, it does not fulfill Hückel's rule which states that a cyclic, planar molecule with 4n+2 π electrons are required for the molecule to be aromatic. Hence, xylylene is anti-aromatic. The formation of a stable aromatic benzene ring in the above 3 reactions would drive product formation, since the products are more stable than the reactants.

Apart from the outer cis-butadiene, there is another inner cis-butadiene fragment present that can participate in a Diels-Alders reaction. However, this site is not favoured due to the presence of steric hinderance and the formation of a strained bicyclic ring in the product as shown in the reaction scheme below.

[[Image:CJC415 Ex3 Extension rxn scheme.jpg |frameless|800x800px]]

It is important to note that in the cheletropic and Diels-Alders reactions involving the outer cis-butadiene, a stable benzene ring is formed in the product. However, this stabilising aromaticity is not found when the inner cis-butadiene reacts, causing it to be unfavoured.

{| class="wikitable"
|-
!
! Log file
! Energy (hartress)
|-
|Exo TS
| [[File:CJC415 Extension EXO TS.LOG]]
| 0.105054
|-
|Exo Product
| [[File:CJC415 Extension EXO PRODUCT.LOG]]
| 0.067301
|-
|Endo TS
| [[File:CJC415 Extension ENDO TS.LOG]]
| 0.102070
|-
|Endo Product
| [[File:CJC415 Extension ENDO PRODUCT.LOG]]
| 0.065607
|}

Similar to the previous section, the combined energies of reactants = 157.9236 KJ/mol. Hence, using the same formulas to calculate the activation and reaction energies, the following values were obtained:

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo DA
| 117.9
| 18.8
|-
|Endo DA
| 110.1
| 14.3
|}

==Conclusion==
Different pericyclic reactions were studied in this lab using Gaussian to optimize the products, reactants and transition states as well as study their optimized geometry. This has allowed us to rationalize and explain the reasoning behind why certain products were favoured over others as well as calculate the activation and reaction energies of these pathways. Doing so has allowed us to draw out the MOs to see the orbital interactions as well as predict product formation, something extremely useful that can be done before experiments are being carried out.

==References==

Rep:Mod:cjc415 TS

2018-03-27T09:25:47Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene */

==Introduction==
This wiki explores a variety of pericyclic reactions, namely Diels-Alders and Cheletropic reactions and their transitions states.

===Potential energy surfaces (PES)===
A potential energy surface gives the energy of a molecule as a function of its geometry. It serves as a tool to help in the analysis of reaction dynamics and molecular geometry. The PES has a total of 3N-6 degrees of freedom.

At the stationary points, the gradient is equal to zero. These energy minima correspond to the physically stable species, such as reactants and products while transition states correspond to saddle points. When the second derivative is calculated, the energy minima and transition states can be differentiated. If a positive value is obtained, it suggests that an energy minima is obtained. Conversely, a negative value corresponds to a transition state.

This is also reflected in Gaussview. A transition state would produce one negative frequency while minima points will not reflect negative values, hence no imaginary frequencies are present.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:28, 21 March 2018 (UTC) what you are actually doing is finding the eigenvalues of the hessian which relate to the force constants. each one relates to a dimension of the PES. a TS only has 1 negative force constant.

===What is a transition state?===
A transition state (TS) is usually defined as a structure along the reaction coordinate which corresponds to the highest potential energy along this coordinate. In terms of mathematics, the TS of a chemical reaction represents a Saddle Point on the Potential Energy Surface (PES).

A transition state of a reactive pathway is the one with lowest energy compared to other paths perpendicular to it. It is also the highest energy point of that reactive pathway.

===Diels Alders reaction===
Otherwise known as a [4+2] cycloaddition, the Diels-Alder reaction involves a conjugated diene and an alkene, known as the dienophile. The reaction is concerted and occurs via a single, cyclic transition state.

Usually, the diene is electron-rich while the dienophile is electron poor. The HOMO of the diene would interact with the LUMO of the dienophile. However, there is also a possibility of an inverse electron demand Diels-Alder reaction, whereby it is the LUMO of the diene interacting with the HOMO of the dienophile. This can occur if electron withdrawing substituents are added to the diene and electron donating substituents are added to the dienophile. There are other types of Diels-Alder reactions, such as Hetero-Diels-Alder, which involves at least one heteroatom and lewis acid activation Diels-Alder reactions, which involves the use of lewis acids such as zinc chloride to act as catalysts of normal-demand Diels-Alder reactions by coordinating to the dienophile.

When selectivity issues arise, in the case of example 2, where the dienophile is substituted, this would give rise to the possibility of either the endo or exo product. The kinetic endo product is favoured in irreversible reactions due to the stabilisation of the endo transition state by dipolar, orbital and van der waals interactions. The exo product is considered the thermodynamic product due better sterics.

===Cheletropic reactions===
Cheletropic reactions are pericyclic reactions involving a transition state with a cyclic array of atoms and interacting orbitals. It would involve a reorganisation of sigma and pi bonds in the cyclic array. A key feature of these reactions are that in one of the reagents, both new bonds are being made on the same atom. In the case of example 3, both new bonds are made on the sulfur atom.

===Studying Transition States using Gaussview===
When more than one product can be formed, it is important to study the transition state. In the formation of kinetic products, the pathway which involves the lower activation energy and hence more stable transition state, is favoured. Should thermodynamic products be favoured, the more stable thermodynamic product is favoured.

Gaussview is being used to study these transition states. By optimising the structures in their transition states, the MOs and their respective energies can be analysed and extracted.

In this lab, semi-empirical PM6 and Density Function Theory (DFT) methods are being used to optimise the structures. PM6 is a faster but less accurate method. It replaces the two electron integrals, exchange and Coulomb integrals, which are challenging to determine.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:36, 21 March 2018 (UTC) Some equations would have been nice in this section, but good understanding.

DFT optimisations defines the energy of the system as a summation of 6 individual components, namely: nuclear-nuclear repulsion, nuclear-electron attraction, electron-electron coloumb repulsion, kinetic energy of electrons, electron-electron exchange energies and correlated movement of electrons of different spins.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:36, 21 March 2018 (UTC) All quantum chem methods split up the hamiltonian into these parts. DFT is only different because you have the exchange correlation term

==Exercise 1: Reaction of Butadiene with Ethylene==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job overall.)

===Overall reaction scheme===
[[Image:CJC Ex1 Rxn scheme.jpg |300px]]

It is to be noted that the trans-butadiene form is the lowest global energy minimum. However, it is the cis conformation that is reacting with ethene.

===Molecular orbitals===
The three tables below show the jmols of the optimised reactants (butadiene and ethene) as well as MO 16, 17, 18 and 19 of the transition state.

{| class="wikitable"
|-
| colspan="3"|'''Butadiene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
It is to be noted that the trans-butadiene form is the lowest global energy minimum. However, it is the cis conformation that is reacting with ethene.

{| class="wikitable"
|-
| colspan="3"|'''Ethene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="5"|'''Transition state'''
|-
! Optimised TS
! MO 16
! MO 17 (HOMO)
! MO 18 (LUMO)
! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The MO diagram for the transition state is shown below, with S representing 'Symmetric' and AS representing 'Asymmetric'.

It is assumed based on prior knowledge that only orbitals of the same symmetry combine.

It is to be noted that the MO for a TS is very much different compared to a reactant-product MO diagram. For a transition state MO, the resulting orbitals which the electrons occupy are destabilised and at a higher energy level with respect to the original orbitals in the reactants.

[[Image:CJC415 Ex1 MO.jpg |500px]]

The antisymmetric HOMO of butadiene (MO 11) reacts with the antisymmetric LUMO of ethene (MO 7) to give two antisymmetric MOs (MO 16 and 19).
Similarly, the symmetric LUMO of butadiene (MO 12) reacts with the symmetric HOMO of ethene (MO 6) to give two symmetric MOs (MO 17 and 18).

When symmetric and asymmetric orbitals overlap, the orbital overlap integral is zero, hence causing them to be unable to overlap, even if they are of similar energies. On the other hand, when two symmetric orbitals or two asymmetric orbitals overlap, the orbital overlap integral is non zero, allowing interaction to occur.

To determine the energy levels of the respective MOs in the TS with respect to the original MOs in butadiene and ethene, the energy levels of the MOs were compared. It was found that MO 16 and 17 were very similar in energy, at -0.32536 and -0.32531 respectively.

===Bond lengths===
{| class="wikitable"
|-
! Butadiene
! Ethene
! Cyclohexene
! Transition state
|-
|[[Image:CJC415 Ex1 Butadiene.bmp |80px]]
|[[Image:CJC415 Ex1 Ethene.bmp |50px]]
|[[Image:CJC415 Ex1 Cyclohexene.jpg |150px]]
|[[Image:CJC415 Ex1 TS.bmp |150px]]
|}

Going from reactants to TS and to products, the shortening of the C5-C6 bond, going from single to double bond was observed. Distances between C1-C2 and C3-C4 were also reduced as bonds were formed. Conversely, lengthening of C1-C6 and C4-C5 bonds were observed, going from double to single bonds.

The typical sp3 and sp2 C-C bond lengths are 1.54 Å and 1.34 Å respectively and the Van der Waals radius of the C atom is 1.70 Å. It can be noted that the partly formed C-C bonds (C1-C2 and C3-C4), which were at lengths 2.11Å in the TS, are longer than the typical sp3 bond, but also shorter than twice the radius of the carbon atom. This would suggest that the orbitals are sufficiently close to interact but the formation of a full C-C bond has yet to be completed.

===Reaction pathway===
From the jmol file shown below, formation of bonds between diene and dienophile took place simultaneously, hence bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 109; vibration 1</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Molecular orbitals===
The jmols of the optimised reactants and products are shown in the tables below. They were optimized using the B3LYP 6-31G(d) level.

{| class="wikitable"
|-
| colspan="3"|'''Cyclohexadiene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="3"|'''1,3 dioxole'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="2"|'''Optimised products'''
|-
! Exo product
! Endo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 EXO PRODUCT MINIMISED B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 ENDO PRODUCT MINIMISED B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

At the transition state, the interactions between the 4 MOs (shown above) produced the following 4 MOs for the endo and exo products accordingly.

{| class="wikitable"
|-
| colspan="5"|'''Transition State MOs - Exo product'''
|-
! Optimised molecule
! MO 40
! MO 41 (HOMO)
! MO 42 (LUMO)
! MO 43
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="5"|'''Transition State MOs - Endo product'''
|-
! Optimised molecule
! MO 40
! MO 41 (HOMO)
! MO 42 (LUMO)
! MO 43
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the energy levels obtained from the log files of the optimised structures, the MO diagram shown below was drawn. For a normal Diels-Alder reaction, where the diene is electron rich and the dienophile is electron poor, the diene has a higher HOMO than the dienophile. However, from the MO diagram in this example, dioxole, which acts as the dienophile, has a higher energy HOMO than cyclohexadiene. This would imply that it is an inverse demand Diels-Alder reaction.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:39, 21 March 2018 (UTC) You havent shown that you have done this quantitatively. you have just said that you have have looked at the MOs. You need to look at the reactant MO energies on the same PES (the first step on the irc)

The dienophile is electron rich due to the presence of two oxygen atoms adjacent to the C=C bond, donating electron density to the double bond, hence resulting in a higher energy HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:CJC415 Ex2 Exo MO.jpg|frameless|658x658px]]
|[[File:CJC415 Ex2 Endo MO.jpg|frameless|678x678px]]
|}

===Calculating Energies===
The energies extracted from the log files of the molecules are from optimisations using the B3LYP/6-31G(d) method at 298K.

{| class="wikitable"
|-
! Structure
! Energy (hartree/particle)
|-
|Cyclohexadiene
| -233.324375
|-
|1,3 dioxole
| -267.068132
|-
|Endo product
| -500.418692
|-
|Endo TS
| -500.332149
|-
|Exo product
| -500.417323
|-
|Exo TS
| -500.329166
|}

To calculate the activation and reaction energies for the products formed, the following calculations were made:

1) Activation energy = Energy of TS - sum of energy of reactants

2) Reaction energy = Energy of product - sum of energy of reactants

The conversion between hartree and KJ/mol is: 1 hartree = 2625.4976 KJ/mol

Combined energies of reactants = -1.313779 x 10<sup>6</sup> KJ/mol

The reaction barriers and reaction energies of the products formed are shown below.

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo
| 166.3
| -65.5
|-
|Endo
| 158.1
| -69.1
|}

===Kinetic and thermodynamic products===

From the calculated reaction energies, it can observed that the endo product is both the kinetic and thermodynamic product. It has a smaller reaction barrier and hence a lower activation energy, making it the kinetic product. Moreover, it also has a lower reaction energy and is more stable than the exo product, hence making it the thermodynamic product.

This is different from the large majority of Diels-Alders reactions, whereby the exo product is more thermodynamically favoured as it has lower steric interactions. The endo product is then the kinetic product due to the presence of stabilising secondary orbital interactions.

The reason for this is as follows. As seen from the 3D chemdraw diagram of the product below, the endo product experiences additional secondary non bonding interactions. It is also slightly less hindered compared to the exo product which experiences a greater steric clash between the two hydrogens (circled in red) which are pointing towards each other in space. The endo product experiences less steric clashes as seen from the fact that the hydrogens are further apart.

[[File:CJC415 Ex2 Steric clashes.jpg|frameless|658x658px]]

Moreover, from the jmols above, the endo TS experiences stabilising secondary orbital interactions between the p orbitals of oxygen in 1,3-dioxole and the p orbitals of carbon in cyclohexadiene. These interactions are not present in the exo product. Hence the TS of the endo product would be lower in energy.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:42, 21 March 2018 (UTC) Your energies are correct and you have come to the correct conclusions. you could have gone into some more detail in certain areas. The diagram of sterics is really nice.

==Exercise 3: Diels-Alder vs Cheletropic==
Unlike the previous two examples, which are purely Diels-Alder reactions, this final example involves a competing cheletropic reaction in addition to the Diels-Alder reaction pathways.

It is common for cheletropic reactions to involve SO<sub>2</sub>. Such a competing reaction arises due to the competing thermodynamic and kinetic products. Experimental work has found that Diels-Alder product is the kinetic product of SO<sub>2</sub> with conjugated dienes. However, this product is thermally unstable and undergoes a retro-Diels-Alder reaction. A thermodynamic product then forms, producing a stable five membered ring. Hence, the dominance of cheletropic products arises not from reactivity but from product instability. <ref>[http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852]</ref>

The optimised structures of the reactants, transition states and products that have been optimized at PM6 level of the 3 different reaction routes are shown below:

{| class="wikitable"
|-
| colspan="8"|'''Optimised structures at 298K'''
|-
! Xylylene
! SO2
! Endo TS
! Exo TS
! Cheletropic TS
! Endo Product
! Exo Product
! Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 XYLYLENE REACTANT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 SO2 REACTANT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 ENDO TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 EXO TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 CHELETROPIC TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 ENDO PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 EXO PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 CHELETROPIC PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(It seems that you've read in the wrong file for the Endo TS (it has frozen bonds). It's also missing 2 hydrogens. For all your JMols you must make sure you select the correct frame [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

===IRC paths===
The IRC paths for these 3 reactions as well as the log file links are shown below.
{| class="wikitable"
|-
|Endo DA reaction
| [[Image:CJC415 Ex3 Endo IRC movie.gif]]
| [[File:CJC415 Ex3 ENDO PRODUCT.LOG]]
[[File:CJC415 Ex3 ENDO TS.LOG]]
|-
|Exo DA reaction
| [[Image:CJC415 Ex3 Exo IRC movie.gif]]
| [[File:CJC415 Ex3 EXO PRODUCT.LOG]]
[[File:CJC415 Ex3 EXO TS.LOG]]
|-
|Cheletropic reaction
| [[Image:CJC415 Ex3 Cheletropic IRC movie.gif]]
| [[File:CJC415 Ex3 CHELETROPIC PRODUCT.LOG]]
[[File:CJC415 Ex3 CHELETROPIC TS.LOG]]
|}

===Energy calculations===

The optimized energies of the structures in hartrees obtained from their log files are tabulated below.
{| class="wikitable"
|-
! Structure
! Energy at RT (hartree/particle)
|-
|Xylylene
| 0.178764
|-
|SO2
| -0.118614
|-
|Exo DA TS
| 0.092077
|-
|Exo DA Product
| 0.021451
|-
|Endo DA TS
| 0.090559
|-
|Endo DA Product
| 0.021697
|-
|Cheletropic TS
| 0.099062
|-
|Cheletropic Product
| 0.000005
|}

(Your xylylene energy is a bit high [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

Similar as the previous calculations:

1) Activation energy = Energy of TS - sum of energy of reactants

2) Reaction energy = Energy of product - sum of energy of reactants

The conversion between hartree and KJ/mol is: 1 hartree = 2625.4976 KJ/mol

Combined energies of reactants = 157.9236 KJ/mol

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo DA
| 83.8
| -101.6
|-
|Endo DA
| 79.8
| -100.9
|-
|Cheletropic
| 102.2
| -157.9
|}

Using the values calculated from above, the following reaction coordinate was drawn.

[[Image:CJC415 Ex3 Reaction coordinate.jpg |frameless|800x800px]]

(Please use straight lines for reaction profiles. But the data is clear [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

From the reaction profile and calculations above, it can be seen that the activation energy of both endo and exo reactions are similar in energy, at +79.8KJ/mol and +83.8KJ/mol respectively. It is much lower than the cheletropic reaction which has an activation of +102.2KJ/mol. This is because both the transition states of the endo and exo pathways experience stabilising secondary interactions while the cheletropic TS, which also has numerous nodes, does not.

(Numerous nodes in the HOMO? It would be good to show this [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

It can be easily seen that the thermodynamic product is the cheletropic product due to the fact that the product is of the lowest energy. However, the amount of activation energy required is the largest. Hence, this pathway is likely to be reactive only under thermodynamic conditions, such as at high temperature and under equilibrating conditions.

Favouring the cheletropic product which is the most stable could be because the product is able to adopt a planar geometry, allowing the distance between the oxygen and neighbouring hydrogen atoms to be maximised.

Based on the activation energy values, it can be deduced that the endo Diels-Alders product is the kinetic product as that reaction pathway has the lowest energy barrier. This is because the endo product has secondary stabilising interactions between the oxygen on sulfur dioxide and the pi system of xylylene. Hence, this route would be favoured when the reaction is irreversible, under low temperatures and non equilibrating conditions.

===Extension: Reaction at second cis-butadiene fragment of xylylene===

One of the key reasons why the cheletropic and Diels-Alders reactions occur (shown above) is due to the reactivity of xylylene. Though it has a conjugated pi system and is planar, it is not aromatic. This is because the π electrons are not in a cyclic arrangement and since xylylene contains 8 π electrons, it does not fulfill Hückel's rule which states that a cyclic, planar molecule with 4n+2 π electrons are required for the molecule to be aromatic. Hence, xylylene is anti-aromatic. The formation of a stable aromatic benzene ring in the above 3 reactions would drive product formation, since the products are more stable than the reactants.

Apart from the outer cis-butadiene, there is another inner cis-butadiene fragment present that can participate in a Diels-Alders reaction. However, this site is not favoured due to the presence of steric hinderance and the formation of a strained bicyclic ring in the product as shown in the reaction scheme below.

[[Image:CJC415 Ex3 Extension rxn scheme.jpg |frameless|800x800px]]

It is important to note that in the cheletropic and Diels-Alders reactions involving the outer cis-butadiene, a stable benzene ring is formed in the product. However, this stabilising aromaticity is not found when the inner cis-butadiene reacts, causing it to be unfavoured.

{| class="wikitable"
|-
!
! Log file
! Energy (hartress)
|-
|Exo TS
| [[File:CJC415 Extension EXO TS.LOG]]
| 0.105054
|-
|Exo Product
| [[File:CJC415 Extension EXO PRODUCT.LOG]]
| 0.067301
|-
|Endo TS
| [[File:CJC415 Extension ENDO TS.LOG]]
| 0.102070
|-
|Endo Product
| [[File:CJC415 Extension ENDO PRODUCT.LOG]]
| 0.065607
|}

Similar to the previous section, the combined energies of reactants = 157.9236 KJ/mol. Hence, using the same formulas to calculate the activation and reaction energies, the following values were obtained:

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo DA
| 117.9
| 18.8
|-
|Endo DA
| 110.1
| 14.3
|}

==Conclusion==
Different pericyclic reactions were studied in this lab using Gaussian to optimize the products, reactants and transition states as well as study their optimized geometry. This has allowed us to rationalize and explain the reasoning behind why certain products were favoured over others as well as calculate the activation and reaction energies of these pathways. Doing so has allowed us to draw out the MOs to see the orbital interactions as well as predict product formation, something extremely useful that can be done before experiments are being carried out.

==References==

Rep:Kh1015TSEx2RD

2018-03-27T09:16:19Z

Fv611: /* Part 1: Determining the Type of Diels-Alder Reaction. */

==Exercise 2 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 4 parts was based on relevant discussion idea and for convenient navigation during the write-up.

===Part 1: Determining the Type of Diels-Alder Reaction.===
Figure 4.2 under Methodology section shows the reaction scheme for Exercise 2.

Referring to Figure 5.2.5 and 5.2.10, both of the endo and exo reactions were calculated to be inverse-electron-demand Diels Alder reactions at B3YLP-6-31 G(D) level, whereby the electron-poor dienophile (cyclohexadiene) interacted with the electron-rich diene (1,3-dioxole).

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Very good MO diagrams.)
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.1: Summary of MO Interactions To Form the TS for Both Endo and Exo Reactions (Same Set of Orbitals for Both, Difference is only in the Relative Approach Orientation).
|-
|'''TS Symmetry Label (in Increasing Energy Level)'''
|'''Constituent Fragment Orbital Interactions (Cyclohexadiene - 1,3 Dioxole)'''
|-
|Anti-Symmetrical
|MO22-MO20 (Bonding)
|-
|Symmetrical
|MO23-MO19 (Bonding)
|-
|Symmetrical*
|MO23-MO19 (Anti-Bonding)
|-
|Anti-Symmetrical*
|MO22-MO20 (Anti-Bonding)
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of Cyclohexadiene (MO22).png|thumb|150px|Figure 5.2.1: HOMO of Cyclohexadiene (MO 22, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXADIENE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexadiene_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of Cyclohexadiene (MO23).png|thumb|150px|Figure 5.2.2: LUMO of Cyclohexadiene (MO 23, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 HOMO of 1,3 Dioxole (MO19).png|thumb|150px|Figure 5.2.3: HOMO of 1,3-Dioxole(MO 19, B3YLP-6-31 G(D) Calculation. Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of 1,3 Dioxole (MO20).png|thumb|150px|Figure 5.2.4: LUMO of 1,3-Dioxole(MO 20, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|}

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Endo.png|thumb|center|400px|Figure 5.2.5: Frontier MO diagram for the formation of the Endo TS.]]
|-
|[[File:KH1015 HOMO-1 MO 40.png|thumb|150px|Figure 5.2.6: HOMO-1 of Endo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO MO 41.png|thumb|150px|Figure 5.2.7: HOMO of Endo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO MO 42.png|thumb|150px|Figure 5.2.8: LUMO of Endo TS (MO 42, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 MO 43.png|thumb|150px|Figure 5.2.9: LUMO+1 of Endo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Exo.png|thumb|center|400px|Figure 5.2.10: Frontier MO diagram for the formation of the Exo TS.]]
|-
|[[File:KH1015 HOMO-1 Exo MO40.png|thumb|150px|Figure 5.2.11: HOMO-1 of Exo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO Exo MO41.png|thumb|150px|Figure 5.2.12: HOMO of Exo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO Exo MO42.png|thumb|150px|Figure 5.2.13: LUMO of Exo TS (MO 42, B3YLP-6-31 G(D) Calculation).Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 Exo MO43.png|thumb|150px|Figure 5.2.14: LUMO+1 of Exo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

===Part 2: Parameters from the Reaction Profile.===

Referring to Table 5.2.2, it can be seen that the Gibbs-Free Energies of the different species are much larger than the Δ Gibbs-Free Energy in Table 5.2.3. From the calculation of this reaction, it can be observed that the activation Gibbs-Free Energy and energy released/absorbed were only a small fraction relative to the total energy of the system (less than 0.01%).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.2: Summary of Calculated Gibbs-Free Energy of Species in Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|rowspan="2"|''' '''
|colspan="6"|'''States'''
|-
|'''Cyclohexadiene'''
|'''1,3-Dioxole'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -612,593
| -701,189
| -1,313,622
| -1,313,849
| -1,313,614
| -1,313,846
|}

Referring to Table 5.2.3, calculations showed that both reactions were spontaneous and that the endo product was the kinetically (based on activation Gibbs-Free Energy) and thermodynamically favourable product (based on Δ Gibbs-Free Energy). The endo path had a lower activation Gibbs-Free Energy (160 against 168 kJ mol<sup>-1</sup>) with higher rate constant at 298.15 K (5.77 against 0.23 x 10<sup>-16</sup>), and had a more negative Δ Gibbs-Free Energy (-67.4 against -63.8 kJ mol<sup>-1</sup>), which meant that it was more stable than the exo form. The rate constant was calculated using the formula described under Introduction > Part D. This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of endo to exo products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.3: Summary of Calculated Reaction Profile Parameters for Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|''' '''
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Predicted Rate of Reaction (x10<sup>-16</sup> s<sup>-1</sup>)'''
|-
|'''Endo-Path'''
|160
| -67.4
|5.77
|-
|'''Exo-Path'''
|168
| -63.8
|0.23
|}

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:59, 22 March 2018 (UTC) Your energies are correct and you have come to the correct conclusions

===Part 3: Secondary Orbital Interactions and Sterics.===
Referring to MO 41 for both endo and exo TS in Figure 5.2.15 and 5.2.17, the calculation showed favourable secondary orbital interaction in the endo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would lower the activation energy. Referring to Figure 5.2.16 and 5.2.18, there are significant non-favourable steric interactions (Red being not favourable and Blue being favourable) in the exo TS between the methyl-group and the 6-membered-ring (Green) that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would raise the activation energy. Conversely, both secondary orbital interaction and steric clash accounted for the lower calculated activation energy of the endo path relative to exo path, 160 kJ mol<sup>-1</sup> against 168 kJ mol<sup>-1</sup>.

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.15: HOMO of Endo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:Kh1015 Endo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.16: Non Covalent Interactions in the Endo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.17: HOMO of Exo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.18: Non Covalent Interactions in the Exo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:01, 22 March 2018 (UTC)This is an excellent way to quantitatively measure the sterics. Well done.

===Part 4: Interactive Vibration Animation of TS for Both Endo and Exo Path.===
Both Figure 5.2.19 and 5.2.20 contained interactive vibration animation of the Endo and Exo TS (B3YLP-6-31 G(D) level).

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.19: Interactive Vibration Animation of the Endo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 2; measure 5 6</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i521/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.20: Interactive Vibration Animation of the Exo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 17; measure 4 15</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>===Select Vibration===</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 21; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i529/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 22; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>99/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

===Part 5: Interactive Vibration Animations (PM6 Level).===
The IRC calculations at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism for both paths and that the TS for both reactions had been optimized.

====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex2 Endo PM6 IRC.gif|frame|left|Figure 5.2.21: IRC for Formation of Diels-Alder Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole) (PM6 Calculation).]]
|| [[File:KH1015 Endo PM6 IRC Graph.png|thumb|Figure 5.2.22: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Crosscheck PM6 IRC.gif|frame|left|Figure 5.2.23: IRC for Formation of Diels-Alder Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole)) (PM6 Calculation).]]
|| [[File:KH1015 Exo PM6 IRC Graph.png|thumb|Figure 5.2.24: IRC Graph of Energy against Reaction Coordinate for the formation of Exo-Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:05, 22 March 2018 (UTC) This is an excellent section. Your energies are correct and therefore came to the correct conclusions. However you didnt investigate the electron demand of the reaction. But everything else was rwally good.

Rep:Kh1015TSEx1RD

2018-03-27T09:11:03Z

Fv611: /* Exercise 1 Results and Discussion. */

==Exercise 1 Results and Discussion.==
__FORCETOC__

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Wonderful section. Well written and a lot of extra effort put into it. Well done!)

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 3 parts was based on relevant discussion idea and for convenient navigation during the write-up.
===Part 1: Symmetry Discussion.===
Figure 4.1 under Methodology section shows the reaction scheme for Exercise 1.

Figure 5.1.5 shows the graphical representation of MO interactions between s-cis butadiene and ethene during the formation of the TS. Figures 5.1.1-5.1.4 and 5.1.6-5.1.9 show the visualized MO output from GaussView (isovalue=0.02 and medium cube grid). Table 5.1.1 summarizes the MO interactions to form the TS in terms of the label of the constituent MOs in Gaussview outputs.

It can be concluded that the symmetry requirement of an allowed reaction is strictly when the constituent MOs have the same symmetry. Consequently, symmetrical-symmetrical or antisymmetrical-antisymmetrical interaction has a non-zero orbital overlap integral. Meanwhile, non-symmetrical interactions of the constituent MOs are symmetry-forbidden. Conversely, symmetrical-antisymmetrical or antisymmetrical-symmetrical interaction has a zero orbital overlap integral.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.1.1: Summary of MO Interactions To Form the TS.
|-
|'''TS Symmetry Label (in Increasing Energy Level)'''
|'''Constituent Fragment Orbital Interactions (S-Cis Butadiene - Ethene)'''
|-
|Anti-Symmetrical
|MO12-MO6 (Bonding)
|-
|Symmetrical
|MO11-MO7 (Bonding)
|-
|Symmetrical*
|MO12-MO6 (Anti-Bonding)
|-
|Anti-Symmetrical*
|MO11-MO7 (Anti-Bonding)
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of S-Cis Butadiene (MO11).png|thumb|150px| Figure 5.1.1: HOMO of S-Cis Butadiene (MO 11, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 LUMO of S-Cis Butadiene (MO 12).png|thumb|150px|Figure 5.1.2: LUMO of S-Cis Butadiene (MO 12, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 HOMO of Ethene (MO6).png|thumb|150px|Figure 5.1.3: HOMO of Ethene (MO 6, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_ETHENE.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Ethene.chk *.chk] output.]]
|[[File:KH1015 LUMO of Ethene (MO7).png|thumb|150px|Figure 5.1.4: LUMO of Ethene (MO 7, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_ETHENE.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Ethene.chk *.chk] output.]]
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital.png|thumb|center|400px| Figure 5.1.5: Frontier MO diagram for the formation of the TS. The numbers on the TS structure (bottom) are atom labels.]]
|-
|[[File:KH1015 HOMO-1 MO16.png|thumb|150px| Figure 5.1.6: HOMO-1 of TS (MO 16, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO MO17.png|thumb|150px|Figure 5.1.7: HOMO of TS (MO 17, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO MO18.png|thumb|150px|Figure 5.1.8: LUMO of TS (MO 18, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 MO19.png|thumb|150px|Figure 5.1.9: LUMO-1 of TS (MO 19, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_Fragment_TS.chk *.chk] output.]]
|}

===Part 2: C-C Bond Length Evolution.===
'''Note: The carbon labels are based on the TS labels in Figure 5.1.5'''.

Referring to table 5.1.2, as the reaction progressed from reactants to product at rtp, {C<sub>1</sub>-C<sub>2</sub>, C<sub>3</sub>-C<sub>4</sub>, C<sub>5</sub>-C<sub>6</sub>} bond lengths (in Å) increased from {1.33343, 1.33343, 1.32726} to {1.37977, 1.37979, 1.38177} to {1.50084, 1.50083, 1.53457}. At the same time, the {C<sub>2</sub>-C<sub>3</sub>, C<sub>4</sub>-C<sub>5</sub>, C<sub>1</sub>-C<sub>6</sub>} bond lengths (in Å) decreased from {1.47078, NA, NA} to {1.41110, 2.11469, 2.11479} to {1.33704, 1.53714, 1.53721}. The change in bond lengths were due to change in hybridization or change in bond order or both.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.1.2: Summary of Evolution of Calculated C-C Bond Length (in Å) through the Reaction at 298.15 K and 1 atm (PM6 Method).
|- style="background: grey; color: white"
|colspan="1" rowspan="2"|'''State'''
|colspan="6"|'''C-C Bond Length (Å)'''
|- style="background: grey; color: white"
|'''C<sub>1</sub>-C<sub>2</sub>'''
|'''C<sub>2</sub>-C<sub>3</sub>'''
|'''C<sub>3</sub>-C<sub>4</sub>'''
|'''C<sub>4</sub>-C<sub>5</sub>'''
|'''C<sub>5</sub>-C<sub>6</sub>'''
|'''C<sub>1</sub>-C<sub>6</sub>'''
|-
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG '''S-Cis Butadiene''']
|1.33343
|1.47078
|1.33343
|NA
|NA
|NA
|-
|'''Hybridization'''
|sp<sup>2</sup>-sp<sup>2</sup> Double Bond
|sp<sup>2</sup>-sp<sup>2</sup> Single Bond
|sp<sup>2</sup>-sp<sup>2</sup> Double Bond
|NA
|NA
|NA
|- style="background: grey; color: white"
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_ETHENE.LOG '''Ethene''']
|NA
|NA
|NA
|NA
|1.32726
|NA
|- style="background: grey; color: white"
|'''Hybridization'''
|NA
|NA
|NA
|NA
|sp<sup>2</sup>-sp<sup>2</sup> Double Bond
|NA
|-
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG '''TS''']
|1.37977
|1.41110
|1.37979
|2.11469
|1.38177
|2.11479
|-
|'''Hybridization'''
|Not clear
|Not clear
|Not clear
|Not clear
|Not clear
|Not clear
|- style="background: grey; color: white"
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE.LOG '''Product''']
|1.50084
|1.33704
|1.50083
|1.53714
|1.53457
|1.53721
|-
|'''Hybridization'''
|sp<sup>3</sup>-sp<sup>2</sup> Single Bond
|sp<sup>2</sup>-sp<sup>2</sup> Double Bond
|sp<sup>2</sup>-sp<sup>3</sup> Single Bond
|sp<sup>3</sup>-sp<sup>3</sup> Single Bond
|sp<sup>3</sup>-sp<sup>3</sup> Single Bond
|sp<sup>3</sup>-sp<sup>3</sup> Single Bond
|}

Table 5.1.3 shows typical sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths in organic compounds at rtp. The calculated values at PM6 level show good agreement with literature values at rtp in table 5.1.3 with less than 1% difference for any given C-C bond length <ref name="C-C" />.

The average value of Van der Waals radius of C atom in literature is 1.88 <ref name="C" />. The calculated distance between the centres of two C atoms of the two fragments in the TS (about 2.115 Å) is less than the sum of their Van der Waals radii (3.76 Å). This suggests presence of partly-formed C-C bond in the TS.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.1.3: Literature Value for Average C-C Bond Length (Experimentally Measured in Å) in Organic Compounds at 298.15 K and 1 atm <ref name="C-C" />.
|-
|'''Hybridization'''
|'''sp<sup>3</sup>-sp<sup>3</sup> Single Bond'''
|'''sp<sup>3</sup>-sp<sup>2</sup> Single Bond'''
|'''sp<sup>2</sup>-sp<sup>2</sup> Double Bond'''
|-
|'''C-C Bond Length (in Å)'''
|1.54
|1.50
|1.47
|}

===Part 3: IRC and Animated Vibrations.===
Referring to Figure 5.1.10, the IRC calculation at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

The calculated reaction profile at PM6 suggested that the reaction was spontaneous at 298.15 K and 1 atm. The activation energy was calculated to be 171 kJ mol<sup>-1</sup> and Δ Gibbs-Free Energy was calculated to be -122 kJ mol<sup>-1</sup> at 298.15 K and 1 atm, which means that there is a very high reaction barrier to be overcome before the reaction could proceed.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Cyclohexene IRC.gif|frame|Figure 5.1.10: IRC for Formation of Cyclohexene (PM6 Method).]]
|| [[File:KH1015 Cyclohexene IRC Graph.png|thumb|Figure 5.1.11: IRC Graph of Energy against Reaction Coordinate for the formation of Cyclohexene at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

Figure 5.1.12 shows the HOMO of the TS system by default (MO 17). It is possible to right-click on the Jmol and choose any MO of interest.

Figure 5.1.13 shows non-covalent interactions at the TS (Red being non-favourable interaction and Blue being favourable interaction). There was no significant non-favourable steric clash in the reaction, which meant that steric clash was not a factor contributing to the high activation barrier.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.1.12: HOMO of the TS (Default view is MO 17, PM6 Method).</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 MO CYCLOHEXENE FRAGMENT TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Cyclohexene Fragment TS Density.png|thumb|Figure 5.1.13: Non Covalent Interactions in the Transition State of Cyclohexene Formation (PM6 Method).]]
|-
|}

Figure 5.1.14 shows an interactive vibration animation of the TS (calculation at PM6 level).

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.1.14: Interactive Vibration Animation of the TS (PM6 Method).</title>
<uploadedFileContents>KH1015 CYCLOHEXENE FRAGMENT TS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 2; measure 3 4</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i950/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>145/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

=='''References.'''==
<references>
<ref name="C-C"> M. A. Fox, J. K. Whitesell, in ''''' '''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen.'', Springer, 1995.
</ref>
<ref name="C"> J. Tsai, R. Taylor, C. Chothia, M. Gerstein, ''J Mol Biol'', 1999, '''290''', 253.</ref>
</references>

Rep:Kh1015TS

2018-03-27T09:06:21Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene. */

=='''1. Abstract.'''==
This paper studied eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:37, 22 March 2018 (UTC) This is really good , you have clearly read beyond the script. However it would have been nice ot have some equations explaining these terms. eg what they represent in the hamiltonian.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:40, 22 March 2018 (UTC) Again good extra reading. DFT is exact if we dont accoutn for 2 electron terms. These get put into the XC correlation term and then different functionals account for this in different ways.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:52, 22 March 2018 (UTC) This is really nicely explained. What is actually happening is you put the derivative wrt to the degrees of freedom into the hessian matrix, then diagonalise it. this give you your eigenvectords as the normal modes and your eigenvalue is the force constant for that normal mode. This normal mode is a linear combination of the degrees of freedom. hence why when you move back and forth along it it looks like a vibration.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:56, 22 March 2018 (UTC) This is an extremely good intro, you have clearly done lots of extra reading and you have backed up a lot of your discussion with equations to make it more clear.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good, in depth discussion, but keep in mind that Berny is the name of the algorithm used for our transition state optimisations rather than the name of a type of transition structure (more information [http://www.cup.uni-muenchen.de/oc/zipse/teaching/computational-chemistry-1/topics/eigenvector-following-with-the-berny-algorithm/ here]).)

Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

Figure 4.1 shows the reaction scheme for Exercise 1.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

Figure 4.2 shows the reaction scheme for Exercise 2.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

Figure 4.3 shows the reaction scheme for Exercise 3.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|500px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

===Exercise 3: Diels-Alder vs Cheletropic.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TS

2018-03-27T09:05:57Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene. */

=='''1. Abstract.'''==
This paper studied eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:37, 22 March 2018 (UTC) This is really good , you have clearly read beyond the script. However it would have been nice ot have some equations explaining these terms. eg what they represent in the hamiltonian.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:40, 22 March 2018 (UTC) Again good extra reading. DFT is exact if we dont accoutn for 2 electron terms. These get put into the XC correlation term and then different functionals account for this in different ways.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:52, 22 March 2018 (UTC) This is really nicely explained. What is actually happening is you put the derivative wrt to the degrees of freedom into the hessian matrix, then diagonalise it. this give you your eigenvectords as the normal modes and your eigenvalue is the force constant for that normal mode. This normal mode is a linear combination of the degrees of freedom. hence why when you move back and forth along it it looks like a vibration.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 09:56, 22 March 2018 (UTC) This is an extremely good intro, you have clearly done lots of extra reading and you have backed up a lot of your discussion with equations to make it more clear.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good, in depth discussion, but keep in mind that Berny is the name of the algorithm used for our transition state optimisations rather than the name of a type of transition structure (more information [http://www.cup.uni-muenchen.de/oc/zipse/teaching/computational-chemistry-1/topics/eigenvector-following-with-the-berny-algorithm/ here].)
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

Figure 4.1 shows the reaction scheme for Exercise 1.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

Figure 4.2 shows the reaction scheme for Exercise 2.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

Figure 4.3 shows the reaction scheme for Exercise 3.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|500px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

===Exercise 3: Diels-Alder vs Cheletropic.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Mod:aps315TS

2018-03-27T09:00:10Z

Fv611: /* Molecular Orbitals */

== Introduction ==

In a simplistic view, a transition state is classified as the highest energy point along a reaction coordinate. As a result, it is characterized as a stationary point and can be confirmed by determining the first derivative of the reaction coordinate as zero. However, this approximation is not an accurate representation of a chemical system undergoing a reaction. This constricted approximation does not account for the possibility of displacement from a system's equilibrium. A chemical system can in fact be displaced in 3N-6 degrees of freedom and a Potential Energy Surface (PES) is a more accurate description of a chemical system undergoing a reaction. A PES is a plot of potential energy against two combinations of these possible degrees of freedom. On a PES a transition state is now characterized as a saddle point and can be confirmed as having a first derivative equal to zero and a second derivative that is negative.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:13, 21 March 2018 (UTC) The surface you are talking about it actually 3N-6. At a TS all the hessian eigen values are positive for all the 3n-6 dimensions apart from 1 which is negative and this is the reaction coord.

This report shall discuss the determination of transition states for three pericyclic reactions. These transition states will be located and characterized using GuassView by optimizing the reagents towards a minimum then subsequently optimizing the transition state using PM6 and B3LYP methods. The PM6 method is semi-empirical; it is effectively a less involved or reduced form of the Hartree-Fock method and is employed for swiftness. The B3LYP method was carried out using a 6-31G(d) basis set, it is a hybrid function utilizing he Hartree-Fock as well as the DFT method and is employed for a more accurate transition state determination.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:13, 21 March 2018 (UTC) You could have gone into more detail here. Possibly added some equations.

In addition, Intrinsic Reaction Coordinate (IRC) calculations were utilized to examine the profile of the minimum energy pathway. An IRC follows the minimum energy pathway along the PES from the transition state towards the reactants and/or the products dependent upon how the calculation was ran. IRC calculations were employed to analyse the reaction profile, changes in bond length and to visualize the reaction.

== Exercise 1: Reaction of Butadiene with Ethylene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job across this section. However, your butadiene is not optimised to a minimum, which led you to the wrong reactant MO energies.)

The reaction between butadiene and ethylene is a Diels-Alder reaction, a [4+2] cycloaddition, producing cyclohexene as the product. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup> In order for the reaction to occur butadiene must adopt the s-cis conformation. This reaction obeys normal electron demand with the diene (butadiene) being more electron rich than the dienophile (ethylene). A reaction scheme is presented below (Scheme 1).
[[File:Diels-Alder(2)_aps315.jpg|350px|thumb|centre|'' '''Scheme 1.''' Reaction of Butadiene with Ethylene.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between butadiene and ethylene was constructed using relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 1). Butadiene's non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

The MOs 16 and 19 produced by Guassian for the transition state are presented below and are correlated to the appropriate interactions in the MO diagram (Figure 1). These demonstrate orbital interactions between the HOMO of butadiene and the LUMO of ethylene, with both having asymmetric symmetry. As a result, it can be inferred that in order for orbital interaction to be favorable and result in overall stabilization of the molecule, the symmetries must be the same (e.g asymmetric and asymmetric) and they must have non-zero orbital overlap integrals. This arises due to the requirement for an overall symmetric function and non-zero overlap integrals corresponding to orbital spacial overlap.<sup>2</sup> A symmetric-symmetric and asymmetric-asymmetric interaction will have a non-zero overlap while opposing symmetries (asymmetric-symmetric/ symmetric-asymmetric) will have zero overlap integral and an overall asymmetric function.

[[File:Diels-Alder aps315(4).jpg|350px|thumb|centre|'' '''Diagram 1.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

<b> Figure 1. </b>

<b> Ethylene </b>

{| class="wikitable"
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<jmol>
<jmolApplet>
<title>Ethylene HOMO</title>
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<uploadedFileContents>ETHENE_OPT(1)_APS315.LOG</uploadedFileContents>
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<jmol>
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<b> Butadiene </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<uploadedFileContents>BUTENE_OPT(1)_APS315.LOG</uploadedFileContents>
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<jmol>
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<title>Butadiene LUMO</title>
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<uploadedFileContents>BUTENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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<b> Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 16 (HOMO-1)</title>
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<jmol>
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<script> frame 32; mo 17; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS LUMO</title>
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<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 18; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>

|
<jmol>
<jmolApplet>
<title>TS 19 (LUMO+1)</title>
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<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 19; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>

|}

=== Carbon Bond Lengths ===
The Diels-Alder reaction involves the formation of two C-C sigma bonds and the breaking of three C-C pi bonds. The C-C bond lengths calculated by Guassian for the reagents, transition state and product are presented below (Table 1). C-C bonds 1,2 and 6 correspond to the bonds of butadiene and bond 4 corresponds to the bond of ethylene (Diagram 2).

Typical bond lengths for C-C sp<sup>2</sup> single and double bond as well as sp<sup>3</sup> single bond are 1.460, 1.316 and 1.507 Å respectively. The values obtained vary by approximately 0.01 Å compared with typical values, however, when compared with literature values for cyclohexene, the values compare well with slight deviation.<sup>3</sup> The double bond calculated is 0.012 Å longer than that in literature, this deviation most likely arises due to the method applied, PM6, providing less accurate values. The use of B3LYP/6-31G(d) would most likely provide a substantially closer value.

The typical van der Waals radius of a carbon atom is 1.70 Å whilst the length of the partly formed C-C bonds in the transition state are 2.113 and 2.116 Å. The van der Waals radius is defined as half the distance of closest approach between two non-bonded atoms, therefore the total distance is 3.40 Å. The values obtained are substantially shorter than this radius by 1.287 and 1.284 Å, aligning with the partial formation of C-C bonds in the transition state.

As the reaction progresses bonds 3 and 5 shorten as the C-C bonds are formed. Simultaneously, bonds 2,4 and 6 all elongate whilst bond 1 shortens, represented below in Graph 1.

[[File:Bond_Numbers_aps315.jpg|250px|thumb|centre|'' '''Figure 2.''' C-C Bond Numbers.'']]

{| class="wikitable" border="1"| centre
|+ '' '''Table 1.''' C-C Bond Lengths during Diels-Alder Reaction''
! Bond !! Reagents Bond Length / Å !! Transition State Bond Length / Å !! Product Bond Length / Å
|-
| '''Bond 1''' || 1.468 || 1.411 || 1.338
|-
| '''Bond 2''' || 1.335 || 1.380 || 1.500
|-
| '''Bond 3''' || - || 2.113 || 1.540
|-
| '''Bond 4''' || 1.327 || 1.382 || 1.541
|-
| '''Bond 5''' || - || 2.116 || 1.540
|-
| '''Bond 6''' || 1.335 || 1.380 || 1.500
|}

[[File:BondLengths_aps315.JPG|550px|thumb|centre|'' '''Graph 1.''' C-C Bond Length Changes with Reaction Coordinate.'']]

=== Bond Vibration ===
The vibration that corresponds to the formation of the transition state is presented below (Image 2). The formation of the new sigma bonds can be seen to occur simultaneously, this demonstrates the synchronous, concerted nature of the Diels-Alder mechanism.

[[File:TS_Vibrations_aps315.gif | centre ]]

=== Relevant Files ===

Butadiene - [[:File:BUTENE_OPT(1)_APS315.LOG]]

Ethylene - [[:File:ETHENE_OPT(1)_APS315.LOG]]

Transition State - [[:File:EX1_TS_APS315.LOG]]

Cyclohexene - [[:File:PRODUCT_aps315.LOG]]

Transition State IRC - [[:File:TS_IRC_aps315.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

The reaction between cyclohexadiene and 1,3-dioxole is a Diels-Alder reaction, a [4+2] cycloaddition, producing two possible products dependent upon the orientation of molecule approach (Scheme 2). An exo product is formed when the substituents of the 1,3-dioxole are facing away from the cyclohexadiene π system. Alternatively, the endo product is formed when the substituents of the 1,3-dioxole are facing towards the cyclohexadiene π system. In general, the endo product is frequently the thermodynamically preferred due to secondary orbital effects that involve stabilizing overlap in the endo transition state. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup>
[[File:Ex2_Scheme(2)_aps315.jpg|450px|thumb|centre|'' '''Scheme 2.''' Reaction of Cyclohexadiene and 1,3-Dioxole.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between cyclohexadiene and 1,3-dioxole was constructed using average relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 2). Non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

Due to the electron-donating nature of the oxygen atoms present in 1,3-dioxole, the dienophile becomes more electron rich, raising the energies of its HOMO and LUMO. This results in a [4+2] cycloaddition that obeys inverse electron demand.<sup>1</sup> When comparing the exo and endo transition states, both still obey inverse electron demand and follow the MO diagram displayed below, however, the relative energies of the molecular orbitals is shifted. The endo transition state can be seen to have a lower energy HOMO by 0.00492 Hartrees/particle and a higher energy LUMO by 0.00237 Hartrees/particle. This shift in energies arises due to stabilization of the endo HOMO by secondary orbital effects; overlap between the π system of cyclohexadiene and 1,3-dioxole. The exo transition state is only stabilized through primary interactions, whereas the endo transition state is stabilized through both primary and secondary interactions. This is presented below (Figure 2).

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:17, 21 March 2018 (UTC) You have just stated that the reaction is inverse and you have not investigated it quantitatively, by comparing reactant orbital energies on the same PES.

The associated MOs are presented below for both the Exo and Endo transition states (Figure 3).
([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) You optimised both TS correctly, but you have not placed the MOs in their correct order so this might come from an incorrect optimisation of your reactants. Your discussion of relative energies should also have been formulated in terms of energy gaps rather than absolute numbers.)

[[File:Ex2_MO_aps315.jpg|350px|thumb|centre|'' '''Diagram 2.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

[[File:Ex2_Secondary_aps315.jpg|350px|thumb|centre|'' '''Figure 2.''' Primary and Secondary Orbital Interactions in Transition State.'']]

<b> Figure 3. </b>

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:19, 21 March 2018 (UTC) This is not correct, furthermore this diagram is quite difficult to understand. you should have drawn it at an angle.

<b> Endo Transition State </b>

{| class="wikitable"
|
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{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 42 (LUMO)</title>
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<script> frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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<jmol>
<jmolApplet>
<title>TS MO 43 (LUMO+1)</title>
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<b> Exo Transition State </b>

{| class="wikitable"
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<jmol>
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{| class="wikitable"
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<jmol>
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<title>TS MO 42 (LUMO)</title>
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|
<jmol>
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<title>TS MO 43 (LUMO+1)</title>
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<script> frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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|}

=== Thermochemistry ===
The energy barriers and the reaction energies at room temperature are presented below (Table 2)(Figure 4). The energy barrier is the activation energy required for a reaction to occur, a product with a lower activation energy is kinetically preferred as it will more readily overcome the energy requirement for the reaction and thus form faster. The endo product can be seen to have a lower activation energy and thus can be determined to be the kinetically preferred product. This arises due to the endo transition state being lower in energy as it is stabilized by secondary orbital effects (Figure 2).

The reaction energy is characterized as the difference in energy between the reactants and products. The product with the more negative reaction energy is thermodynamically preferred as it is the more stable. The endo product can be seen to have a more negative reaction energy and thus can be determined to be the thermodynamically preferred product. This most likely arises due to steric clash that can be observed in the exo product between the carbon bridge and five-membered ring which is not observed for the endo product.

{| class="wikitable" border="1"| centre
|+ '' '''Table 2.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.057016 || 149.695519 || -0.030848 || -80.99143017
|-
| '''Exo''' || 0.060002 || 157.535263 || -0.028146 || -73.89732863
|}

[[File:Ex2_ReactionProf2_aps315.jpg|350px|thumb|centre|'' '''Figure 4.''' Reaction Profile for the Formation of Exo and Endo Products'']]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:22, 21 March 2018 (UTC) Your energies are slightly out. I suspect that your reactant energies have been slightly miss calculated. However you have still come to the correct conclusions. There were points where you could have gone into more detail.

=== Relevant Files ===

Cyclohexadiene(BL3YP) - [[:File:CYCLOHEXADIENE(2)_aps315.LOG]]

1,3-Dioxole(B3LYP) - [[:File:DIOXOLE(2)_APS315.LOG]]

Endo Product(B3LYP) - [[:File:ENDOPROD_APS315.LOG]]

Exo Product(BL3YP) - [[:File:EXOPROD(2)_APS315.LOG]]

Exo TS (BL3YP) - [[:File:EXO_TS(3)_aps315.LOG]]

Endo TS (BL3YP) - [[:File:ENDO_TS(7)_aps315.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic ==
The reaction between xylylene and sulfur dioxide can proceed via two possible reaction mechanisms; a Diels-Alder reaction, a [4+2] cycloaddition, or a cheletropic reaction (Scheme 2). The Diels-Alder reaction can again proceed via endo or exo mechanisms dependent upon the orientation of approach of sulfur dioxide. The cheletropic reaction generates a five-membered heterocyclic ring product. Due to the significantly different mechanisms, as expected, the reaction profiles of these reactions vary greatly.

[[File:Ex3_ReactionScheme_aps315.jpg|450px|thumb|centre|'' '''Scheme 3.''' Reaction of Xylylene and Sulfur Dioxide.'']]

=== IRC ===

The IRC calculations performed for these three alternative mechanisms have been visualised and are presented below. The endo and exo Diels-Alder reactions can be seen to be asynchronous whereas the cheletropic reaction can be seen to be synchronous. Xylylene's lack of stability is displayed through the IRCs for the reactions; the bond lengths of the six-membered ring undergo variations throughout the IRC and equalize upon the formation of the product.

''' Endo Diels-Alder '''
[[File:EndoIRC_aps315.gif | centre ]]

''' Exo Diels-Alder '''
[[File:ExoIRC_aps315(1).gif | centre ]]

''' Cheletropic '''
[[File:CheleIRC_aps315.gif | centre ]]

=== Thermochemistry ===

The energy barriers and the reaction energies at room temperature are presented below (Table 3)(Figure 5). The data collected suggests that the endo Diels-Alder product is kinetically preferred with the mechanism having the lowest activation energy. This result arises due to reasons discussed for the previous example; secondary orbital interactions stabilise the endo product's transition state. However, the endo product can be seen to be at a higher energy than that of the exo product; this arises due to the destabilizing steric clash between the oxygen atom and the six-membered heterocyclic ring. The reaction energies of the three mechanisms are all substantially large, this arises due to the stability of the aromatic ring formed that provides a strong driving force to the products. The cheletropic product has a substantially higher activation energy than the Diels-Alder, however has the lowest energy product and thus is the thermodynamically preferred product. This result can be explained by examining bond energies; C-S 272 kj/mol, C-O 358 kj/mol and S=O 522 kj/mol. The S=O is markedly more stable than the alternative C-O and S-O bonds formed during the Diels-Alder reaction, making the cheletropic product more stable.

{| class="wikitable" border="1"| centre
|+ '' '''Table 3.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.031064 || 81.55853821 || -0.037798 || -99.23865656
|-
| '''Exo''' || 0.032581 || 85.541422 || -0.038043 || -99.88190411
|-
| '''Cheletropic''' || 0.039566 || 103.880541 || -0.059492 || -156.1962579
|}

(You're using far too many decimal places - 10 micro J/mol in the reactants! [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

[[File:Ex3_ReactionProf3_aps315.jpg|450px|thumb|centre|'' '''Figure 5.''' Reaction Profile of Xylylene and Sulfur Dioxide.'']]

(Label the energy axis. If you put values on the profile it will make it easier to read the data [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

Xylylene has an additional site where a Diels-Alder reaction can occur. This reaction is 'endocyclic', occuring with the diene present in the six-membered ring, the 'exocyclic' reaction was previously analysed. The energy barriers and the reaction energies at room temperature for these reactions are presented below (Table 4)(Figure 6). As can be seen, the product energies for both the endo and exo reaction are higher than the energies of the reagents. In addition, the activation energies are substantially higher than for the 'exocyclic' reaction. These results arise due to the lack of aromatic stability provided by the 'endocyclic' products.

{| class="wikitable" border="1"| centre
|+ '' '''Table 4.'''Activation and Reaction Energies for 'Endocyclic' Reaction''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.042574 || 111.778046 || 0.006113 || 16.0496827
|-
| '''Exo''' || 0.045558 || 119.612538 || 0.00781 || 20.505157
|}

[[File:Ex3(1)_ReactionProf_aps315.jpg|450px|thumb|centre|'' '''Figure 6.''' Reaction Profile of 'Endocyclic' Xylylene and Sulfur Dioxide.'']]

=== Relevant Files ===

''' 'Exocyclic' Diels-Alder '''

Xylylene - [[:File:XYLYLENE_APS315.LOG]]

Sulfur Dioxide - [[:File:SO2_APS315.LOG]]

Endo TS - [[:File:EX3_ENDO_TS(8)_APS315.LOG]]

Endo IRC - [[:File:EX3_ENDO_IRC(1)_APS315.LOG]]

Endo Product - [[:File:EX3_ENDOPROD_APS315.LOG]]

Exo TS - [[:File:EX3_Exo_TS(1)_APS315.LOG]]

Exo IRC - [[:File:EX3_EXO_IRC_APS315.LOG]]

Exo Product - [[:File:EX3_EXOPPROD(1)_APS315.LOG]]

''' Cheletropic '''

Cheletropic TS - [[:File:EX3_CHELE_TS(2)_APS315.LOG]]

Cheletropic IRC - [[:File:EX3_CHELE_IRC(1)_APS315.LOG]]

Cheletropic Product - [[:File:EX3_CHELE_PROD_APS315.LOG]]

''' 'Endocyclic' Diels-Alder '''

Endo TS - [[:File:EX3(1)_ENDO_TS_APS315.LOG]]

Endo Product - [[:File:EX3(1)_ENDOPRODUCT_APS315.LOG]]

Exo TS - [[:File:EXO(1)_Exo_TS(1)_APS315.LOG]]

Exo Product - [[:File:EX3(1)_EXOPRODUCT_APS315.LOG]]

== Conclusion ==

The data produced by GuassView correlates well with pre-existing theory. For instance, the effects of the endo rule, aromatic stability and steric clash could all be employed to explain and align with the results obtained. The computational methods employed proved highly effective with limited knowledge of the reactions required. Only a fundamental understanding of chemistry is required to conduct and analyse these methods.

The approach of modelling provides unparalleled access to understanding chemical reactions and pathways and allows for chemistry to be conducted theoretically with well estimated outcomes that align with experimental values.

== References ==
1. J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', ''Oxford University Press'', '''2''', 2012.

2. P. Atkins, J. Rourke, T. Overton and F. Armstrong, '' Shriver & Atkins Inorganic Chemistry'', ''Oxford University Press'', '''5''', 2010.

3. A. Orpen and D. Watson, ''J. Chem. Soc. Dalt. Trans.'', 1987.

Rep:Mod:aps315TS

2018-03-27T08:58:17Z

Fv611: /* Molecular Orbitals */

== Introduction ==

In a simplistic view, a transition state is classified as the highest energy point along a reaction coordinate. As a result, it is characterized as a stationary point and can be confirmed by determining the first derivative of the reaction coordinate as zero. However, this approximation is not an accurate representation of a chemical system undergoing a reaction. This constricted approximation does not account for the possibility of displacement from a system's equilibrium. A chemical system can in fact be displaced in 3N-6 degrees of freedom and a Potential Energy Surface (PES) is a more accurate description of a chemical system undergoing a reaction. A PES is a plot of potential energy against two combinations of these possible degrees of freedom. On a PES a transition state is now characterized as a saddle point and can be confirmed as having a first derivative equal to zero and a second derivative that is negative.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:13, 21 March 2018 (UTC) The surface you are talking about it actually 3N-6. At a TS all the hessian eigen values are positive for all the 3n-6 dimensions apart from 1 which is negative and this is the reaction coord.

This report shall discuss the determination of transition states for three pericyclic reactions. These transition states will be located and characterized using GuassView by optimizing the reagents towards a minimum then subsequently optimizing the transition state using PM6 and B3LYP methods. The PM6 method is semi-empirical; it is effectively a less involved or reduced form of the Hartree-Fock method and is employed for swiftness. The B3LYP method was carried out using a 6-31G(d) basis set, it is a hybrid function utilizing he Hartree-Fock as well as the DFT method and is employed for a more accurate transition state determination.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:13, 21 March 2018 (UTC) You could have gone into more detail here. Possibly added some equations.

In addition, Intrinsic Reaction Coordinate (IRC) calculations were utilized to examine the profile of the minimum energy pathway. An IRC follows the minimum energy pathway along the PES from the transition state towards the reactants and/or the products dependent upon how the calculation was ran. IRC calculations were employed to analyse the reaction profile, changes in bond length and to visualize the reaction.

== Exercise 1: Reaction of Butadiene with Ethylene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job across this section. However, your butadiene is not optimised to a minimum, which led you to the wrong reactant MO energies.)

The reaction between butadiene and ethylene is a Diels-Alder reaction, a [4+2] cycloaddition, producing cyclohexene as the product. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup> In order for the reaction to occur butadiene must adopt the s-cis conformation. This reaction obeys normal electron demand with the diene (butadiene) being more electron rich than the dienophile (ethylene). A reaction scheme is presented below (Scheme 1).
[[File:Diels-Alder(2)_aps315.jpg|350px|thumb|centre|'' '''Scheme 1.''' Reaction of Butadiene with Ethylene.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between butadiene and ethylene was constructed using relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 1). Butadiene's non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

The MOs 16 and 19 produced by Guassian for the transition state are presented below and are correlated to the appropriate interactions in the MO diagram (Figure 1). These demonstrate orbital interactions between the HOMO of butadiene and the LUMO of ethylene, with both having asymmetric symmetry. As a result, it can be inferred that in order for orbital interaction to be favorable and result in overall stabilization of the molecule, the symmetries must be the same (e.g asymmetric and asymmetric) and they must have non-zero orbital overlap integrals. This arises due to the requirement for an overall symmetric function and non-zero overlap integrals corresponding to orbital spacial overlap.<sup>2</sup> A symmetric-symmetric and asymmetric-asymmetric interaction will have a non-zero overlap while opposing symmetries (asymmetric-symmetric/ symmetric-asymmetric) will have zero overlap integral and an overall asymmetric function.

[[File:Diels-Alder aps315(4).jpg|350px|thumb|centre|'' '''Diagram 1.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

<b> Figure 1. </b>

<b> Ethylene </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>Ethylene HOMO</title>
<color>white</color>
<uploadedFileContents>ETHENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>Ethylene LUMO</title>
<color>white</color>
<uploadedFileContents>ETHENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

<b> Butadiene </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<uploadedFileContents>BUTENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<uploadedFileContents>BUTENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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|}

<b> Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 16 (HOMO-1)</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 16; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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|
<jmol>
<jmolApplet>
<title>TS HOMO</title>
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<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 17; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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|}

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS LUMO</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 18; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>

|
<jmol>
<jmolApplet>
<title>TS 19 (LUMO+1)</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 19; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>

|}

=== Carbon Bond Lengths ===
The Diels-Alder reaction involves the formation of two C-C sigma bonds and the breaking of three C-C pi bonds. The C-C bond lengths calculated by Guassian for the reagents, transition state and product are presented below (Table 1). C-C bonds 1,2 and 6 correspond to the bonds of butadiene and bond 4 corresponds to the bond of ethylene (Diagram 2).

Typical bond lengths for C-C sp<sup>2</sup> single and double bond as well as sp<sup>3</sup> single bond are 1.460, 1.316 and 1.507 Å respectively. The values obtained vary by approximately 0.01 Å compared with typical values, however, when compared with literature values for cyclohexene, the values compare well with slight deviation.<sup>3</sup> The double bond calculated is 0.012 Å longer than that in literature, this deviation most likely arises due to the method applied, PM6, providing less accurate values. The use of B3LYP/6-31G(d) would most likely provide a substantially closer value.

The typical van der Waals radius of a carbon atom is 1.70 Å whilst the length of the partly formed C-C bonds in the transition state are 2.113 and 2.116 Å. The van der Waals radius is defined as half the distance of closest approach between two non-bonded atoms, therefore the total distance is 3.40 Å. The values obtained are substantially shorter than this radius by 1.287 and 1.284 Å, aligning with the partial formation of C-C bonds in the transition state.

As the reaction progresses bonds 3 and 5 shorten as the C-C bonds are formed. Simultaneously, bonds 2,4 and 6 all elongate whilst bond 1 shortens, represented below in Graph 1.

[[File:Bond_Numbers_aps315.jpg|250px|thumb|centre|'' '''Figure 2.''' C-C Bond Numbers.'']]

{| class="wikitable" border="1"| centre
|+ '' '''Table 1.''' C-C Bond Lengths during Diels-Alder Reaction''
! Bond !! Reagents Bond Length / Å !! Transition State Bond Length / Å !! Product Bond Length / Å
|-
| '''Bond 1''' || 1.468 || 1.411 || 1.338
|-
| '''Bond 2''' || 1.335 || 1.380 || 1.500
|-
| '''Bond 3''' || - || 2.113 || 1.540
|-
| '''Bond 4''' || 1.327 || 1.382 || 1.541
|-
| '''Bond 5''' || - || 2.116 || 1.540
|-
| '''Bond 6''' || 1.335 || 1.380 || 1.500
|}

[[File:BondLengths_aps315.JPG|550px|thumb|centre|'' '''Graph 1.''' C-C Bond Length Changes with Reaction Coordinate.'']]

=== Bond Vibration ===
The vibration that corresponds to the formation of the transition state is presented below (Image 2). The formation of the new sigma bonds can be seen to occur simultaneously, this demonstrates the synchronous, concerted nature of the Diels-Alder mechanism.

[[File:TS_Vibrations_aps315.gif | centre ]]

=== Relevant Files ===

Butadiene - [[:File:BUTENE_OPT(1)_APS315.LOG]]

Ethylene - [[:File:ETHENE_OPT(1)_APS315.LOG]]

Transition State - [[:File:EX1_TS_APS315.LOG]]

Cyclohexene - [[:File:PRODUCT_aps315.LOG]]

Transition State IRC - [[:File:TS_IRC_aps315.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

The reaction between cyclohexadiene and 1,3-dioxole is a Diels-Alder reaction, a [4+2] cycloaddition, producing two possible products dependent upon the orientation of molecule approach (Scheme 2). An exo product is formed when the substituents of the 1,3-dioxole are facing away from the cyclohexadiene π system. Alternatively, the endo product is formed when the substituents of the 1,3-dioxole are facing towards the cyclohexadiene π system. In general, the endo product is frequently the thermodynamically preferred due to secondary orbital effects that involve stabilizing overlap in the endo transition state. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup>
[[File:Ex2_Scheme(2)_aps315.jpg|450px|thumb|centre|'' '''Scheme 2.''' Reaction of Cyclohexadiene and 1,3-Dioxole.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between cyclohexadiene and 1,3-dioxole was constructed using average relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 2). Non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

Due to the electron-donating nature of the oxygen atoms present in 1,3-dioxole, the dienophile becomes more electron rich, raising the energies of its HOMO and LUMO. This results in a [4+2] cycloaddition that obeys inverse electron demand.<sup>1</sup> When comparing the exo and endo transition states, both still obey inverse electron demand and follow the MO diagram displayed below, however, the relative energies of the molecular orbitals is shifted. The endo transition state can be seen to have a lower energy HOMO by 0.00492 Hartrees/particle and a higher energy LUMO by 0.00237 Hartrees/particle. This shift in energies arises due to stabilization of the endo HOMO by secondary orbital effects; overlap between the π system of cyclohexadiene and 1,3-dioxole. The exo transition state is only stabilized through primary interactions, whereas the endo transition state is stabilized through both primary and secondary interactions. This is presented below (Figure 2).

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:17, 21 March 2018 (UTC) You have just stated that the reaction is inverse and you have not investigated it quantitatively, by comparing reactant orbital energies on the same PES.

The associated MOs are presented below for both the Exo and Endo transition states (Figure 3).
([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) All you have done is here is copy the MO from exercise 1 and (incorrectly) raise the relative energy of the TS LUMO+1. You actually optimised both TS correctly, so this might come from an incorrect optimisation of your reactants. Your discussion of relative energies should also have been formulated in terms of energy gaps rather than absolute numbers.)

[[File:Ex2_MO_aps315.jpg|350px|thumb|centre|'' '''Diagram 2.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

[[File:Ex2_Secondary_aps315.jpg|350px|thumb|centre|'' '''Figure 2.''' Primary and Secondary Orbital Interactions in Transition State.'']]

<b> Figure 3. </b>

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:19, 21 March 2018 (UTC) This is not correct, furthermore this diagram is quite difficult to understand. you should have drawn it at an angle.

<b> Endo Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 40 (HOMO-1)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
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<jmol>
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{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 42 (LUMO)</title>
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<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
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<jmol>
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<title>TS MO 43 (LUMO+1)</title>
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<script> frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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<b> Exo Transition State </b>

{| class="wikitable"
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<jmol>
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<title>TS MO 40 (HOMO-1)</title>
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<jmol>
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{| class="wikitable"
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<jmol>
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<title>TS MO 42 (LUMO)</title>
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<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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|
<jmol>
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<title>TS MO 43 (LUMO+1)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat; ""</script>
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|}

=== Thermochemistry ===
The energy barriers and the reaction energies at room temperature are presented below (Table 2)(Figure 4). The energy barrier is the activation energy required for a reaction to occur, a product with a lower activation energy is kinetically preferred as it will more readily overcome the energy requirement for the reaction and thus form faster. The endo product can be seen to have a lower activation energy and thus can be determined to be the kinetically preferred product. This arises due to the endo transition state being lower in energy as it is stabilized by secondary orbital effects (Figure 2).

The reaction energy is characterized as the difference in energy between the reactants and products. The product with the more negative reaction energy is thermodynamically preferred as it is the more stable. The endo product can be seen to have a more negative reaction energy and thus can be determined to be the thermodynamically preferred product. This most likely arises due to steric clash that can be observed in the exo product between the carbon bridge and five-membered ring which is not observed for the endo product.

{| class="wikitable" border="1"| centre
|+ '' '''Table 2.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.057016 || 149.695519 || -0.030848 || -80.99143017
|-
| '''Exo''' || 0.060002 || 157.535263 || -0.028146 || -73.89732863
|}

[[File:Ex2_ReactionProf2_aps315.jpg|350px|thumb|centre|'' '''Figure 4.''' Reaction Profile for the Formation of Exo and Endo Products'']]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:22, 21 March 2018 (UTC) Your energies are slightly out. I suspect that your reactant energies have been slightly miss calculated. However you have still come to the correct conclusions. There were points where you could have gone into more detail.

=== Relevant Files ===

Cyclohexadiene(BL3YP) - [[:File:CYCLOHEXADIENE(2)_aps315.LOG]]

1,3-Dioxole(B3LYP) - [[:File:DIOXOLE(2)_APS315.LOG]]

Endo Product(B3LYP) - [[:File:ENDOPROD_APS315.LOG]]

Exo Product(BL3YP) - [[:File:EXOPROD(2)_APS315.LOG]]

Exo TS (BL3YP) - [[:File:EXO_TS(3)_aps315.LOG]]

Endo TS (BL3YP) - [[:File:ENDO_TS(7)_aps315.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic ==
The reaction between xylylene and sulfur dioxide can proceed via two possible reaction mechanisms; a Diels-Alder reaction, a [4+2] cycloaddition, or a cheletropic reaction (Scheme 2). The Diels-Alder reaction can again proceed via endo or exo mechanisms dependent upon the orientation of approach of sulfur dioxide. The cheletropic reaction generates a five-membered heterocyclic ring product. Due to the significantly different mechanisms, as expected, the reaction profiles of these reactions vary greatly.

[[File:Ex3_ReactionScheme_aps315.jpg|450px|thumb|centre|'' '''Scheme 3.''' Reaction of Xylylene and Sulfur Dioxide.'']]

=== IRC ===

The IRC calculations performed for these three alternative mechanisms have been visualised and are presented below. The endo and exo Diels-Alder reactions can be seen to be asynchronous whereas the cheletropic reaction can be seen to be synchronous. Xylylene's lack of stability is displayed through the IRCs for the reactions; the bond lengths of the six-membered ring undergo variations throughout the IRC and equalize upon the formation of the product.

''' Endo Diels-Alder '''
[[File:EndoIRC_aps315.gif | centre ]]

''' Exo Diels-Alder '''
[[File:ExoIRC_aps315(1).gif | centre ]]

''' Cheletropic '''
[[File:CheleIRC_aps315.gif | centre ]]

=== Thermochemistry ===

The energy barriers and the reaction energies at room temperature are presented below (Table 3)(Figure 5). The data collected suggests that the endo Diels-Alder product is kinetically preferred with the mechanism having the lowest activation energy. This result arises due to reasons discussed for the previous example; secondary orbital interactions stabilise the endo product's transition state. However, the endo product can be seen to be at a higher energy than that of the exo product; this arises due to the destabilizing steric clash between the oxygen atom and the six-membered heterocyclic ring. The reaction energies of the three mechanisms are all substantially large, this arises due to the stability of the aromatic ring formed that provides a strong driving force to the products. The cheletropic product has a substantially higher activation energy than the Diels-Alder, however has the lowest energy product and thus is the thermodynamically preferred product. This result can be explained by examining bond energies; C-S 272 kj/mol, C-O 358 kj/mol and S=O 522 kj/mol. The S=O is markedly more stable than the alternative C-O and S-O bonds formed during the Diels-Alder reaction, making the cheletropic product more stable.

{| class="wikitable" border="1"| centre
|+ '' '''Table 3.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.031064 || 81.55853821 || -0.037798 || -99.23865656
|-
| '''Exo''' || 0.032581 || 85.541422 || -0.038043 || -99.88190411
|-
| '''Cheletropic''' || 0.039566 || 103.880541 || -0.059492 || -156.1962579
|}

(You're using far too many decimal places - 10 micro J/mol in the reactants! [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

[[File:Ex3_ReactionProf3_aps315.jpg|450px|thumb|centre|'' '''Figure 5.''' Reaction Profile of Xylylene and Sulfur Dioxide.'']]

(Label the energy axis. If you put values on the profile it will make it easier to read the data [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

Xylylene has an additional site where a Diels-Alder reaction can occur. This reaction is 'endocyclic', occuring with the diene present in the six-membered ring, the 'exocyclic' reaction was previously analysed. The energy barriers and the reaction energies at room temperature for these reactions are presented below (Table 4)(Figure 6). As can be seen, the product energies for both the endo and exo reaction are higher than the energies of the reagents. In addition, the activation energies are substantially higher than for the 'exocyclic' reaction. These results arise due to the lack of aromatic stability provided by the 'endocyclic' products.

{| class="wikitable" border="1"| centre
|+ '' '''Table 4.'''Activation and Reaction Energies for 'Endocyclic' Reaction''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.042574 || 111.778046 || 0.006113 || 16.0496827
|-
| '''Exo''' || 0.045558 || 119.612538 || 0.00781 || 20.505157
|}

[[File:Ex3(1)_ReactionProf_aps315.jpg|450px|thumb|centre|'' '''Figure 6.''' Reaction Profile of 'Endocyclic' Xylylene and Sulfur Dioxide.'']]

=== Relevant Files ===

''' 'Exocyclic' Diels-Alder '''

Xylylene - [[:File:XYLYLENE_APS315.LOG]]

Sulfur Dioxide - [[:File:SO2_APS315.LOG]]

Endo TS - [[:File:EX3_ENDO_TS(8)_APS315.LOG]]

Endo IRC - [[:File:EX3_ENDO_IRC(1)_APS315.LOG]]

Endo Product - [[:File:EX3_ENDOPROD_APS315.LOG]]

Exo TS - [[:File:EX3_Exo_TS(1)_APS315.LOG]]

Exo IRC - [[:File:EX3_EXO_IRC_APS315.LOG]]

Exo Product - [[:File:EX3_EXOPPROD(1)_APS315.LOG]]

''' Cheletropic '''

Cheletropic TS - [[:File:EX3_CHELE_TS(2)_APS315.LOG]]

Cheletropic IRC - [[:File:EX3_CHELE_IRC(1)_APS315.LOG]]

Cheletropic Product - [[:File:EX3_CHELE_PROD_APS315.LOG]]

''' 'Endocyclic' Diels-Alder '''

Endo TS - [[:File:EX3(1)_ENDO_TS_APS315.LOG]]

Endo Product - [[:File:EX3(1)_ENDOPRODUCT_APS315.LOG]]

Exo TS - [[:File:EXO(1)_Exo_TS(1)_APS315.LOG]]

Exo Product - [[:File:EX3(1)_EXOPRODUCT_APS315.LOG]]

== Conclusion ==

The data produced by GuassView correlates well with pre-existing theory. For instance, the effects of the endo rule, aromatic stability and steric clash could all be employed to explain and align with the results obtained. The computational methods employed proved highly effective with limited knowledge of the reactions required. Only a fundamental understanding of chemistry is required to conduct and analyse these methods.

The approach of modelling provides unparalleled access to understanding chemical reactions and pathways and allows for chemistry to be conducted theoretically with well estimated outcomes that align with experimental values.

== References ==
1. J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', ''Oxford University Press'', '''2''', 2012.

2. P. Atkins, J. Rourke, T. Overton and F. Armstrong, '' Shriver & Atkins Inorganic Chemistry'', ''Oxford University Press'', '''5''', 2010.

3. A. Orpen and D. Watson, ''J. Chem. Soc. Dalt. Trans.'', 1987.

Rep:Mod:aps315TS

2018-03-27T08:48:04Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Introduction ==

In a simplistic view, a transition state is classified as the highest energy point along a reaction coordinate. As a result, it is characterized as a stationary point and can be confirmed by determining the first derivative of the reaction coordinate as zero. However, this approximation is not an accurate representation of a chemical system undergoing a reaction. This constricted approximation does not account for the possibility of displacement from a system's equilibrium. A chemical system can in fact be displaced in 3N-6 degrees of freedom and a Potential Energy Surface (PES) is a more accurate description of a chemical system undergoing a reaction. A PES is a plot of potential energy against two combinations of these possible degrees of freedom. On a PES a transition state is now characterized as a saddle point and can be confirmed as having a first derivative equal to zero and a second derivative that is negative.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:13, 21 March 2018 (UTC) The surface you are talking about it actually 3N-6. At a TS all the hessian eigen values are positive for all the 3n-6 dimensions apart from 1 which is negative and this is the reaction coord.

This report shall discuss the determination of transition states for three pericyclic reactions. These transition states will be located and characterized using GuassView by optimizing the reagents towards a minimum then subsequently optimizing the transition state using PM6 and B3LYP methods. The PM6 method is semi-empirical; it is effectively a less involved or reduced form of the Hartree-Fock method and is employed for swiftness. The B3LYP method was carried out using a 6-31G(d) basis set, it is a hybrid function utilizing he Hartree-Fock as well as the DFT method and is employed for a more accurate transition state determination.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:13, 21 March 2018 (UTC) You could have gone into more detail here. Possibly added some equations.

In addition, Intrinsic Reaction Coordinate (IRC) calculations were utilized to examine the profile of the minimum energy pathway. An IRC follows the minimum energy pathway along the PES from the transition state towards the reactants and/or the products dependent upon how the calculation was ran. IRC calculations were employed to analyse the reaction profile, changes in bond length and to visualize the reaction.

== Exercise 1: Reaction of Butadiene with Ethylene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job across this section. However, your butadiene is not optimised to a minimum, which led you to the wrong reactant MO energies.)

The reaction between butadiene and ethylene is a Diels-Alder reaction, a [4+2] cycloaddition, producing cyclohexene as the product. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup> In order for the reaction to occur butadiene must adopt the s-cis conformation. This reaction obeys normal electron demand with the diene (butadiene) being more electron rich than the dienophile (ethylene). A reaction scheme is presented below (Scheme 1).
[[File:Diels-Alder(2)_aps315.jpg|350px|thumb|centre|'' '''Scheme 1.''' Reaction of Butadiene with Ethylene.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between butadiene and ethylene was constructed using relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 1). Butadiene's non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

The MOs 16 and 19 produced by Guassian for the transition state are presented below and are correlated to the appropriate interactions in the MO diagram (Figure 1). These demonstrate orbital interactions between the HOMO of butadiene and the LUMO of ethylene, with both having asymmetric symmetry. As a result, it can be inferred that in order for orbital interaction to be favorable and result in overall stabilization of the molecule, the symmetries must be the same (e.g asymmetric and asymmetric) and they must have non-zero orbital overlap integrals. This arises due to the requirement for an overall symmetric function and non-zero overlap integrals corresponding to orbital spacial overlap.<sup>2</sup> A symmetric-symmetric and asymmetric-asymmetric interaction will have a non-zero overlap while opposing symmetries (asymmetric-symmetric/ symmetric-asymmetric) will have zero overlap integral and an overall asymmetric function.

[[File:Diels-Alder aps315(4).jpg|350px|thumb|centre|'' '''Diagram 1.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

<b> Figure 1. </b>

<b> Ethylene </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>Ethylene HOMO</title>
<color>white</color>
<uploadedFileContents>ETHENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>Ethylene LUMO</title>
<color>white</color>
<uploadedFileContents>ETHENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

<b> Butadiene </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<uploadedFileContents>BUTENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<uploadedFileContents>BUTENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

<b> Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 16 (HOMO-1)</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 16; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS HOMO</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 17; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS LUMO</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 18; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>

|
<jmol>
<jmolApplet>
<title>TS 19 (LUMO+1)</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 19; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>

|}

=== Carbon Bond Lengths ===
The Diels-Alder reaction involves the formation of two C-C sigma bonds and the breaking of three C-C pi bonds. The C-C bond lengths calculated by Guassian for the reagents, transition state and product are presented below (Table 1). C-C bonds 1,2 and 6 correspond to the bonds of butadiene and bond 4 corresponds to the bond of ethylene (Diagram 2).

Typical bond lengths for C-C sp<sup>2</sup> single and double bond as well as sp<sup>3</sup> single bond are 1.460, 1.316 and 1.507 Å respectively. The values obtained vary by approximately 0.01 Å compared with typical values, however, when compared with literature values for cyclohexene, the values compare well with slight deviation.<sup>3</sup> The double bond calculated is 0.012 Å longer than that in literature, this deviation most likely arises due to the method applied, PM6, providing less accurate values. The use of B3LYP/6-31G(d) would most likely provide a substantially closer value.

The typical van der Waals radius of a carbon atom is 1.70 Å whilst the length of the partly formed C-C bonds in the transition state are 2.113 and 2.116 Å. The van der Waals radius is defined as half the distance of closest approach between two non-bonded atoms, therefore the total distance is 3.40 Å. The values obtained are substantially shorter than this radius by 1.287 and 1.284 Å, aligning with the partial formation of C-C bonds in the transition state.

As the reaction progresses bonds 3 and 5 shorten as the C-C bonds are formed. Simultaneously, bonds 2,4 and 6 all elongate whilst bond 1 shortens, represented below in Graph 1.

[[File:Bond_Numbers_aps315.jpg|250px|thumb|centre|'' '''Figure 2.''' C-C Bond Numbers.'']]

{| class="wikitable" border="1"| centre
|+ '' '''Table 1.''' C-C Bond Lengths during Diels-Alder Reaction''
! Bond !! Reagents Bond Length / Å !! Transition State Bond Length / Å !! Product Bond Length / Å
|-
| '''Bond 1''' || 1.468 || 1.411 || 1.338
|-
| '''Bond 2''' || 1.335 || 1.380 || 1.500
|-
| '''Bond 3''' || - || 2.113 || 1.540
|-
| '''Bond 4''' || 1.327 || 1.382 || 1.541
|-
| '''Bond 5''' || - || 2.116 || 1.540
|-
| '''Bond 6''' || 1.335 || 1.380 || 1.500
|}

[[File:BondLengths_aps315.JPG|550px|thumb|centre|'' '''Graph 1.''' C-C Bond Length Changes with Reaction Coordinate.'']]

=== Bond Vibration ===
The vibration that corresponds to the formation of the transition state is presented below (Image 2). The formation of the new sigma bonds can be seen to occur simultaneously, this demonstrates the synchronous, concerted nature of the Diels-Alder mechanism.

[[File:TS_Vibrations_aps315.gif | centre ]]

=== Relevant Files ===

Butadiene - [[:File:BUTENE_OPT(1)_APS315.LOG]]

Ethylene - [[:File:ETHENE_OPT(1)_APS315.LOG]]

Transition State - [[:File:EX1_TS_APS315.LOG]]

Cyclohexene - [[:File:PRODUCT_aps315.LOG]]

Transition State IRC - [[:File:TS_IRC_aps315.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

The reaction between cyclohexadiene and 1,3-dioxole is a Diels-Alder reaction, a [4+2] cycloaddition, producing two possible products dependent upon the orientation of molecule approach (Scheme 2). An exo product is formed when the substituents of the 1,3-dioxole are facing away from the cyclohexadiene π system. Alternatively, the endo product is formed when the substituents of the 1,3-dioxole are facing towards the cyclohexadiene π system. In general, the endo product is frequently the thermodynamically preferred due to secondary orbital effects that involve stabilizing overlap in the endo transition state. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup>
[[File:Ex2_Scheme(2)_aps315.jpg|450px|thumb|centre|'' '''Scheme 2.''' Reaction of Cyclohexadiene and 1,3-Dioxole.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between cyclohexadiene and 1,3-dioxole was constructed using average relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 2). Non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

Due to the electron-donating nature of the oxygen atoms present in 1,3-dioxole, the dienophile becomes more electron rich, raising the energies of its HOMO and LUMO. This results in a [4+2] cycloaddition that obeys inverse electron demand.<sup>1</sup> When comparing the exo and endo transition states, both still obey inverse electron demand and follow the MO diagram displayed below, however, the relative energies of the molecular orbitals is shifted. The endo transition state can be seen to have a lower energy HOMO by 0.00492 Hartrees/particle and a higher energy LUMO by 0.00237 Hartrees/particle. This shift in energies arises due to stabilization of the endo HOMO by secondary orbital effects; overlap between the π system of cyclohexadiene and 1,3-dioxole. The exo transition state is only stabilized through primary interactions, whereas the endo transition state is stabilized through both primary and secondary interactions. This is presented below (Figure 2).

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:17, 21 March 2018 (UTC) You have just stated that the reaction is inverse and you have not investigated it quantitatively, by comparing reactant orbital energies on the same PES.

The associated MOs are presented below for both the Exo and Endo transition states (Figure 3).

[[File:Ex2_MO_aps315.jpg|350px|thumb|centre|'' '''Diagram 2.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

[[File:Ex2_Secondary_aps315.jpg|350px|thumb|centre|'' '''Figure 2.''' Primary and Secondary Orbital Interactions in Transition State.'']]

<b> Figure 3. </b>

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:19, 21 March 2018 (UTC) This is not correct, furthermore this diagram is quite difficult to understand. you should have drawn it at an angle.

<b> Endo Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 40 (HOMO-1)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
<script> frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS MO 41 (HOMO)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
<script> frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 42 (LUMO)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
<script> frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS MO 43 (LUMO+1)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
<script> frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

<b> Exo Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 40 (HOMO-1)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS MO 41 (HOMO)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 42 (LUMO)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS MO 43 (LUMO+1)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

=== Thermochemistry ===
The energy barriers and the reaction energies at room temperature are presented below (Table 2)(Figure 4). The energy barrier is the activation energy required for a reaction to occur, a product with a lower activation energy is kinetically preferred as it will more readily overcome the energy requirement for the reaction and thus form faster. The endo product can be seen to have a lower activation energy and thus can be determined to be the kinetically preferred product. This arises due to the endo transition state being lower in energy as it is stabilized by secondary orbital effects (Figure 2).

The reaction energy is characterized as the difference in energy between the reactants and products. The product with the more negative reaction energy is thermodynamically preferred as it is the more stable. The endo product can be seen to have a more negative reaction energy and thus can be determined to be the thermodynamically preferred product. This most likely arises due to steric clash that can be observed in the exo product between the carbon bridge and five-membered ring which is not observed for the endo product.

{| class="wikitable" border="1"| centre
|+ '' '''Table 2.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.057016 || 149.695519 || -0.030848 || -80.99143017
|-
| '''Exo''' || 0.060002 || 157.535263 || -0.028146 || -73.89732863
|}

[[File:Ex2_ReactionProf2_aps315.jpg|350px|thumb|centre|'' '''Figure 4.''' Reaction Profile for the Formation of Exo and Endo Products'']]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:22, 21 March 2018 (UTC) Your energies are slightly out. I suspect that your reactant energies have been slightly miss calculated. However you have still come to the correct conclusions. There were points where you could have gone into more detail.

=== Relevant Files ===

Cyclohexadiene(BL3YP) - [[:File:CYCLOHEXADIENE(2)_aps315.LOG]]

1,3-Dioxole(B3LYP) - [[:File:DIOXOLE(2)_APS315.LOG]]

Endo Product(B3LYP) - [[:File:ENDOPROD_APS315.LOG]]

Exo Product(BL3YP) - [[:File:EXOPROD(2)_APS315.LOG]]

Exo TS (BL3YP) - [[:File:EXO_TS(3)_aps315.LOG]]

Endo TS (BL3YP) - [[:File:ENDO_TS(7)_aps315.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic ==
The reaction between xylylene and sulfur dioxide can proceed via two possible reaction mechanisms; a Diels-Alder reaction, a [4+2] cycloaddition, or a cheletropic reaction (Scheme 2). The Diels-Alder reaction can again proceed via endo or exo mechanisms dependent upon the orientation of approach of sulfur dioxide. The cheletropic reaction generates a five-membered heterocyclic ring product. Due to the significantly different mechanisms, as expected, the reaction profiles of these reactions vary greatly.

[[File:Ex3_ReactionScheme_aps315.jpg|450px|thumb|centre|'' '''Scheme 3.''' Reaction of Xylylene and Sulfur Dioxide.'']]

=== IRC ===

The IRC calculations performed for these three alternative mechanisms have been visualised and are presented below. The endo and exo Diels-Alder reactions can be seen to be asynchronous whereas the cheletropic reaction can be seen to be synchronous. Xylylene's lack of stability is displayed through the IRCs for the reactions; the bond lengths of the six-membered ring undergo variations throughout the IRC and equalize upon the formation of the product.

''' Endo Diels-Alder '''
[[File:EndoIRC_aps315.gif | centre ]]

''' Exo Diels-Alder '''
[[File:ExoIRC_aps315(1).gif | centre ]]

''' Cheletropic '''
[[File:CheleIRC_aps315.gif | centre ]]

=== Thermochemistry ===

The energy barriers and the reaction energies at room temperature are presented below (Table 3)(Figure 5). The data collected suggests that the endo Diels-Alder product is kinetically preferred with the mechanism having the lowest activation energy. This result arises due to reasons discussed for the previous example; secondary orbital interactions stabilise the endo product's transition state. However, the endo product can be seen to be at a higher energy than that of the exo product; this arises due to the destabilizing steric clash between the oxygen atom and the six-membered heterocyclic ring. The reaction energies of the three mechanisms are all substantially large, this arises due to the stability of the aromatic ring formed that provides a strong driving force to the products. The cheletropic product has a substantially higher activation energy than the Diels-Alder, however has the lowest energy product and thus is the thermodynamically preferred product. This result can be explained by examining bond energies; C-S 272 kj/mol, C-O 358 kj/mol and S=O 522 kj/mol. The S=O is markedly more stable than the alternative C-O and S-O bonds formed during the Diels-Alder reaction, making the cheletropic product more stable.

{| class="wikitable" border="1"| centre
|+ '' '''Table 3.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.031064 || 81.55853821 || -0.037798 || -99.23865656
|-
| '''Exo''' || 0.032581 || 85.541422 || -0.038043 || -99.88190411
|-
| '''Cheletropic''' || 0.039566 || 103.880541 || -0.059492 || -156.1962579
|}

(You're using far too many decimal places - 10 micro J/mol in the reactants! [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

[[File:Ex3_ReactionProf3_aps315.jpg|450px|thumb|centre|'' '''Figure 5.''' Reaction Profile of Xylylene and Sulfur Dioxide.'']]

(Label the energy axis. If you put values on the profile it will make it easier to read the data [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

Xylylene has an additional site where a Diels-Alder reaction can occur. This reaction is 'endocyclic', occuring with the diene present in the six-membered ring, the 'exocyclic' reaction was previously analysed. The energy barriers and the reaction energies at room temperature for these reactions are presented below (Table 4)(Figure 6). As can be seen, the product energies for both the endo and exo reaction are higher than the energies of the reagents. In addition, the activation energies are substantially higher than for the 'exocyclic' reaction. These results arise due to the lack of aromatic stability provided by the 'endocyclic' products.

{| class="wikitable" border="1"| centre
|+ '' '''Table 4.'''Activation and Reaction Energies for 'Endocyclic' Reaction''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.042574 || 111.778046 || 0.006113 || 16.0496827
|-
| '''Exo''' || 0.045558 || 119.612538 || 0.00781 || 20.505157
|}

[[File:Ex3(1)_ReactionProf_aps315.jpg|450px|thumb|centre|'' '''Figure 6.''' Reaction Profile of 'Endocyclic' Xylylene and Sulfur Dioxide.'']]

=== Relevant Files ===

''' 'Exocyclic' Diels-Alder '''

Xylylene - [[:File:XYLYLENE_APS315.LOG]]

Sulfur Dioxide - [[:File:SO2_APS315.LOG]]

Endo TS - [[:File:EX3_ENDO_TS(8)_APS315.LOG]]

Endo IRC - [[:File:EX3_ENDO_IRC(1)_APS315.LOG]]

Endo Product - [[:File:EX3_ENDOPROD_APS315.LOG]]

Exo TS - [[:File:EX3_Exo_TS(1)_APS315.LOG]]

Exo IRC - [[:File:EX3_EXO_IRC_APS315.LOG]]

Exo Product - [[:File:EX3_EXOPPROD(1)_APS315.LOG]]

''' Cheletropic '''

Cheletropic TS - [[:File:EX3_CHELE_TS(2)_APS315.LOG]]

Cheletropic IRC - [[:File:EX3_CHELE_IRC(1)_APS315.LOG]]

Cheletropic Product - [[:File:EX3_CHELE_PROD_APS315.LOG]]

''' 'Endocyclic' Diels-Alder '''

Endo TS - [[:File:EX3(1)_ENDO_TS_APS315.LOG]]

Endo Product - [[:File:EX3(1)_ENDOPRODUCT_APS315.LOG]]

Exo TS - [[:File:EXO(1)_Exo_TS(1)_APS315.LOG]]

Exo Product - [[:File:EX3(1)_EXOPRODUCT_APS315.LOG]]

== Conclusion ==

The data produced by GuassView correlates well with pre-existing theory. For instance, the effects of the endo rule, aromatic stability and steric clash could all be employed to explain and align with the results obtained. The computational methods employed proved highly effective with limited knowledge of the reactions required. Only a fundamental understanding of chemistry is required to conduct and analyse these methods.

The approach of modelling provides unparalleled access to understanding chemical reactions and pathways and allows for chemistry to be conducted theoretically with well estimated outcomes that align with experimental values.

== References ==
1. J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', ''Oxford University Press'', '''2''', 2012.

2. P. Atkins, J. Rourke, T. Overton and F. Armstrong, '' Shriver & Atkins Inorganic Chemistry'', ''Oxford University Press'', '''5''', 2010.

3. A. Orpen and D. Watson, ''J. Chem. Soc. Dalt. Trans.'', 1987.

Rep:Mod:aps315TS

2018-03-27T08:42:58Z

Fv611: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Introduction ==

In a simplistic view, a transition state is classified as the highest energy point along a reaction coordinate. As a result, it is characterized as a stationary point and can be confirmed by determining the first derivative of the reaction coordinate as zero. However, this approximation is not an accurate representation of a chemical system undergoing a reaction. This constricted approximation does not account for the possibility of displacement from a system's equilibrium. A chemical system can in fact be displaced in 3N-6 degrees of freedom and a Potential Energy Surface (PES) is a more accurate description of a chemical system undergoing a reaction. A PES is a plot of potential energy against two combinations of these possible degrees of freedom. On a PES a transition state is now characterized as a saddle point and can be confirmed as having a first derivative equal to zero and a second derivative that is negative.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:13, 21 March 2018 (UTC) The surface you are talking about it actually 3N-6. At a TS all the hessian eigen values are positive for all the 3n-6 dimensions apart from 1 which is negative and this is the reaction coord.

This report shall discuss the determination of transition states for three pericyclic reactions. These transition states will be located and characterized using GuassView by optimizing the reagents towards a minimum then subsequently optimizing the transition state using PM6 and B3LYP methods. The PM6 method is semi-empirical; it is effectively a less involved or reduced form of the Hartree-Fock method and is employed for swiftness. The B3LYP method was carried out using a 6-31G(d) basis set, it is a hybrid function utilizing he Hartree-Fock as well as the DFT method and is employed for a more accurate transition state determination.

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:13, 21 March 2018 (UTC) You could have gone into more detail here. Possibly added some equations.

In addition, Intrinsic Reaction Coordinate (IRC) calculations were utilized to examine the profile of the minimum energy pathway. An IRC follows the minimum energy pathway along the PES from the transition state towards the reactants and/or the products dependent upon how the calculation was ran. IRC calculations were employed to analyse the reaction profile, changes in bond length and to visualize the reaction.

== Exercise 1: Reaction of Butadiene with Ethylene ==

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) Good job across the whole first exercise. Well done!)

The reaction between butadiene and ethylene is a Diels-Alder reaction, a [4+2] cycloaddition, producing cyclohexene as the product. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup> In order for the reaction to occur butadiene must adopt the s-cis conformation. This reaction obeys normal electron demand with the diene (butadiene) being more electron rich than the dienophile (ethylene). A reaction scheme is presented below (Scheme 1).
[[File:Diels-Alder(2)_aps315.jpg|350px|thumb|centre|'' '''Scheme 1.''' Reaction of Butadiene with Ethylene.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between butadiene and ethylene was constructed using relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 1). Butadiene's non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

The MOs 16 and 19 produced by Guassian for the transition state are presented below and are correlated to the appropriate interactions in the MO diagram (Figure 1). These demonstrate orbital interactions between the HOMO of butadiene and the LUMO of ethylene, with both having asymmetric symmetry. As a result, it can be inferred that in order for orbital interaction to be favorable and result in overall stabilization of the molecule, the symmetries must be the same (e.g asymmetric and asymmetric) and they must have non-zero orbital overlap integrals. This arises due to the requirement for an overall symmetric function and non-zero overlap integrals corresponding to orbital spacial overlap.<sup>2</sup> A symmetric-symmetric and asymmetric-asymmetric interaction will have a non-zero overlap while opposing symmetries (asymmetric-symmetric/ symmetric-asymmetric) will have zero overlap integral and an overall asymmetric function.

[[File:Diels-Alder aps315(4).jpg|350px|thumb|centre|'' '''Diagram 1.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

<b> Figure 1. </b>

<b> Ethylene </b>

{| class="wikitable"
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<b> Butadiene </b>

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<b> Transition State </b>

{| class="wikitable"
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{| class="wikitable"
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=== Carbon Bond Lengths ===
The Diels-Alder reaction involves the formation of two C-C sigma bonds and the breaking of three C-C pi bonds. The C-C bond lengths calculated by Guassian for the reagents, transition state and product are presented below (Table 1). C-C bonds 1,2 and 6 correspond to the bonds of butadiene and bond 4 corresponds to the bond of ethylene (Diagram 2).

Typical bond lengths for C-C sp<sup>2</sup> single and double bond as well as sp<sup>3</sup> single bond are 1.460, 1.316 and 1.507 Å respectively. The values obtained vary by approximately 0.01 Å compared with typical values, however, when compared with literature values for cyclohexene, the values compare well with slight deviation.<sup>3</sup> The double bond calculated is 0.012 Å longer than that in literature, this deviation most likely arises due to the method applied, PM6, providing less accurate values. The use of B3LYP/6-31G(d) would most likely provide a substantially closer value.

The typical van der Waals radius of a carbon atom is 1.70 Å whilst the length of the partly formed C-C bonds in the transition state are 2.113 and 2.116 Å. The van der Waals radius is defined as half the distance of closest approach between two non-bonded atoms, therefore the total distance is 3.40 Å. The values obtained are substantially shorter than this radius by 1.287 and 1.284 Å, aligning with the partial formation of C-C bonds in the transition state.

As the reaction progresses bonds 3 and 5 shorten as the C-C bonds are formed. Simultaneously, bonds 2,4 and 6 all elongate whilst bond 1 shortens, represented below in Graph 1.

[[File:Bond_Numbers_aps315.jpg|250px|thumb|centre|'' '''Figure 2.''' C-C Bond Numbers.'']]

{| class="wikitable" border="1"| centre
|+ '' '''Table 1.''' C-C Bond Lengths during Diels-Alder Reaction''
! Bond !! Reagents Bond Length / Å !! Transition State Bond Length / Å !! Product Bond Length / Å
|-
| '''Bond 1''' || 1.468 || 1.411 || 1.338
|-
| '''Bond 2''' || 1.335 || 1.380 || 1.500
|-
| '''Bond 3''' || - || 2.113 || 1.540
|-
| '''Bond 4''' || 1.327 || 1.382 || 1.541
|-
| '''Bond 5''' || - || 2.116 || 1.540
|-
| '''Bond 6''' || 1.335 || 1.380 || 1.500
|}

[[File:BondLengths_aps315.JPG|550px|thumb|centre|'' '''Graph 1.''' C-C Bond Length Changes with Reaction Coordinate.'']]

=== Bond Vibration ===
The vibration that corresponds to the formation of the transition state is presented below (Image 2). The formation of the new sigma bonds can be seen to occur simultaneously, this demonstrates the synchronous, concerted nature of the Diels-Alder mechanism.

[[File:TS_Vibrations_aps315.gif | centre ]]

=== Relevant Files ===

Butadiene - [[:File:BUTENE_OPT(1)_APS315.LOG]]

Ethylene - [[:File:ETHENE_OPT(1)_APS315.LOG]]

Transition State - [[:File:EX1_TS_APS315.LOG]]

Cyclohexene - [[:File:PRODUCT_aps315.LOG]]

Transition State IRC - [[:File:TS_IRC_aps315.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

The reaction between cyclohexadiene and 1,3-dioxole is a Diels-Alder reaction, a [4+2] cycloaddition, producing two possible products dependent upon the orientation of molecule approach (Scheme 2). An exo product is formed when the substituents of the 1,3-dioxole are facing away from the cyclohexadiene π system. Alternatively, the endo product is formed when the substituents of the 1,3-dioxole are facing towards the cyclohexadiene π system. In general, the endo product is frequently the thermodynamically preferred due to secondary orbital effects that involve stabilizing overlap in the endo transition state. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup>
[[File:Ex2_Scheme(2)_aps315.jpg|450px|thumb|centre|'' '''Scheme 2.''' Reaction of Cyclohexadiene and 1,3-Dioxole.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between cyclohexadiene and 1,3-dioxole was constructed using average relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 2). Non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

Due to the electron-donating nature of the oxygen atoms present in 1,3-dioxole, the dienophile becomes more electron rich, raising the energies of its HOMO and LUMO. This results in a [4+2] cycloaddition that obeys inverse electron demand.<sup>1</sup> When comparing the exo and endo transition states, both still obey inverse electron demand and follow the MO diagram displayed below, however, the relative energies of the molecular orbitals is shifted. The endo transition state can be seen to have a lower energy HOMO by 0.00492 Hartrees/particle and a higher energy LUMO by 0.00237 Hartrees/particle. This shift in energies arises due to stabilization of the endo HOMO by secondary orbital effects; overlap between the π system of cyclohexadiene and 1,3-dioxole. The exo transition state is only stabilized through primary interactions, whereas the endo transition state is stabilized through both primary and secondary interactions. This is presented below (Figure 2).

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:17, 21 March 2018 (UTC) You have just stated that the reaction is inverse and you have not investigated it quantitatively, by comparing reactant orbital energies on the same PES.

The associated MOs are presented below for both the Exo and Endo transition states (Figure 3).

[[File:Ex2_MO_aps315.jpg|350px|thumb|centre|'' '''Diagram 2.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

[[File:Ex2_Secondary_aps315.jpg|350px|thumb|centre|'' '''Figure 2.''' Primary and Secondary Orbital Interactions in Transition State.'']]

<b> Figure 3. </b>

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:19, 21 March 2018 (UTC) This is not correct, furthermore this diagram is quite difficult to understand. you should have drawn it at an angle.

<b> Endo Transition State </b>

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<b> Exo Transition State </b>

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=== Thermochemistry ===
The energy barriers and the reaction energies at room temperature are presented below (Table 2)(Figure 4). The energy barrier is the activation energy required for a reaction to occur, a product with a lower activation energy is kinetically preferred as it will more readily overcome the energy requirement for the reaction and thus form faster. The endo product can be seen to have a lower activation energy and thus can be determined to be the kinetically preferred product. This arises due to the endo transition state being lower in energy as it is stabilized by secondary orbital effects (Figure 2).

The reaction energy is characterized as the difference in energy between the reactants and products. The product with the more negative reaction energy is thermodynamically preferred as it is the more stable. The endo product can be seen to have a more negative reaction energy and thus can be determined to be the thermodynamically preferred product. This most likely arises due to steric clash that can be observed in the exo product between the carbon bridge and five-membered ring which is not observed for the endo product.

{| class="wikitable" border="1"| centre
|+ '' '''Table 2.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.057016 || 149.695519 || -0.030848 || -80.99143017
|-
| '''Exo''' || 0.060002 || 157.535263 || -0.028146 || -73.89732863
|}

[[File:Ex2_ReactionProf2_aps315.jpg|350px|thumb|centre|'' '''Figure 4.''' Reaction Profile for the Formation of Exo and Endo Products'']]

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 21:22, 21 March 2018 (UTC) Your energies are slightly out. I suspect that your reactant energies have been slightly miss calculated. However you have still come to the correct conclusions. There were points where you could have gone into more detail.

=== Relevant Files ===

Cyclohexadiene(BL3YP) - [[:File:CYCLOHEXADIENE(2)_aps315.LOG]]

1,3-Dioxole(B3LYP) - [[:File:DIOXOLE(2)_APS315.LOG]]

Endo Product(B3LYP) - [[:File:ENDOPROD_APS315.LOG]]

Exo Product(BL3YP) - [[:File:EXOPROD(2)_APS315.LOG]]

Exo TS (BL3YP) - [[:File:EXO_TS(3)_aps315.LOG]]

Endo TS (BL3YP) - [[:File:ENDO_TS(7)_aps315.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic ==
The reaction between xylylene and sulfur dioxide can proceed via two possible reaction mechanisms; a Diels-Alder reaction, a [4+2] cycloaddition, or a cheletropic reaction (Scheme 2). The Diels-Alder reaction can again proceed via endo or exo mechanisms dependent upon the orientation of approach of sulfur dioxide. The cheletropic reaction generates a five-membered heterocyclic ring product. Due to the significantly different mechanisms, as expected, the reaction profiles of these reactions vary greatly.

[[File:Ex3_ReactionScheme_aps315.jpg|450px|thumb|centre|'' '''Scheme 3.''' Reaction of Xylylene and Sulfur Dioxide.'']]

=== IRC ===

The IRC calculations performed for these three alternative mechanisms have been visualised and are presented below. The endo and exo Diels-Alder reactions can be seen to be asynchronous whereas the cheletropic reaction can be seen to be synchronous. Xylylene's lack of stability is displayed through the IRCs for the reactions; the bond lengths of the six-membered ring undergo variations throughout the IRC and equalize upon the formation of the product.

''' Endo Diels-Alder '''
[[File:EndoIRC_aps315.gif | centre ]]

''' Exo Diels-Alder '''
[[File:ExoIRC_aps315(1).gif | centre ]]

''' Cheletropic '''
[[File:CheleIRC_aps315.gif | centre ]]

=== Thermochemistry ===

The energy barriers and the reaction energies at room temperature are presented below (Table 3)(Figure 5). The data collected suggests that the endo Diels-Alder product is kinetically preferred with the mechanism having the lowest activation energy. This result arises due to reasons discussed for the previous example; secondary orbital interactions stabilise the endo product's transition state. However, the endo product can be seen to be at a higher energy than that of the exo product; this arises due to the destabilizing steric clash between the oxygen atom and the six-membered heterocyclic ring. The reaction energies of the three mechanisms are all substantially large, this arises due to the stability of the aromatic ring formed that provides a strong driving force to the products. The cheletropic product has a substantially higher activation energy than the Diels-Alder, however has the lowest energy product and thus is the thermodynamically preferred product. This result can be explained by examining bond energies; C-S 272 kj/mol, C-O 358 kj/mol and S=O 522 kj/mol. The S=O is markedly more stable than the alternative C-O and S-O bonds formed during the Diels-Alder reaction, making the cheletropic product more stable.

{| class="wikitable" border="1"| centre
|+ '' '''Table 3.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.031064 || 81.55853821 || -0.037798 || -99.23865656
|-
| '''Exo''' || 0.032581 || 85.541422 || -0.038043 || -99.88190411
|-
| '''Cheletropic''' || 0.039566 || 103.880541 || -0.059492 || -156.1962579
|}

(You're using far too many decimal places - 10 micro J/mol in the reactants! [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

[[File:Ex3_ReactionProf3_aps315.jpg|450px|thumb|centre|'' '''Figure 5.''' Reaction Profile of Xylylene and Sulfur Dioxide.'']]

(Label the energy axis. If you put values on the profile it will make it easier to read the data [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

Xylylene has an additional site where a Diels-Alder reaction can occur. This reaction is 'endocyclic', occuring with the diene present in the six-membered ring, the 'exocyclic' reaction was previously analysed. The energy barriers and the reaction energies at room temperature for these reactions are presented below (Table 4)(Figure 6). As can be seen, the product energies for both the endo and exo reaction are higher than the energies of the reagents. In addition, the activation energies are substantially higher than for the 'exocyclic' reaction. These results arise due to the lack of aromatic stability provided by the 'endocyclic' products.

{| class="wikitable" border="1"| centre
|+ '' '''Table 4.'''Activation and Reaction Energies for 'Endocyclic' Reaction''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.042574 || 111.778046 || 0.006113 || 16.0496827
|-
| '''Exo''' || 0.045558 || 119.612538 || 0.00781 || 20.505157
|}

[[File:Ex3(1)_ReactionProf_aps315.jpg|450px|thumb|centre|'' '''Figure 6.''' Reaction Profile of 'Endocyclic' Xylylene and Sulfur Dioxide.'']]

=== Relevant Files ===

''' 'Exocyclic' Diels-Alder '''

Xylylene - [[:File:XYLYLENE_APS315.LOG]]

Sulfur Dioxide - [[:File:SO2_APS315.LOG]]

Endo TS - [[:File:EX3_ENDO_TS(8)_APS315.LOG]]

Endo IRC - [[:File:EX3_ENDO_IRC(1)_APS315.LOG]]

Endo Product - [[:File:EX3_ENDOPROD_APS315.LOG]]

Exo TS - [[:File:EX3_Exo_TS(1)_APS315.LOG]]

Exo IRC - [[:File:EX3_EXO_IRC_APS315.LOG]]

Exo Product - [[:File:EX3_EXOPPROD(1)_APS315.LOG]]

''' Cheletropic '''

Cheletropic TS - [[:File:EX3_CHELE_TS(2)_APS315.LOG]]

Cheletropic IRC - [[:File:EX3_CHELE_IRC(1)_APS315.LOG]]

Cheletropic Product - [[:File:EX3_CHELE_PROD_APS315.LOG]]

''' 'Endocyclic' Diels-Alder '''

Endo TS - [[:File:EX3(1)_ENDO_TS_APS315.LOG]]

Endo Product - [[:File:EX3(1)_ENDOPRODUCT_APS315.LOG]]

Exo TS - [[:File:EXO(1)_Exo_TS(1)_APS315.LOG]]

Exo Product - [[:File:EX3(1)_EXOPRODUCT_APS315.LOG]]

== Conclusion ==

The data produced by GuassView correlates well with pre-existing theory. For instance, the effects of the endo rule, aromatic stability and steric clash could all be employed to explain and align with the results obtained. The computational methods employed proved highly effective with limited knowledge of the reactions required. Only a fundamental understanding of chemistry is required to conduct and analyse these methods.

The approach of modelling provides unparalleled access to understanding chemical reactions and pathways and allows for chemistry to be conducted theoretically with well estimated outcomes that align with experimental values.

== References ==
1. J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', ''Oxford University Press'', '''2''', 2012.

2. P. Atkins, J. Rourke, T. Overton and F. Armstrong, '' Shriver & Atkins Inorganic Chemistry'', ''Oxford University Press'', '''5''', 2010.

3. A. Orpen and D. Watson, ''J. Chem. Soc. Dalt. Trans.'', 1987.