'''This is William Micou's report on the Transition States computational lab, starting Monday 11th December 2017.'''
==Introduction==

Transition state analysis is a powerful technique to predict major products and observed stereochemistry; to rationalise reaction rates with different substituents; to examine reaction mechanisms and to understand catalytic cycles. Transition states are very difficult to probe experimentally: in this experiment, transition states for a variety of pericyclic reactions will be calculated computationally.

The potential energy surface of a molecule consisting of N atoms exists in (3N-6) dimensions. The potential energy can be expressed as a function of (3N-6) independent nuclear coordinates, <math>q_{i}</math>:

<center><math>E = f(q_{1}, q_{2}, ..., q_{3N-6})</math></center>

A stable structure sits in a local minimum on the potential energy surface, whereas a transition state is a saddle point on the PES. These are both stationary points, where:

<center><math>\frac{\partial E(q_{i})}{\partial q_{i}}=0</math> along every coordinate <math>q_{i}</math></center>.

Minima and transition states can be distinguished by their second derivatives. At a minimum, the energy must increase in all directions from that point on the PES: therefore, <math>\frac{\partial^{2}E}{\partial q_{i}^{2}}>0</math> for all <math>q_{i}</math>. At a transition state, the energy increases in all directions except one: the energy decreases along the reaction path. A transition state is hence defined as a stationary point on the PES with one negative Hessian eigenvalue.[ref]

The second derivatives of the PES correspond to the force constants of the vibrations along the chosen nuclear coordinates: <math>k=\frac{\partial^{2}E}{\partial q^{2}}</math>. The frequencies of the vibration can be found from the familiar expression <math>\omega=\frac{1}{2\pi}\sqrt{\frac{k}{\mu}}</math>. Therefore, a transition state will have an optimised structure with a single negative frequency - this corresponds to the collective motions of the atoms forming the products and lowering the energy. In contrast, optimised reactants or products which sit at a local minimum have only positive frequency vibrations.

==Methodology==

Calculations were executed with Gaussian 09, Revision D.01, with input files prepared in GaussView 5.0.9. Transition states were located and reaction paths calculated using the following sequence:
*Products optimised at the desired level of approximation.
*Bonds formed in the reaction are broken and these bond lengths are frozen to around 2.2 Å for C-C bonds, 2.0 Å for C-O and 2.4 Å for C-S bonds. The structure is reoptimised.
*Bonds are unfrozen and the transition state is located using the Berny algorithm, calculating the force constants only once.
*The transition state structure is checked with an IRC (intrinsic reaction coordinate) calculation at the PM6 level (as more accurate calculations are computationally expensive) and a frequency calculation.

The B3LYP level of approximation makes use of Density Functional Theory (DFT)[ref-b3lyp]. The electron energy is a functional [ref-review] of the electronic density, <math>E[\rho]</math>. The B3LYP force field is a hybrid density functional method [ref-review], incorporating the exchange correlation predicted by gradient-corrected functionals [ref-b3lyp] (GGA methods - Generalised Gradient Approximation) along with exact, Hartree-Fock exchange [ref-b3lyp]. These calculations are considerably heavier and time allowed for B3LYP calculations in Exercise 2 only.

The PM6 approximation is a semi-empirical model: reference data is used [pm6 paper] in combination with calculations based on a Hartree-Fock model (with considerable simplifications). These calculations are fast and successful for reasonably small molecules, although the PM6 method has been modified to model proteins [ref pm6 small molecule].

==Exercise 1: Butadiene + Ethene Diels-Alder Reaction==

===Optimised structures of the reactants and transition state (PM6 level)===

The table below contains Jmol applets of the reactants and transition state structures optimised at the PM6 level.

{| class = "wikitable" align = "center"
!Ethene
!Butadiene (s-cis)
!Transition state
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>350</size>
<uploadedFileContents>wm1415_ETHENE_PM6_OPT_GFPRINT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<name>ethene</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>frame 6; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>frame 6; mo off</script>
<text>MO OFF</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==6) frame=7; vibrating=0; endif</script>
<script>frame 7; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Lowest Frequency</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 4]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ethene</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ethene</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 6</script>
<text>HOMO</text>
<target>ethene</target>
</item>
<item>
<script>mo 7</script>
<text>LUMO</text>
<target>ethene</target>
</item>
</jmolmenu>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>350</size>
<uploadedFileContents>wm1415_BUTADIENE_SCIS_PM6_OPT_GFPRINT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 6; mo 10; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<name>butadiene</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 6; mo 10; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>frame 6; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>frame 6; mo off</script>
<text>MO OFF</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==6) frame=7; vibrating=0; endif</script>
<script>frame 7; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Lowest Frequency</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 4 6 8]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 6; mo 10; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>butadiene</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 10</script>
<text>MO 10</text>
<target>butadiene</target>
</item>
<item>
<script>mo 11</script>
<text>HOMO</text>
<target>butadiene</target>
</item>
<item>
<script>mo 12</script>
<text>LUMO</text>
<target>butadiene</target>
</item>
<item>
<script>mo 13</script>
<text>MO 13</text>
<target>butadiene</target>
</item>
</jmolmenu>
</jmol></center>
|<center><jmol> //Group all the HTML within "jmol"
<jmolApplet>
<color>#F9F9F9</color>
<size>350</size> //Initialise the applet
<uploadedFileContents>wm1415_DIELS_ALDER_TS_PM6_GFPRINT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<name>DielsAlderTS</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 14; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script> //Turn on MO
<text>MO ON</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 14; mo off</script>
<text>MO OFF</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==14) frame=15; vibrating=0; endif</script>
<script>frame 15; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 4 6 8 14 11]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 16</script>
<text>MO 16</text>
<target>DielsAlderTS</target>
</item>
<item>
<script>mo 17</script>
<text>MO 17</text>
<target>DielsAlderTS</target>
</item>
<item>
<script>mo 18</script>
<text>MO 18</text>
<target>DielsAlderTS</target>
</item>
<item>
<script>mo 19</script>
<text>MO 19</text>
<target>DielsAlderTS</target>
</item>
</jmolmenu>
</jmol></center>
|}

===Confirmation of Transition State===

The frequency calculation on the TS structure yielded an imaginary vibration at -948 cm<sup>-1</sup>: this corresponds to the motion of atoms that leads to the formation of products. Further evidence for a correct TS was obtained through an IRC calculation: this structure is indeed the maximum along the minimum energy path. The table below provides a plot of the C-C bond lengths during the reaction; an animation of the reaction calculated reaction path; and a plot of the energy, along with its derivative, against the reaction coordinate. It is worth noting that in this case, the IRC path was calculated from the products to the reactants: hence the reversed animation. The same atom labels were used as in the Jmol structures above.

{| class = "wikitable"
!Internuclear distances in IRC path
!Diels-Alder Reaction Animation
!IRC Path Energy Plot
|-
|<center>[[File:wm1415_Diels_alder_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Diels_alder_resized_gif.gif]]</center>
|<center>[[File:wm1415_Irc_energy_diels_alder.PNG|200 px]]</center>
|}

The animation shows that this Diels-Alder reaction is synchronous: the new σ bonds (C8-C14 and C11-C1) are formed at the same time. These bond lengths are identical in the internuclear distances plot, which also show shortening of the C4-C6 bond as it becomes a double bond (around 1.35 Å). Also shown is the lengthening of the 3 double bonds involved in the cycloaddition, which all become single bonds (C14-C11, C1-C4 and C6-C8) with lengths of between 1.50-1.54 Å (C1-C4 and C6-C8, which are adjacent to the double bond in the product, are slightly shorter). Carbon has a van der Waals radius of 1.70 Å.

In the transition state, the C8-C14/C11-C1 bonds measure around 2.12 Å - the new σ bonds are not yet fully formed, but well within twice the van der Waals radius. The original double bonds are all elongated - around 1.38 Å, and the originally singly-bonded C4-C6 is shorted to 1.41 Å.

===Optimisation and Analysis of Product===
To reduce the number of Jmol applets on this page, these structures have not been embedded - they can be opened in a new window by clicking the following links. A PM6-level optimisation of the products of the IRC yields <jmolFile text="boat cyclohexene">wm1415_DA_LAST_IRC_STRUCTURE_PM6_OPT.LOG</jmolFile>: this was compared to a PM6-level optimisation of <jmolFile text="chair cyclohexene.">wm1415_CYCLOHEXENE_PM6_OPT.LOG</jmolFile> The boat structure features an imaginary frequency: this corresponds to the collective motion of atoms that would yield the chair cyclohexene structure, lowering the energy.

===Orbital Description of the Diels-Alder Reaction===
{| align="left"
|[[File:wm1415_Final_diels_alder_MO_diagram.PNG|550 px|thumb|left|MO Diagram showing the orbitals involved in the Diels-Alder reaction. While the ordering of the energies of the reactant frontier orbitals has been respected, the diagram is not drawn to scale and the transition state energy levels are skewed for clarity. Approximate energy levels calculated at the PM6-level approximation are listed in the table opposite.]]
|
{| class="wikitable" align="center"
!Ethene
!Energy / a.u.
!Butadiene
!Energy / a.u.
!Transition State
!Energy / a.u.
|-
|
|
|MO 13
|0.0636
|MO 19
|0.0307
|-
|LUMO
|0.0426
|LUMO
|0.0194
|MO 18
|0.0173
|-
|HOMO
| -0.3923
|HOMO
| -0.3590
|MO 17
| -0.3253
|-
|
|
|MO 10
| -0.4133
|MO 16
| -0.3276
|}
LUMO<sub>dienophile</sub> - HOMO<sub>diene</sub> = 0.4016 a.u.

LUMO<sub>diene</sub> - HOMO<sub>dienophile</sub> = 0.4117 a.u.

The smallest energy gap is that between the LUMO of ethene and the HOMO of butadiene (the antisymmetric orbitals). The interaction between these orbitals is stronger as there is greater orbital overlap: the reaction proceeds by electrons from the HOMO of the diene populating the LUMO of the dienophile (MO 16) - normal electron demand. The other bonding orbital in the TS, MO 17, is formed from the interaction between the HOMO of ethene and the LUMO of butadiene.
|}

The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric orbital interactions; but the orbital overlap integral is zero for symmetric-antisymmetric interactions. The Woodward-Hoffmann rules can be used to predict whether a pericyclic reaction is allowed by symmetry. According to the Woodward-Hoffman rules, a cycloaddition is thermally allowed if the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components is odd [ref - WH]. Here, the 's' label refers to a suprafacial component, which forms new bonds on the same side at both ends ('a' label - antarafacial, opposite sides). The Diels-Alder reaction is a [<sub>π</sub>4<sub>s</sub>+<sub>π</sub>2<sub>s</sub>] cycloaddition: (4q+2)<sub>s</sub> + (4r)<sub>a</sub> = 1, so it is allowed.

==Exercise 2==

===Optimised Reactants: B3LYP/6-31G(d)===

These Jmol files have been excluded from this page to speed up loading time. The applets can be accessed here: <jmolFile text="cyclohexadiene">wm1415_CYCLOHEXADIENE_B3LYP_OPT.LOG</jmolFile> and <jmolFile text="1,3-dioxole">wm1415_LAST_DIOXOLE_TRY_B3LYP.LOG</jmolFile>. There are no negative frequencies as these are stable structures.

===Endo/Exo Transition States and Products: B3LYP/6-31G(d)===

{| class = "wikitable" align = "center"
!Endo TS
!Endo Product
!Exo TS
!Exo Product
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_ENDO_TS_B3LYP.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 36; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<name>ex2_endoTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 36; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 36; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 36; mo off</script>
<text>MO OFF</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==36) frame=37; vibrating=0; endif</script>
<script>frame 37; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 4 5 6]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ex2_endoTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 36; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 40</script>
<text>MO 40</text>
<target>ex2_endoTS</target>
</item>
<item>
<script>mo 41</script>
<text>MO 41</text>
<target>ex2_endoTS</target>
</item>
<item>
<script>mo 42</script>
<text>MO 42</text>
<target>ex2_endoTS</target>
</item>
<item>
<script>mo 43</script>
<text>MO 43</text>
<target>ex2_endoTS</target>
</item>
</jmolmenu>
<jmolmenu>
<item>
<script>mo cutoff 0.02</script>
<text>Cutoff 0.02</text>
<target>ex2_endoTS</target>
</item>
<item>
<script>mo cutoff 0.01</script>
<text>Cutoff 0.01</text>
<target>ex2_endoTS</target>
</item>
</jmolmenu>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_ENDO_PRODUCTS_B3LYP_OPT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 18; frank off</script>
<name>ex2_endoproduct</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 18; frank off</script>
<text>Reload</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==18) frame=19; vibrating=0; endif</script>
<script>frame 19; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Lowest Frequency</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 4 5 6]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 18; frank off</script>
<text>Reload</text>
<target>ex2_endoproduct</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_EXO_TS_B3LYP.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<name>ex2_exoTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 18; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 18; mo off</script>
<text>MO OFF</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==18) frame=19; vibrating=0; endif</script>
<script>frame 19; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 4 5 6]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ex2_exoTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 40</script>
<text>MO 40</text>
<target>ex2_exoTS</target>
</item>
<item>
<script>mo 41</script>
<text>MO 41</text>
<target>ex2_exoTS</target>
</item>
<item>
<script>mo 42</script>
<text>MO 42</text>
<target>ex2_exoTS</target>
</item>
<item>
<script>mo 43</script>
<text>MO 43</text>
<target>ex2_exoTS</target>
</item>
</jmolmenu>
<jmolmenu>
<item>
<script>mo cutoff 0.02</script>
<text>Cutoff 0.02</text>
<target>ex2_exoTS</target>
</item>
<item>
<script>mo cutoff 0.01</script>
<text>Cutoff 0.01</text>
<target>ex2_exoTS</target>
</item>
</jmolmenu>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_EXO_PRODUCTS_B3LYP_OPT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 14; frank off</script>
<name>ex2_exoproduct</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 14; frank off</script>
<text>Reload</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==14) frame=15; vibrating=0; endif</script>
<script>frame 15; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Lowest Frequency</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 4 5 6]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 14; frank off</script>
<text>Reload</text>
<target>ex2_exoproduct</target>
</jmolbutton>
</jmol></center>
|}

===Endo/Exo IRC Paths (PM6 Level)===
{| class = "wikitable"
!Endo Internuclear distances
!Endo Reaction Animation
!Endo IRC Energy Plot
|-
|<center>[[File:wm1415_Ex2_endo_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Ex2_endo_resized.gif]]</center>
|<center>[[File:wm1415_ex2_Irc_energy_endo_cyclo.PNG|200 px]]</center>
|-
!Exo Internuclear distances
!Exo Reaction Animation
!Exo IRC Energy Plot
|-
|<center>[[File:wm1415_Ex2_exo_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Ex2_exo_resized.gif]]</center>
|<center>[[File:wm1415_ex2_Irc_energy_exo_cyclo.PNG|200 px]]</center>
|}

===MO Diagram: Diels-Alder Inverse Electron Demand===
{| align="left"
|[[File:wm1415_Ex2_mo_diagram.PNG|550 px|thumb|left|MO Diagram showing the FMOs. While the ordering of the energies of the reactant FMOs has been respected, the diagram is not drawn to scale and the transition state energy levels are skewed for clarity. Approximate energy levels calculated at the B3LYP 6-31G(d)-level approximation are listed in the table opposite.]]
|
{| class="wikitable" align="center"
!1,3-dioxole
!Energy / a.u.
!Cyclohexadiene
!Energy / a.u.
!Endo TS
!Energy / a.u.
|-
|
|
|MO 24
| 0.0874
|MO 43
| -0.0154
|-
|LUMO
|0.0380
|LUMO
| -0.0171
|MO 42
| -0.0046
|-
|HOMO
| -0.1959
|HOMO
| -0.2055
|MO 41
| -0.1905
|-
|
|
|MO 21
| -0.2994
|MO 40
| -0.1965
|}
LUMO<sub>dienophile</sub> - HOMO<sub>diene</sub> = 0.2435 a.u.

LUMO<sub>diene</sub> - HOMO<sub>dienophile</sub> = 0.1788 a.u.

In this case, it is the energy gap between the LUMO of the diene and the HOMO of the dienophile that is smallest and leads to the greatest orbital overlap. The dienophile, 1,3-dioxole, is electron-rich: electrons flow from its HOMO to the diene LUMO - this is inverse electron demand. This interaction can be visualised as MO 41 in both the endo and exo transition states. Interactions between the dienophile LUMO and diene HOMO form MO 40 in the transition state.
|}

Because the energies of the interacting orbitals are a better match than in the butadiene and ethene reaction, there is greater orbital overlap and hence greater stabilisation of the transition state: the reaction with the electron-rich 1,3-dioxole would be much faster.

===Energy Profile: Secondary Orbital Interactions===

{| align="left"
|[[File:wm1415_Ex2_energy_profile.png|300px]]
|The endo product is both the kinetic and thermodynamic product of the reaction: it is formed from a lower energy TS and releases more energy in the reaction. The exo product is comparatively destabilised because of the unfavourable steric clash between the heteroatomic 5-membered ring and the bridging ethyl group across the newly-formed 6-membered ring from the Diels-Alder reaction.

The endo transition state is stabilised by secondary orbital interactions [ref] (SOI). These interactions come about between atomic orbitals that are not involved in the formation or cleavage of σ bonds [ref]. In the endo TS, the O atoms are aligned with the back of the diene. While this configuration is sterically unfavourable, it allows for the SOI between the O lone pairs and the orbitals at the back end of the diene LUMO. This is a favourable interaction which is only accessible to the endo TS, and more than makes up for the increased steric clash - resulting in a lower energy transition state. These interactions can be clearly seen in the Jmol files above: select MO 41 in the transition state structures (and adjusting the MO cutoff value if necessary).
|[[File:wm1415_SOI_interaction.PNG|200 px]]
{| class="wikitable"
|+ '''Free energies / kJ/mol'''
! <math>\Delta G^{o}_{endo}</math>
| -67.4
! <math>\Delta G^{o}_{exo}</math>
| -63.8
|-
! <math>\Delta G^{*}_{endo}</math>
| 160
! <math>\Delta G^{*}_{exo}</math>
| 168
|}
|}

'''text to fix formatting'''

==Exercise 3==
===The Reaction between SO<sub>2</sub> and Xylylene===
Sulfur dioxide can undergo Diels-Alder and Cheletropic pericyclic reactions with dienes. Xylylene contains two diene fragments: what will be deemed the main fragment undergoes aromatisation in the considered reactions. The following sections contain calculations for the formation of the each of the possible products for both the main and second fragments of xylylene: from these calculations, a reaction profile will be constructed.

Jmol applets for PM6-optimised structures of <jmolFile text="xylylene">wm1415_XYLYLENE_OPT2_PM6.LOG</jmolFile> and <jmolFile text="sulfur dioxide">wm1415_SO2_OPT_PM6.LOG</jmolFile> have been excluded from the report, but can be opened in a new window from these links.

===Main Fragment: Optimised TS (PM6-level) and IRC Paths===

[[File:wm1415_Main_Fragment_Scheme.PNG|400 px]]

{| class = "wikitable" align = "center"
!Endo TS
!Exo TS
!Cheletropic TS
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_ENDO_PRODUCT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<name>ex3_endoTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==22) frame=23; vibrating=0; endif</script>
<script>frame 23; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[11 4 3 10 16 15]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_endoTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_endoTS</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_ENDO_PRODUCT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<name>ex3_exoTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==22) frame=23; vibrating=0; endif</script>
<script>frame 23; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[11 4 3 10 16 15]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_exoTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_exoTS</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_CHELO_PM6_TS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<name>ex3_cheloTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<text>Reload</text>
<target>ex3_cheloTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_cheloTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==12) frame=13; vibrating=0; endif</script>
<script>frame 13; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_cheloTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[11 4 3 10 16 15 17]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_cheloTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_cheloTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<text>Reload</text>
<target>ex3_cheloTS</target>
</jmolbutton>
</jmol></center>
|-
!Endo IRC Path
!Exo IRC Path
!Cheletropic IRC Path
|-
|<center>[[File:wm1415_Ex3_endo1_regif.gif|300 px]]</center>
|<center>[[File:wm1415_Ex3_exo1_regif.gif|300 px]]</center>
|<center>[[File:wm1415_Ex3_chelo1_regif.gif|300 px]]</center>
|-
!Endo Internuclear Distances
!Exo Internuclear Distances
!Cheletropic Internuclear Distances
|-
|<center>[[File:wm1415_Endo31_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Exo31_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Che1_internucdist.png|400 px]]</center>
|-
!<jmolFile text="Endo Product Jmol">wm1415_ENDO_PRODUCT_OPT_PM6.LOG</jmolFile>
!<jmolFile text="Exo Product Jmol">wm1415_INITIAL_PM6_OPT.LOG</jmolFile>
!<jmolFile text="Cheletropic Product Jmol">wm1415_CHELO_PRODUCTS_INITIAL_PM6_OPT.LOG</jmolFile>
|}

===Second Fragment: Optimised TS (PM6-level) and IRC Paths===

[[File:wm1415_Second_fragment_scheme.PNG|300 px]]

{| class = "wikitable" align = "center"
!Endo TS
!Exo TS
!Cheletropic TS
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_SECOND_ENDO_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<name>ex3_endoTS2</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<text>Reload</text>
<target>ex3_endoTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_endoTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==12) frame=13; vibrating=0; endif</script>
<script>frame 13; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_endoTS2</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 6 16 17 18]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_endoTS2</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_endoTS2</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<text>Reload</text>
<target>ex3_endoTS2</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_SECOND_EXO_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 24; frank off</script>
<name>ex3_exoTS2</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 24; frank off</script>
<text>Reload</text>
<target>ex3_exoTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_exoTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==24) frame=25; vibrating=0; endif</script>
<script>frame 25; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_exoTS2</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 6 16 17 18]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_exoTS2</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_exoTS2</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 24; frank off</script>
<text>Reload</text>
<target>ex3_exoTS2</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_SECOND_CHELO_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<name>ex3_cheloTS2</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==22) frame=23; vibrating=0; endif</script>
<script>frame 23; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 4 5 6 11 12 13]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_cheloTS2</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
</jmol></center>
|-
!Endo IRC Path
!Exo IRC Path
!Cheletropic IRC Path
|-
|<center>[[File:wm1415_Ex3_endo2_regif.gif|300 px]]</center>
|<center>[[File:wm1415_Ex3_exo2_regif.gif|300 px]]</center>
|<center>[[File:wm1415_Ex3_chelo2_regif.gif|300 px]]</center>
|-
!Endo Internuclear Distances
!Exo Internuclear Distances
!Cheletropic Internuclear Distances
|-
|<center>[[File:wm1415_Endo32_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Exo32_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Che2_internucdist.png|400 px]]</center>
|-
!<jmolFile text="Endo Product Jmol">wm1415_SECOND_ENDO_PRODUCTS_PM6_OPT.LOG</jmolFile>
!<jmolFile text="Exo Product Jmol">wm1415_SECOND_EXO_PRODUCTS_PM6_OPT.LOG</jmolFile>
!<jmolFile text="Cheletropic Product Jmol">wm1415_SECOND_CHELO_PRODUCTS_OPT_PM6.LOG</jmolFile>
|}

===Reaction Profile===

[[File:wm1415_Energy_profile_ex3.png|400 px|left]]
{| align="left"
|
{| class="wikitable"
|+ '''Main Fragment: Free energies / kJ/mol'''
! <math>\Delta G^{o}_{endo}</math>
| -99.2
! <math>\Delta G^{o}_{exo}</math>
| -84.1
! <math>\Delta G^{o}_{chel}</math>
| -156
|-
! <math>\Delta G^{*}_{endo}</math>
| 81.6
! <math>\Delta G^{*}_{exo}</math>
| 85.6
! <math>\Delta G^{*}_{chel}</math>
| 104
|}

{| class="wikitable"
|+ '''Second Fragment: Free energies / kJ/mol'''
! <math>\Delta G^{o}_{endo}</math>
| 16.1
! <math>\Delta G^{o}_{exo}</math>
| 20.6
! <math>\Delta G^{o}_{chel}</math>
| 47.1
|-
! <math>\Delta G^{*}_{endo}</math>
| 112
! <math>\Delta G^{*}_{exo}</math>
| 120
! <math>\Delta G^{*}_{chel}</math>
| 141
|}
|
|}

Reaction with the second fragment are clearly very thermodynamically and kinetically unfavourable: the overall reactions are endothermic, and all activation energies are larger than in reactions with the main fragment. The products from these theoretical reactions would not be observed experimentally.

Reaction with the main fragment is much more favourable on account of the formation of the benzene ring. The aromatisation confers stability to both the products and the transition states. The cheletropic reaction yields the thermodynamic product, which contains the more stable 5-membered ring and an additional strong S=O bond. However, the chelotropic rearrangement proceeds via a considerably higher reaction barrier, and at very low temperatures one might observe the kinetic product: the endo Diels-Alder product. The endo configuration has a stabilised TS due to secondary orbital interactions, as discussed previously. Endo-selectivity for this Diels-Alder reaction is reported by the literature [ref-cheletropic].

The reaction between xylylene and SO<sub>2</sub> has been performed in the literature [ref-chelotropic]. At 20 <sup>o</sup>C, SO<sub>2</sub> adds reversibly and a 1:9 mixture of the Diels-Alder and cheletropic products was obtained. Low temperatures are required for the reaction to proceed, because of the reduction in entropy as SO<sub>2</sub> gas is consumed. Prior simulations of this reaction have included a second molecule of SO<sub>2</sub> that may help stabilise the Diels-Alder transition state [ref-chelotropic 2so2].

==Extension: 4π Electrocyclic Ring Closure with Conrotation==
According to the Woodward-Hoffmann rules, an electrocyclic reaction involving 4n π electrons should proceed via a conrotary mechanism [ref-WH]. The subject of this extension is to demonstrate this stereospecifity, using the same methods as previously in this experiment:

[[File:wm1415_Extension_reaction_scheme.PNG|400 px]]

{| class = "wikitable" align = "center"
!Electrocyclic TS
!IRC Path Animation
!IRC Energy Plot
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>350</size>
<uploadedFileContents>wm1415_EXT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 92; mo 24; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<name>extension</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 92; mo 24; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>extension</target>
</jmolbutton>
<jmolbutton>
<script>frame 92; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>extension</target>
</jmolbutton>
<jmolbutton>
<script>frame 92; mo off</script>
<text>MO OFF</text>
<target>extension</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>extension</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==92) frame=93; vibrating=0; endif</script>
<script>frame 93; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>extension</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 3 5 7]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>extension</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>extension</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 92; mo 24; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>extension</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 24</script>
<text>MO 24</text>
<target>extension</target>
</item>
<item>
<script>mo 25</script>
<text>MO 25</text>
<target>extension</target>
</item>
<item>
<script>mo 26</script>
<text>MO 26</text>
<target>extension</target>
</item>
<item>
<script>mo 27</script>
<text>MO 27</text>
<target>extension</target>
</item>
</jmolmenu>
<jmolmenu>
<item>
<script>mo cutoff 0.02</script>
<text>Cutoff 0.02</text>
<target>extension</target>
</item>
<item>
<script>mo cutoff 0.01</script>
<text>Cutoff 0.01</text>
<target>extension</target>
</item>
</jmolmenu>
</jmol></center>
|[[File:wm1415_Ext_gif.gif]]
|[[File:wm1415_ext_Irc_path_energy.PNG|250 px]]
|}

The calculated IRC path clearly shows the conrotation about the migrating carbon atoms, confirming the predicted stereochemistry of the products.

==Conclusion==

==References==

Rep:Wm1415TransitionStates

2017-12-19T05:30:57Z

2017-12-18T23:50:38Z

Wm1415: /* Introduction */

'''This is William Micou's report on the Transition States computational lab, starting Monday 11th December 2017.'''
==Introduction==

Transition state analysis is a powerful technique to predict major products and observed stereochemistry; to rationalise reaction rates with different substituents; to examine reaction mechanisms and to understand catalytic cycles. Transition states are very difficult to probe experimentally: in this experiment, transition states for a variety of pericyclic reactions will be calculated computationally.

The potential energy surface of a molecule consisting of N atoms exists in (3N-6) dimensions. The potential energy can be expressed as a function of (3N-6) independent nuclear coordinates, <math>q_{i}</math>:

<center><math>E = f(q_{1}, q_{2}, ..., q_{3N-6})</math></center>

A stable structure sits in a local minimum on the potential energy surface, whereas a transition state is a saddle point on the PES. These are both stationary points, where:

<center><math>\frac{\partial E(q_{i})}{\partial q_{i}}=0</math> along every coordinate <math>q_{i}</math></center>.

Minima and transition states can be distinguished by their second derivatives. At a minimum, the energy must increase in all directions from that point on the PES: therefore, <math>\frac{\partial^{2}E}{\partial q_{i}^{2}}>0</math> for all <math>q_{i}</math>. At a transition state, the energy increases in all directions except one: the energy decreases along the reaction path. A transition state is hence defined as a stationary point on the PES with one negative Hessian eigenvalue.[ref]

The second derivatives of the PES correspond to the force constants of the vibrations along the chosen nuclear coordinates: <math>k=\frac{\partial^{2}E}{\partial q^{2}}</math>. The frequencies of the vibration can be found from the familiar expression <math>\omega=\frac{1}{2\pi}\sqrt{\frac{k}{\mu}}</math>. Therefore, a transition state will have an optimised structure with a single negative frequency - this corresponds to the collective motions of the atoms forming the products and lowering the energy. In contrast, optimised reactants or products which sit at a local minimum have only positive frequency vibrations.

==Methodology==

==Exercise 1: Butadiene + Ethene Diels-Alder Reaction==

===Optimised structures of the reactants and transition state (PM6 level)===

The table below contains Jmol applets of the reactants and transition state structures optimised at the PM6 level.

{| class = "wikitable" align = "center"
!Ethene
!Butadiene (s-cis)
!Transition state
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>350</size>
<uploadedFileContents>wm1415_ETHENE_PM6_OPT_GFPRINT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<name>ethene</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>frame 6; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>frame 6; mo off</script>
<text>MO OFF</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==6) frame=7; vibrating=0; endif</script>
<script>frame 7; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Lowest Frequency</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 4]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ethene</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ethene</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ethene</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 6</script>
<text>HOMO</text>
<target>ethene</target>
</item>
<item>
<script>mo 7</script>
<text>LUMO</text>
<target>ethene</target>
</item>
</jmolmenu>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>350</size>
<uploadedFileContents>wm1415_BUTADIENE_SCIS_PM6_OPT_GFPRINT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 6; mo 10; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<name>butadiene</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 6; mo 10; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>frame 6; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>frame 6; mo off</script>
<text>MO OFF</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==6) frame=7; vibrating=0; endif</script>
<script>frame 7; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Lowest Frequency</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 4 6 8]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>butadiene</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 6; mo 10; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>butadiene</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 10</script>
<text>MO 10</text>
<target>butadiene</target>
</item>
<item>
<script>mo 11</script>
<text>HOMO</text>
<target>butadiene</target>
</item>
<item>
<script>mo 12</script>
<text>LUMO</text>
<target>butadiene</target>
</item>
<item>
<script>mo 13</script>
<text>MO 13</text>
<target>butadiene</target>
</item>
</jmolmenu>
</jmol></center>
|<center><jmol> //Group all the HTML within "jmol"
<jmolApplet>
<color>#F9F9F9</color>
<size>350</size> //Initialise the applet
<uploadedFileContents>wm1415_DIELS_ALDER_TS_PM6_GFPRINT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<name>DielsAlderTS</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 14; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script> //Turn on MO
<text>MO ON</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 14; mo off</script>
<text>MO OFF</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==14) frame=15; vibrating=0; endif</script>
<script>frame 15; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 4 6 8 14 11]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>DielsAlderTS</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 16</script>
<text>MO 16</text>
<target>DielsAlderTS</target>
</item>
<item>
<script>mo 17</script>
<text>MO 17</text>
<target>DielsAlderTS</target>
</item>
<item>
<script>mo 18</script>
<text>MO 18</text>
<target>DielsAlderTS</target>
</item>
<item>
<script>mo 19</script>
<text>MO 19</text>
<target>DielsAlderTS</target>
</item>
</jmolmenu>
</jmol></center>
|}

===Confirmation of Transition State===

The frequency calculation on the TS structure yielded an imaginary vibration at -948 cm<sup>-1</sup>: this corresponds to the motion of atoms that leads to the formation of products. This motion lowers the energy - hence it yields an imaginary frequency. A transition state is defined as a stationary point with a single negative Hessian eigenvalue [ref].

Further evidence for a correct TS was obtained through an IRC calculation: this structure is the stationary point in the energy plot along the reaction coordinate. The table below provides a plot of the C-C bond lengths during the reaction; an animation of the reaction calculated reaction path; and a plot of the energy, along with its derivative, against the reaction coordinate. It is worth noting that in this case, the IRC path was calculated from the products to the reactants: hence the reversed animation. The same atom labels were used as in the Jmol structures above.

{| class = "wikitable"
!Internuclear distances in IRC path
!Diels-Alder Reaction Animation
!IRC Path Energy Plot
|-
|<center>[[File:wm1415_Diels_alder_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Diels_alder_resized_gif.gif]]</center>
|<center>[[File:wm1415_Irc_energy_diels_alder.PNG|200 px]]</center>
|}

'''Analysis of bond lengths'''

===Optimisation and Analysis of Product===
To reduce the number of Jmol applets on this page, these structures have not been embedded - they can be opened in a new window by clicking the following links. A PM6-level optimisation of the products of the IRC yields <jmolFile text="boat cyclohexene">wm1415_DA_LAST_IRC_STRUCTURE_PM6_OPT.LOG</jmolFile>: this was compared to a PM6-level optimisation of <jmolFile text="chair cyclohexene.">wm1415_CYCLOHEXENE_PM6_OPT.LOG</jmolFile> The boat structure features an imaginary frequency: this corresponds to the collective motion of atoms that would yield the chair cyclohexene structure, lowering the energy.

===Orbital Description of the Diels-Alder Reaction===
{| align="left"
|[[File:wm1415_Final_diels_alder_MO_diagram.PNG|550 px|thumb|left|MO Diagram showing the orbitals involved in the Diels-Alder reaction. While the ordering of the energies of the reactant frontier orbitals has been respected, the diagram is not drawn to scale and the transition state energy levels are skewed for clarity. Approximate energy levels calculated at the PM6-level approximation are listed in the table opposite.]]
|
{| class="wikitable" align="center"
!Ethene
!Energy / a.u.
!Butadiene
!Energy / a.u.
!Transition State
!Energy / a.u.
|-
|
|
|MO 13
|0.0636
|MO 19
|0.0307
|-
|LUMO
|0.0426
|LUMO
|0.0194
|MO 18
|0.0173
|-
|HOMO
| -0.3923
|HOMO
| -0.3590
|MO 17
| -0.3253
|-
|
|
|MO 10
| -0.4133
|MO 16
| -0.3276
|}
LUMO<sub>dienophile</sub> - HOMO<sub>diene</sub> = 0.4016 a.u.

LUMO<sub>diene</sub> - HOMO<sub>dienophile</sub> = 0.4117 a.u.

The energy gap between the LUMO of ethene and the HOMO of butadiene (the antisymmetric orbitals) is smaller than the energy gap between the HOMO of ethene and the LUMO of butadiene (symmetric orbitals). The interaction between the antisymmetric orbitals is stronger as there is greater orbital overlap: by visualising MO 16 of the transition state, it is clear that the bond-forming interaction comes about from electrons in the HOMO of the diene populating the LUMO of the dienophile - the reaction proceeds via normal electron demand.
|}

'''Some text here to fix the formatting issues.'''

==Exercise 2==

===Optimised Reactants: B3LYP/6-31G(d)===

These Jmol files have been excluded from this page to speed up loading time. The applets can be accessed here: <jmolFile text="cyclohexadiene">wm1415_CYCLOHEXADIENE_B3LYP_OPT.LOG</jmolFile> and <jmolFile text="1,3-dioxole">wm1415_LAST_DIOXOLE_TRY_B3LYP.LOG</jmolFile>. There are no negative frequencies as these are stable structures.

===Endo/Exo Transition States and Products===

{| class = "wikitable" align = "center"
!Endo TS
!Endo Product
!Exo TS
!Exo Product
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_ENDO_TS_B3LYP.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 36; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<name>ex2_endoTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 36; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 36; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 36; mo off</script>
<text>MO OFF</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==36) frame=37; vibrating=0; endif</script>
<script>frame 37; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 4 5 6]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ex2_endoTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 36; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ex2_endoTS</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 40</script>
<text>MO 40</text>
<target>ex2_endoTS</target>
</item>
<item>
<script>mo 41</script>
<text>MO 41</text>
<target>ex2_endoTS</target>
</item>
<item>
<script>mo 42</script>
<text>MO 42</text>
<target>ex2_endoTS</target>
</item>
<item>
<script>mo 43</script>
<text>MO 43</text>
<target>ex2_endoTS</target>
</item>
</jmolmenu>
<jmolmenu>
<item>
<script>mo cutoff 0.02</script>
<text>Cutoff 0.02</text>
<target>ex2_endoTS</target>
</item>
<item>
<script>mo cutoff 0.01</script>
<text>Cutoff 0.01</text>
<target>ex2_endoTS</target>
</item>
</jmolmenu>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_ENDO_PRODUCTS_B3LYP_OPT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 18; frank off</script>
<name>ex2_endoproduct</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 18; frank off</script>
<text>Reload</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==18) frame=19; vibrating=0; endif</script>
<script>frame 19; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Lowest Frequency</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 4 5 6]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex2_endoproduct</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 18; frank off</script>
<text>Reload</text>
<target>ex2_endoproduct</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_EXO_TS_B3LYP.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<name>ex2_exoTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 18; mo on; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>MO ON</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>frame 18; mo off</script>
<text>MO OFF</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==18) frame=19; vibrating=0; endif</script>
<script>frame 19; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 4 5 6]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ex2_exoTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.02; mo titleformat ""; frank off</script>
<text>Reload</text>
<target>ex2_exoTS</target>
</jmolbutton>
<jmolmenu>
//The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>mo 40</script>
<text>MO 40</text>
<target>ex2_exoTS</target>
</item>
<item>
<script>mo 41</script>
<text>MO 41</text>
<target>ex2_exoTS</target>
</item>
<item>
<script>mo 42</script>
<text>MO 42</text>
<target>ex2_exoTS</target>
</item>
<item>
<script>mo 43</script>
<text>MO 43</text>
<target>ex2_exoTS</target>
</item>
</jmolmenu>
<jmolmenu>
<item>
<script>mo cutoff 0.02</script>
<text>Cutoff 0.02</text>
<target>ex2_exoTS</target>
</item>
<item>
<script>mo cutoff 0.01</script>
<text>Cutoff 0.01</text>
<target>ex2_exoTS</target>
</item>
</jmolmenu>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_EXO_PRODUCTS_B3LYP_OPT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 14; frank off</script>
<name>ex2_exoproduct</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 14; frank off</script>
<text>Reload</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==14) frame=15; vibrating=0; endif</script>
<script>frame 15; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Lowest Frequency</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 4 5 6]; label display; color label lime; font label 16</script>
<text>Carbon Labels ON</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex2_exoproduct</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 14; frank off</script>
<text>Reload</text>
<target>ex2_exoproduct</target>
</jmolbutton>
</jmol></center>
|}

===Endo/Exo IRC Paths===
{| class = "wikitable"
!Endo Internuclear distances
!Endo Reaction Animation
!Endo IRC Energy Plot
|-
|<center>[[File:wm1415_Ex2_endo_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Ex2_endo_resized.gif]]</center>
|<center>[[File:wm1415_ex2_Irc_energy_endo_cyclo.PNG|200 px]]</center>
|-
!Exo Internuclear distances
!Exo Reaction Animation
!Exo IRC Energy Plot
|-
|<center>[[File:wm1415_Ex2_exo_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Ex2_exo_resized.gif]]</center>
|<center>[[File:wm1415_ex2_Irc_energy_exo_cyclo.PNG|200 px]]</center>
|}

===MO Diagram===
{| align="left"
|[[File:wm1415_Ex2_mo_diagram.PNG|550 px|thumb|left|MO Diagram showing the FMOs. While the ordering of the energies of the reactant FMOs has been respected, the diagram is not drawn to scale and the transition state energy levels are skewed for clarity. Approximate energy levels calculated at the B3LYP 6-31G(d)-level approximation are listed in the table opposite.]]
|
{| class="wikitable" align="center"
!1,3-dioxole
!Energy / a.u.
!Cyclohexadiene
!Energy / a.u.
!Endo TS
!Energy / a.u.
|-
|
|
|MO 24
| 0.0874
|MO 43
| -0.0154
|-
|LUMO
|0.0380
|LUMO
| -0.0171
|MO 42
| -0.0046
|-
|HOMO
| -0.1959
|HOMO
| -0.2055
|MO 41
| -0.1905
|-
|
|
|MO 21
| -0.2994
|MO 40
| -0.1965
|}
LUMO<sub>dienophile</sub> - HOMO<sub>diene</sub> = 0.2435 a.u.

LUMO<sub>diene</sub> - HOMO<sub>dienophile</sub> = 0.1788 a.u.

In this case, it is the energy gap between the LUMO of the diene and the HOMO of the dienophile that is smallest and leads to the greatest orbital overlap. The dienophile, 1,3-dioxole, is electron-rich: electrons flow from its HOMO to the diene LUMO - this is inverse electron demand. This interaction can be visualised as MO 41 in both the endo and exo transition states.
|}

'''text here to avoid formatting issues'''

===Energy Profile: Secondary Orbital Interactions===

{| align="left"
|[[File:wm1415_Ex2_energy_profile.png|300px]]

{| class="wikitable"
|+ '''Free energies / kJ/mol'''
! <math>\Delta G^{o}_{endo}</math>
| -67.4
! <math>\Delta G^{o}_{exo}</math>
| -63.8
|-
! <math>\Delta G^{*}_{endo}</math>
| 160
! <math>\Delta G^{*}_{exo}</math>
| 168
|}
|
[[File:wm1415_SOI_interaction.PNG|200 px|thumb|right]]The endo product is both the kinetic and thermodynamic product of the reaction: it is formed from a lower energy TS and releases more energy in the reaction. The exo product is comparatively destabilised because of the unfavourable steric clash between the heteroatomic 5-membered ring and the bridging ethyl group across the newly-formed 6-membered ring from the Diels-Alder reaction.

The endo transition state is stabilised by secondary orbital interactions [ref] (SOI). These interactions come about between atomic orbitals that are not involved in the formation or cleavage of <math>\sigma</math> bonds [ref]. In the endo TS, the O atoms are aligned with the back of the diene. While this configuration is sterically unfavourable, it allows for the SOI between the O lone pairs and the orbitals at the back end of the diene LUMO. This is a favourable interaction which is only accessible to the endo TS, and more than makes up for the increased steric clash - resulting in a lower energy transition state. These interactions can be clearly seen in the Jmol files above: select MO 41 in the transition state structures (choosing a lower MO cutoff value may show it more clearly).
|}

'''text here to avoid formatting issues'''

==Exercise 3==
===The Reaction between SO<sub>2</sub> and Xylylene===
Sulfur dioxide can undergo Diels-Alder and Cheletropic pericyclic reactions with dienes. Xylylene contains two diene fragments: what will be deemed the main fragment undergoes aromatisation in the considered reactions. The following sections contain calculations for the formation of the each of the possible products for both the main and second fragments of xylylene: from these calculations, a reaction profile will be constructed.

Jmol applets for PM6-optimised structures of <jmolFile text="xylylene">wm1415_XYLYLENE_OPT2_PM6.LOG</jmolFile> and <jmolFile text="sulfur dioxide">wm1415_SO2_OPT_PM6.LOG</jmolFile> have been excluded from the report, but can be opened in a new window from these links.

===Main Fragment: Optimised TS (PM6-level) and IRC Paths===

[[File:wm1415_Main_Fragment_Scheme.PNG|300 px]]

{| class = "wikitable" align = "center"
!Endo TS
!Exo TS
!Cheletropic TS
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_ENDO_PRODUCT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<name>ex3_endoTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==22) frame=23; vibrating=0; endif</script>
<script>frame 23; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[11 4 3 10 16 15]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_endoTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_endoTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_endoTS</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_ENDO_PRODUCT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<name>ex3_exoTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==22) frame=23; vibrating=0; endif</script>
<script>frame 23; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[11 4 3 10 16 15]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_exoTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_exoTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_exoTS</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_CHELO_PM6_TS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<name>ex3_cheloTS</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<text>Reload</text>
<target>ex3_cheloTS</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_cheloTS</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==12) frame=13; vibrating=0; endif</script>
<script>frame 13; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_cheloTS</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[11 4 3 10 16 15 17]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_cheloTS</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_cheloTS</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<text>Reload</text>
<target>ex3_cheloTS</target>
</jmolbutton>
</jmol></center>
|-
!Endo IRC Path
!Exo IRC Path
!Cheletropic IRC Path
|-
|<center>[[File:wm1415_Ex3_endo1_regif.gif|300 px]]</center>
|<center>[[File:wm1415_Ex3_exo1_regif.gif|300 px]]</center>
|<center>[[File:wm1415_Ex3_chelo1_regif.gif|300 px]]</center>
|-
!Endo Internuclear Distances
!Exo Internuclear Distances
!Cheletropic Internuclear Distances
|-
|<center>[[File:wm1415_Endo31_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Exo31_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Che1_internucdist.png|400 px]]</center>
|-
!<jmolFile text="Endo Product Jmol">wm1415_ENDO_PRODUCT_OPT_PM6.LOG</jmolFile>
!<jmolFile text="Exo Product Jmol">wm1415_INITIAL_PM6_OPT.LOG</jmolFile>
!<jmolFile text="Cheletropic Product Jmol">wm1415_CHELO_PRODUCTS_INITIAL_PM6_OPT.LOG</jmolFile>
|}

===Second Fragment===

[[File:wm1415_Second_fragment_scheme.PNG|300 px]]

{| class = "wikitable" align = "center"
!Endo TS
!Exo TS
!Cheletropic TS
|-
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_SECOND_ENDO_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<name>ex3_endoTS2</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<text>Reload</text>
<target>ex3_endoTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_endoTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==12) frame=13; vibrating=0; endif</script>
<script>frame 13; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_endoTS2</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 6 16 17 18]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_endoTS2</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_endoTS2</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 12; frank off</script>
<text>Reload</text>
<target>ex3_endoTS2</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_SECOND_EXO_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 24; frank off</script>
<name>ex3_exoTS2</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 24; frank off</script>
<text>Reload</text>
<target>ex3_exoTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_exoTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==24) frame=25; vibrating=0; endif</script>
<script>frame 25; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_exoTS2</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 2 3 6 16 17 18]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_exoTS2</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_exoTS2</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 24; frank off</script>
<text>Reload</text>
<target>ex3_exoTS2</target>
</jmolbutton>
</jmol></center>
|<center><jmol>
<jmolApplet>
<color>#F9F9F9</color>
<size>300</size>
<uploadedFileContents>wm1415_SECOND_CHELO_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<name>ex3_cheloTS2</name>
</jmolApplet>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
<jmolbutton>
<script>if(frame==22) frame=23; vibrating=0; endif</script>
<script>frame 23; if(vibrating==0) vibrating=1; vibration 1.5; else; vibrating=0; vibration off; endif</script>
<text>Toggle Imaginary Frequency</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
<jmolbutton>
<script>select atomno=[1 4 5 6 11 12 13]; label display; color label lime; font label 16</script>
<text>Labels ON</text>
<target>ex3_cheloTS2</target>
</jmolbutton>

<jmolbutton>
<script>label hide</script>
<text>Labels OFF</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
<jmolbutton>
<script>vibrating=0; spinning=0; frame 22; frank off</script>
<text>Reload</text>
<target>ex3_cheloTS2</target>
</jmolbutton>
</jmol></center>
|-
!Endo IRC Path
!Exo IRC Path
!Cheletropic IRC Path
|-
|<center>[[File:wm1415_Ex3_endo2_regif.gif|300 px]]</center>
|<center>[[File:wm1415_Ex3_exo2_regif.gif|300 px]]</center>
|<center>[[File:wm1415_Ex3_chelo2_regif.gif|300 px]]</center>
|-
!Endo Internuclear Distances
!Exo Internuclear Distances
!Cheletropic Internuclear Distances
|-
|<center>[[File:wm1415_Endo32_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Exo32_internucdist.png|400 px]]</center>
|<center>[[File:wm1415_Che2_internucdist.png|400 px]]</center>
|-
!<jmolFile text="Endo Product Jmol">wm1415_SECOND_ENDO_PRODUCTS_PM6_OPT.LOG</jmolFile>
!<jmolFile text="Exo Product Jmol">wm1415_SECOND_EXO_PRODUCTS_PM6_OPT.LOG</jmolFile>
!<jmolFile text="Cheletropic Product Jmol">wm1415_SECOND_CHELO_PRODUCTS_OPT_PM6.LOG</jmolFile>
|}

===Reaction Profile===

[[File:wm1415_Energy_profile_ex3.png|400 px|left]]
{| align="left"
|
{| class="wikitable"
|+ '''Main Fragment: Free energies / kJ/mol'''
! <math>\Delta G^{o}_{endo}</math>
| -99.2
! <math>\Delta G^{o}_{exo}</math>
| -84.1
! <math>\Delta G^{o}_{chel}</math>
| -156
|-
! <math>\Delta G^{*}_{endo}</math>
| 81.6
! <math>\Delta G^{*}_{exo}</math>
| 85.6
! <math>\Delta G^{*}_{chel}</math>
| 104
|}

{| class="wikitable"
|+ '''Second Fragment: Free energies / kJ/mol'''
! <math>\Delta G^{o}_{endo}</math>
| 16.1
! <math>\Delta G^{o}_{exo}</math>
| 20.6
! <math>\Delta G^{o}_{chel}</math>
| 47.1
|-
! <math>\Delta G^{*}_{endo}</math>
| 112
! <math>\Delta G^{*}_{exo}</math>
| 120
! <math>\Delta G^{*}_{chel}</math>
| 141
|}
|
|}

Reaction with the second fragment is very thermodynamically and kinetically unfavourable: the overall reactions are endothermic, and all activation energies are larger than in reactions with the main fragment.

Reaction with the main fragment is much more favourable on account of the formation of the benzene ring. The aromatisation confers stability to both the products and the transition states. The cheletropic reaction yields the thermodynamic product, which contains an additional strong S=O bond. However, the chelotropic rearrangement proceeds via a considerably higher reaction barrier, and at low temperatures one would observe the kinetic product: the endo Diels-Alder product. The endo configuration has a stabilised TS due to secondary orbital interactions, as discussed previously.

==Extension==

==References==