File:Endo iso 0.05 LUMOSJ1815.jpg

2018-02-12T13:45:40Z

Sj1815:

File:Endo iso 0.05 HOMO SJ1815.jpg

2018-02-12T13:44:55Z

Sj1815:

Rep:SJ1815 Transition States

2018-02-12T13:43:56Z

Sj1815:

<h1>Investigating Transition States of Various Pericyclic Reaction</h1>
<h2>Introduction</h2>
<h3>Transition States: What do we mean?</h3>
Transition states are energy maxima along the path of a reaction and the dynamic bottleneck through which a reaction must proceed. Real energy profiles are dependent on multiple variables and you can move the reactants along the energy profile diagram in any direction, so you can encounter many maxima. However, only the one that occurs on your reaction pathway is considered a transition state. To put this in another way, I could take a flask of but-1,3-diene and ethene and expect a Diels-Alder reaction to occur. The transition state would be somewhere where the C-C bonds are being made from the C=Cs in the substrates. I could, given enough energy, stretch one of the C-C bonds to the moon (admittedly, probably breaking it in the process) and you'd have an energy maximum but it wouldn't be a transition state as it isn't part of the reaction in question.
Normally for a C-C bond forming process, we take the transition state to be somewhere between the van der Waals radii of the 2 atoms and the C-C bond length.

<h3>Locating a transition state</h3>
<h4>Use Hammond's Postulate</h4>
Take a guess at where the Transition State is and optimise using Gaussian. Use Hammond's postulate for where to guess. This is fast, but unreliable, as you have to be a very good guesser.

<b>N.B. Hammond's Postulate: 'The structure of the transition states resembles either the reactants or products (whichever is closest in energy)'</b><ref name="HammondPost" />

For C-C bond forming reactions, a guess of 2.2 for the bond length is a good place to start.

To actually run the job, use Opt+Freq (geometry optimisation via 'solving' the Schrödinger equation, which is ĤΨ=EΨ, and then moving along in small steps of energy, scaled using the second derivative d<sup>2</sup>E/dq<sup>2</sup>, where q is the reaction coordinate and frequency calculation using k=d<sup>2</sup>E/dq<sup>2</sup> and [[File:Spring frequency1.png|100px]]<ref name="Bearparklecture" />

The computer uses variational theorem to run calculations and solve the Schrödinger equation. Variational theorem takes a guess at the wavefunction of a system and then minimises the energy. This means that it hits the potential energy surface after a number of iterations. Depending on where it hits, the optimised .log file can look like a range of different things. A potential energy surface has a lot of local minima- it's 'bumpy'. If the guess wavefunction hits any of these bumps, Gaussview may tell you that it's found a transition state when it hasn't. This is why we need to analyse the results by checking the imaginary vibration and seeing if it matches with our idea of what 'going towards the products' looks like.

<table class="image">
<tr><td>[[File:PE_surface_SJ1815.gif]]</td></tr>
<tr><td class="caption"><i><span style="color:gray">Figure 1: A depiction of a 3D potential energy surface taken from reference 3 <ref name="PE surface"></ref>. We can only represent energy surfaces in 3D, yet they actually have many more dimensions than this (there are 3N-6 dimensions to consider, where N is the number of atoms in the molecule).</span></i></td></tr>
</table>

One approximation to make calculations easier is that we assume that molecular orbitals can be constructed from a linear combination of atomic orbitals. These all have different weightings called <b> orbital coefficients</b>. The wavefunction can therefore be broken down into <math>|\psi\rangle</math>=Σ<sup>N</sup><sub>i</sub>c<sub>i</sub><math>|\ \phi_i\rangle</math>

As <math>\langle\psi|</math>H<math>|\psi\rangle</math>=E<math>\psi</math>, we then have Σ<sup>N</sup><sub>m</sub>Σ<sup>N</sup><sub>n</sub>c<sub>m</sub><math>\langle\phi_m|</math>H<math>|\phi_n\rangle</math>c<sub>n</sub>

This can be written as a set of matrices with the first being a 1xn matrix of the c<sub>n</sub> coefficients, then a Hessian matrix of all of the different atomic orbital integrals and then an mx1 matrix of the c<sub>m</sub> coefficients or, more succinctly, c<sup>T</sup>Hc, where H is the Hessian here. This equals the energy and from this you can get the eigenvalue equation of Hc=Ec, which the computer solves

Each eigenvector of the eigenvalue equation yields 1 molecular orbital.

<b> What are the individual atomic wavefunctions?</b>

These represent electron densityand are best represented by Slater functions.

Slater functions have the form <math>R(r) = N r^{n-1} e^{-\zeta r}\,</math><ref name="Slater"></ref>

This, however, is too computationally costly to solve, so we use an approximation by using Gaussians.

Gaussian functions have the form <math>ae^{-ar^2}</math> An example of thhe form of one of these is shown below.

[[File:SJ1815_Gaussian.jpg]]

As these don't represent the orbitals as well as Slater functions, several of them are often summed to better represent these orbitals. This sum adds computational complexity, as there are more integrals to compute, yet this is still faster than using Slater functions. Combining three Gaussians gives a basis set of STO-3G (<b>S</b>later-<b>T</b>ype <b>O</b>rbitals-<b>3</b> functions <b>G</b>aussians)<ref name="Basis"></ref>.

<h2>Optimisation methods</h2>

PM6 is a semi-empirical optimisation method. It takes into account the valence electrons for the species and then solves the integrals in relation to them, employing code already on the Gaussian programme <ref name="PM6Gauss"></ref>. It also uses fixed numbers as approximations for the integrals in the Hessian. This makes it much faster at doing calculations, yet more imprecise in the answers obtained.

B3LYP is a DFT (density functional theory) method, which takes advantage of density fitting (expansion of atomic density rather than computing all of the 2-electron integrals individually)<ref name="DensityGauss"></ref>. B3LYP differs from other DFT calculations insofar as it optimises the nuclear wavefunctions, then adds on some electron interactions to see how things change (most DFT calculations just use the nuclei) <ref name="DFTGauss"></ref>. However, these are not easily calculated by Gaussian, causing approximations to be formed.

<h2>Tutorial</h2>

<h3>Tutorial 1- Cope rearrangement of hexa-1,5-diene</h3>
[[File:Cope_rearrangementSJ1815.png|500px]]

The first method for finding a transition state is to guess and then optimise using Opt+Freq, Optimise to a TS (Berny) and calculate the force constants once. There should be 1 negative frequency at the output, which confirms that a transition state has been found and animation of said transition state should make it look like you go from reactants to products.
There are 2 different transition states (boat and chair), both of which have been accounted for below
{| class="wikitable"
!
!Boat
!Chair
|-
|
|[[File:SJ1815Boat.jpg|100px]]
|[[File:SJ1815Chair.jpg|100px]]
|-
|'''PM6'''
|[[File:SJ1815TRIAL COPE TS 2 RADICALS PM6.LOG]]
|[[File:SJ1815TRIAL COPE TS RADICAL CHAIRTS.LOG]]
|-
|'''B3LYP'''
|[[File:SJ1815COPEBOATTSB3LYP.LOG]]
|[[File:SJ1815COPECHAIRTSB3LYP.LOG]]
|}

<b>IRC</b>

[[File:SJ1815 BOAT COPE TS IRC PM6.LOG]]

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815 BOAT COPE TS IRC PM6.LOG </uploadedFileContents></jmolApplet></jmol>
<h3>Tutorial 2- Dimerisation of Cyclopentadiene</h3>
[[File:SJ1815Cyclopentadiene dimerisation.jpg|500px]]

The second method relies on generating a guess transition state, freezing the atoms in space and then uses method 1 to find exactly where the transition state lies. The keyword opt=modredundant will appear in the submission window, but submit the job as normal, optimising to a minimum. Then, unfreeze the bonds and optimise to a TS, as in method 1. To distinguish between endo and exo conformers, run IRC calculations.

<b>Optimisation:</b>

<b>PM6:</b> [[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS OPT+FREQ PM6.LOG]]

<b>B3LYP:</b>[[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS B3LYP.LOG]]

<h3>Tutorial 3-Xylylene SO2 Diels-Alder</h3>
The third method uses the reactants or products, alters the bond lengths and/or angles (normally of those involved in the reaction, but can be of neighbouring atoms too) and then runs the same way as method 2.

<b>Opt+Freq of Diels-Alder</b>

[[File:SJ1815_SO2_DIELS-ALDER_PM6_MIN.LOG]]

<h2>Exercise 1- Cis-butadiene and ethene Diels-Alder ([4+2]-cycloaddition)</h2>
[[File:Diels-Alder cyclohexene product.jpg|500px]]

This reaction is often seen as the classic Diels-Alder reaction, due to the fact that the diene and dienophile are as simple as they can be. However, this reaction is purely hypothetical as neither fragment is particularly electron rich or poor (we need this disparity in energies for both normal electron demand and inverse electron demand Diels-Alder reactions).

<h3>Optimisation</h3>

{| class="wikitable"
!
! style="background: #8b0c0c; color: white;" | Butadiene
! style="background: #8b0c0c; color: white;" | Ethene
! style="background: #8b0c0c; color: white;" | Cyclohexene
! style="background: #8b0c0c; color: white;"|Transition state
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> BUTADIENE_SJ1815.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 ETHENE_OPT+FREQ_PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXENE PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:BUTADIENE_SJ1815.LOG]]
|[[File:SJ1815 ETHENE_OPT+FREQ_PM6.LOG]]
|[[File:SJ1815 CYCLOHEXENE PM6.LOG]]
|[[File:SJ1815_DIELS-ALDER_TS10.LOG]]
|-
|'''C-C bond Lengths/Å'''
|1.33343
|1.32742
|1.33698
|1.37977 (original C=C of butadiene)
|-
|
|1.47077
|X
|1.50068
|1.41111 (original C-C of butadiene)
|-
|
|1.33343
|X
|1.53703
|1.37977 (original C=C of butadiene)
|-
|
|X
|X
|1.53491
|1.38176 (original C=C of ethene)
|-
|
|X
|X
|1.53736
|X
|-
|
|X
|X
|1.50077
|X
|}
The bond length for a C-C bond is 1.54Å <ref name="C-C"></ref> while the C=C bond length is 1.34Å <ref name="C=C"></ref>
This matches fairly well with the bond lengths in the table above, with the transition state having bond lengths partway between the two lengths. The van der Waals radius of carbon is 1.77Å <ref name="CvdW"></ref> and all C-C lengths are closer than this, so they are interacting (the van der Waals radius tells us how close atoms have to be for some interaction to take place).

<h3>MO analysis</h3>

The MO diagram for the reaction is as depicted below

[[File:SJ1815Diels-Alder2.jpg]]

We can see that only orbitals of the same symmetry can interact and have non-zero integrals. This means only fully symmetric or fully antisymmetric combinations are allowed.

The actual, calculated MOs are depicted here:

{| class="wikitable"
!MO label
!MOs
!Corresponding diagram
|-
|LUMO
|[[File:SJ1815_DA_LUMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw.jpg|150px]]
|-
|HOMO
|[[File:SJ1815_DA_HOMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw1.jpg|150px]]
|-
|HOMO-1
|[[File:SJ1815_DA_HOMO-1.png|150px]]
|[[File:SJ1815_DA_HOMO-1chemdraw.jpg|150px]]
|-
|HOMO-2
|[[File:SJ1815_DA_HOMO-2.png|150px]]
|[[File:SJ1815_DA_HOMO-2chemdraw.jpg|150px]]
|-
|HOMO-3
|[[File:SJ1815_DA_HOMO-3.png|150px]]
|[[File:SJ1815_DA_HOMO-3chemdraw.jpg|150px]]
|}

<b>The transition state</b>

[[File:SJ1815 DIELS-ALDER TS10.LOG]]

[[File:TS_DA_SJ1815.gif|thumb|none|alt=A depiction of the transition state|A depiction of the transition state (click to animate)]]

<jmol><jmolApplet><size>200</size><script>frame 15; vibration 2;rotate x -20; </script><uploadedFileContents>SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>

We can see that this is a transition state as it has a vibration at -948.72 cm<sup>-1</sup> in the log file.

Two IRC calculations were run, as the first only showed progression from products to reactants, even though the graph showed entire reaction coordinates.

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ1815_DA_IRC1.jpg|caption=The IRC path going backwards in the reaction]]
|[[File:SJ1815_DA_IRC2.jpg|caption=The IRC path going forwards in the reaction]]
|-
|'''IRC LOG files'''
|[[File:SJ1815 DIELS-ALDER IRC.LOG]]
|[[File:SJ1815_DIELS_ALDERIRCFORWARDS.LOG]]
|-
|'''IRC animations'''
|[[File:SJ1815_TS_IRC_DA.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|[[File:SJ1815_TS_IRC_DAforwards.gif|caption=The IRC path going forwards in the reaction (click to animate)]]
|}

The IRC shows synchronous bond formation between cis-butadiene and ethene.

<h2>Exercise 2- Reaction of Cyclohexa-1,3-diene and 1,3-Dioxole ([4+2] cycloaddition)</h2>
[[File:SJ18151,3-dioxole endo and exo.jpg|500px]]

{| class="wikitable"
!
!Dioxole
!Cyclohexa-1,3-diene
!Endo product
!Exo product
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 DIOXOLEPM6OPT+FREQ.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG </uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:SJ1815 DIOXOLEPM6OPT+FREQ.LOG]]
|[[File:SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG]]
|[[File:SJ1815_OPT+FREQPM6_2NDPRODUCT.LOG]]
|[[File:SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG]]
|-
|'''B3LYP'''
|[[File:DIOXOLEB3LYPOPT+FREQ_SJ1815(1).LOG]]
|[[File:SJ1815_CYCLOHEXADIENEB3LYPOPT+FREQ(1).LOG]]
|[[File:SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG]]
|[[File:SJ1815_B3LYP1STPRODUCT.LOG]]
|}

<h3>Thermochemistry</h3>

{|class= "wikitable"
!
!Energy
!Energy difference from Reactants
|-
|'''1,3-dioxole'''
||-267.068138 Hartrees/particle
|X
|-
|'''Cyclohexa-1,3-diene'''
||-233.321307 Hartrees/particle
|X
|-
|'''Total Reactants'''
||-500.389175 Hartrees/particle
|X
|-
|'''Exo TS'''
||-500.329165 Hartrees/particle
||+0.06001 Hartrees/particle = +157.556255 kJ/mol
|-
|'''Exo Product'''
||-500.418691 Hartrees/particle
||-0.029516 Hartree/particle = -77.494258.8973 kJ/mol
|-
|'''Endo TS'''
||-500.332149 Hartrees/particle
||+0.057026 Hartrees/particle = +149.7218 kJ/mol
|-
|'''Endo Product'''
||-500.417315 Hartrees/particle
||-0.02814 Hartrees/particle = -73.88157 kJ/mol
|-
|}

[[File:SJ1815DioxoleEnergydiagram.jpg]]

The thermodynamic product is therefore the exo product (the endo product has a higher energy due to steric clash within the molecule) while the kinetic product is the endo product, as the transition state is lower in energy, due to the fact that secondary orbital interactions are greater for the endo transition state.

<h4>MO diagrams</h4>

<b>Endo</b>

[[File:Diels-AlderdioxoleSJ1815exo1.jpg]]

<b>Exo</b>

[[File:Diels-AlderdioxoleSJ1815endo1.jpg]]

It can't be obtained directly from these MO diagrams as to whether the reaction proceeds via normal or inverse electron demand, as all optimisations were done on different potential energy surfaces. We can, however, say it is likely to be inverse electron demand due to the oxygen atoms of 1,3-dioxole donating electron density into the dienophile C=C.

<h3> The Transition State</h3>

The transition state for this reaction is depicted below, optimised to the B3LYP level.

<b>Endo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815EndoTSvibration.gif]]

[[File:SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG]]

Vibration occurs at -523.01cm<sup>-1</sup>.

<b>Exo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>2NDPRODUCTB3LYPTS_SJ1815.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:2NDPRODUCTB3LYPTS_SJ1815.LOG]]

[[File:ExoTSvibrationSJ1815.gif]]

Vibration occurs at -528.84cm<sup>-1</sup>.

<h4>Molecular orbitals</h4>

<b>Exo HOMO:</b>

[[File:SJ1815HOMO calledEndo product.jpg]]

Energy: -0.19052 Hartrees/particle

<b>Exo LUMO</b>

[[File:Sj1815LUMO_calledEndo_product.jpg]]

Energy:-0.00462 Hartrees/particle

<b>Endo HOMO</b>

[[File:SJ1815HOMO_TS_2nd_product.jpg]]

Energy: -0.18560 Hartrees/particle

<b>Endo LUMO</b>

[[File:SJ1815LUMO_TS_2nd_product.jpg]]

Energy:-0.00699 Hartrees/particle

There is obvious, visible secondary orbital interaction between orbitals on the oxygen atoms and those on the cyclohexa-1,3-diene's cis-butadiene fragment. This lowers the endo transition state's energy, yet both exo and endo benefit from these interactions (the overlap is just greater for the endo transition state).

<h2>Exercise 3-Diels-Alder ([4+2]) vs Cheleotropic ([4+1])</h2>
[[File:Diels-Alder SO2.jpg|500px]]

[[File:SJ1815Cheleotropic SO2 (1).jpg|500px]]

[[File:SJ1815Diels-Alder_SO2_(1)(endo).jpg|500px]]

[[File:2ndC=C-C=C_Diels-Alder_SJ1815.jpg|500px]]

{| class="wikitable"
!
!Cheleotropic
!Outer fragment Endo
!Inner fragment Endo
!Outer fragment Exo
!Inner fragment Exo
|-
|'''Products'''
|<jmol><jmolApplet><uploadedFileContents>SJ1815CHELEOTROPIC_SO2_PM6.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815CHELEOTROPIC_SO2_PM6.LOG]]
|<jmol><jmolApplet><uploadedFileContents>SJ1815OUTERC=CPRODUCTENDO.LOG </uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815OUTERC=CPRODUCTENDO.LOG]]
|<jmol><jmolApplet><uploadedFileContents>DA1STotherC=CSJ1815PRODUCT(Exo).LOG </uploadedFileContents></jmolApplet></jmol>

[[File:DA1STotherC=CSJ1815PRODUCT(Exo).LOG]] (This has, in fact, been named incorrectly and is endo, as stated in the table).
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG]]
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG</uploadedFileContents></jmolApplet></jmol>
[[File:SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).
|-
|'''Transition states'''
|[[File:SJ1815_PM6CHELEOTS3.LOG]]

[[File:SJ1815_PM6CheleoTS3.gif]]

Vibration occurs at -484.77cm<sup>-1</sup>.
|[[File:DA2NDTSFROMFROZENSJ1815(endo)(1stC=C).LOG]]

[[File:SJ1815EndoTSfromfrozen(1stC=C).gif]]

Vibration occurs at -333.62cm<sup>-1</sup>.
|[[File:SJ1815EXODA2NDC=C-C=CTS(3).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:Exo_TS_Sj1815_innerC-C(real_exo).gif]]

Vibration occurs at -453.52cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(1stC=C)(exo).LOG]]

[[File:SJ1815_SO2_DA_TS_PM6.gif]]

Vibration occurs at -351.55cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(2NDC=C)(ENDO)(REALPM6).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:SJ1815_endoDAinnerC-CTS(real_endo).gif]]

Vibration occurs at -482.80cm<sup>-1</sup>.
|-
|'''IRC graphs'''
|[[File:SJ1815_Cheleo_IRC.jpg]]
|[[File:DA2ndTSfromfrozenSJ1815Endo(1stC=C).jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|[[File:SJ1815_IRCexo1stC=C.jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|-
|'''IRC animations'''
|[[File:SJ1815_Cheleo_Both_IRCPM6.gif]]

[[File:SJ1815_CHELEO_BOTH_IRCPM6.LOG]]
|[[File:SJ1815_endoIRC1stC=C.gif]]

[[File:DA2NDTSFROMFROZENSJ1815(ENDO)(1STC=C)IRC.LOG]]
|[[File:SJ1815otherC=CExoIRC.gif]]

[[File:DA2NDOTHERC=CSJ1815FROZENIRC.LOG]]
|[[File:SJ1815_outerC=CEndoIRC.gif]]

[[File:SJ1815_DA_1ST_SO2_IRCPM6(exo)(1stC=C).LOG]]

|[[File:SJ1815_innerC-C_endoDAIRC.gif]]

[[File:SJ1815INNERC=C-C=CENDOIRCPM6.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

|}

Xylylene is highly unstable as the bonding changes from 4 distinct double bonds to an aromatic ring and 2 single bonds pointing out of the ring. Due to the stability of the aromatic ring, xylylene may form a 4 membered ring to establish aromaticity or may polymerise.

<h4> Thermochemistry</h4>

[[File:SJ1815_Ex3Energydiagram.jpg]]

<h5>Outer fragment thermochemistry</h5>

<b>Cheleotropic</b>

<b>Reaction barrier</b>= +0.036864 Hartrees/particle or +96.786432 kJ/mol

<b>Reaction energy</b>= -0.062913 Hartrees/particle or -163.2877215 kJ/mol

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.028369 Hartrees/particle or +74.4828095 kJ/mol

<b>Reaction energy</b>= -0.040484 Hartrees/particle or -106.290742 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.029887 Hartrees/particle or +78.4683185 kJ/mol

<b>Reaction energy</b>= -0.040735 Hartrees/particle or -106.9497425 kJ/mol

The thermodynamic product is the cheleotropic product (it's lowest in energy) and the kinetic product is the endo product (the transition state is lowest in energy).

<h5>Inner fragment thermochemistry</h5>

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.042864 Hartrees/particle or +112.539432 kJ/mol

<b>Reaction energy</b>= +0.005114 Hartrees/particle or +13.426807 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.039882 Hartrees/particle or +104.710191 kJ/mol

<b>Reaction energy</b>= +0.003415 Hartrees/particle or 8.9660825 kJ/mol

Attack at the inner cis-butadiene fragment is disfavoured and doesn't occur.

<h2> Exercise 4- the ring opening of dimethyl (1R,2S)-cyclobut-3-ene-1,2-dicarboxylate</h2>

[[File:SJ1815ringopening.jpg]]

The ring opening of a 4-membered ring is only thermally allowed if the transition state is a Möbius transition state (that is, the 2 ends of the ring are conrotatory and twist in the same sense).

This can be seen when you look at the IRC for the reaction

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ18152+2IRC.jpg]]
|-
|'''IRC LOG files'''
|[[File:SJ18152+2TS4IRC.LOG]]
|-
|'''IRC animations'''
|[[File:SJ18152+2IRC.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|}

<h3>The transition state</h3>

[[File:SJ18152+2TSvib.gif]]

[[File:SJ18152+2TS4.LOG]]

This vibration occurs at -696.41cm<sup>-1</sup>. This negative vibration confirms the fact that this is a transition state.

<h2>References</h2>
<references>
<ref name="HammondPost">https://chem.libretexts.org/Reference/Organic_Chemistry_Glossary/Hammond%E2%80%99s_Postulate accessed on 8/11/2017 </ref>
<ref name="Bearparklecture"> Michael J Bearpark, 2017, <i>Calculating Molecular Geometries</i>, Lecture, Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Imperial College London, 6th November 2017 </ref>
<ref name="C-C"> Stark J.G., Wallace H.G. in <i>Chemistry Data Book</i> ed. Hodder Education, Hodder Education, 2nd edn, 1982, ch.19, pp. 27 </ref>
<ref name="C=C"> http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html accessed on 5/2/2018 </ref>
<ref name="PE surface">https://www.nrl.navy.mil/mstd/branches/6390/surfaces-and-interfaces accessed on 6/2/2018</ref>
<ref name="Slater">adapted from F. Jensen in <i>Introduction to Computational Chemistry </i> ed. Wiley, Wiley, Indianapolis, 1st edn., 1999, ch. 5. Adaptation obtained from https://lcbc.epfl.ch/files/content/users/232236/files/lecture_2016_2.pdf accessed on 12/2/2018</ref>
<ref name="PM6Gauss">http://gaussian.com/semiempirical/ accessed on 8/2/2108 </ref>
<ref name="DFTGauss">http://gaussian.com/dft/ accessed on 8/2/2018 </ref>
<ref name="DensityGauss">http://gaussian.com/basissets/?tabid=2 accessed on 8/2/2018</ref>
<ref name= "CvdW">https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf accessed on 11/2/2018 </ref>
<ref name="Basis"> A. Szabo, N. Oatlands in <i>Modern Quantum Chemistry </i> ed. Dover Publications Inc., Dover Publications Inc., Mineola, 1st edn., 1996, ch. 3, pp. 156 </ref>
</references>

File:SJ1815CHELEOTROPIC SO2 PM6.LOG

2018-02-12T13:42:13Z

Sj1815: Sj1815 uploaded a new version of File:SJ1815CHELEOTROPIC SO2 PM6.LOG

Rep:SJ1815 Transition States

2018-02-12T13:41:41Z

Sj1815:

<h1>Investigating Transition States of Various Pericyclic Reaction</h1>
<h2>Introduction</h2>
<h3>Transition States: What do we mean?</h3>
Transition states are energy maxima along the path of a reaction and the dynamic bottleneck through which a reaction must proceed. Real energy profiles are dependent on multiple variables and you can move the reactants along the energy profile diagram in any direction, so you can encounter many maxima. However, only the one that occurs on your reaction pathway is considered a transition state. To put this in another way, I could take a flask of but-1,3-diene and ethene and expect a Diels-Alder reaction to occur. The transition state would be somewhere where the C-C bonds are being made from the C=Cs in the substrates. I could, given enough energy, stretch one of the C-C bonds to the moon (admittedly, probably breaking it in the process) and you'd have an energy maximum but it wouldn't be a transition state as it isn't part of the reaction in question.
Normally for a C-C bond forming process, we take the transition state to be somewhere between the van der Waals radii of the 2 atoms and the C-C bond length.

<h3>Locating a transition state</h3>
<h4>Use Hammond's Postulate</h4>
Take a guess at where the Transition State is and optimise using Gaussian. Use Hammond's postulate for where to guess. This is fast, but unreliable, as you have to be a very good guesser.

<b>N.B. Hammond's Postulate: 'The structure of the transition states resembles either the reactants or products (whichever is closest in energy)'</b><ref name="HammondPost" />

For C-C bond forming reactions, a guess of 2.2 for the bond length is a good place to start.

To actually run the job, use Opt+Freq (geometry optimisation via 'solving' the Schrödinger equation, which is ĤΨ=EΨ, and then moving along in small steps of energy, scaled using the second derivative d<sup>2</sup>E/dq<sup>2</sup>, where q is the reaction coordinate and frequency calculation using k=d<sup>2</sup>E/dq<sup>2</sup> and [[File:Spring frequency1.png|100px]]<ref name="Bearparklecture" />

The computer uses variational theorem to run calculations and solve the Schrödinger equation. Variational theorem takes a guess at the wavefunction of a system and then minimises the energy. This means that it hits the potential energy surface after a number of iterations. Depending on where it hits, the optimised .log file can look like a range of different things. A potential energy surface has a lot of local minima- it's 'bumpy'. If the guess wavefunction hits any of these bumps, Gaussview may tell you that it's found a transition state when it hasn't. This is why we need to analyse the results by checking the imaginary vibration and seeing if it matches with our idea of what 'going towards the products' looks like.

<table class="image">
<tr><td>[[File:PE_surface_SJ1815.gif]]</td></tr>
<tr><td class="caption"><i><span style="color:gray">Figure 1: A depiction of a 3D potential energy surface taken from reference 3 <ref name="PE surface"></ref>. We can only represent energy surfaces in 3D, yet they actually have many more dimensions than this (there are 3N-6 dimensions to consider, where N is the number of atoms in the molecule).</span></i></td></tr>
</table>

One approximation to make calculations easier is that we assume that molecular orbitals can be constructed from a linear combination of atomic orbitals. These all have different weightings called <b> orbital coefficients</b>. The wavefunction can therefore be broken down into <math>|\psi\rangle</math>=Σ<sup>N</sup><sub>i</sub>c<sub>i</sub><math>|\ \phi_i\rangle</math>

As <math>\langle\psi|</math>H<math>|\psi\rangle</math>=E<math>\psi</math>, we then have Σ<sup>N</sup><sub>m</sub>Σ<sup>N</sup><sub>n</sub>c<sub>m</sub><math>\langle\phi_m|</math>H<math>|\phi_n\rangle</math>c<sub>n</sub>

This can be written as a set of matrices with the first being a 1xn matrix of the c<sub>n</sub> coefficients, then a Hessian matrix of all of the different atomic orbital integrals and then an mx1 matrix of the c<sub>m</sub> coefficients or, more succinctly, c<sup>T</sup>Hc, where H is the Hessian here. This equals the energy and from this you can get the eigenvalue equation of Hc=Ec, which the computer solves

Each eigenvector of the eigenvalue equation yields 1 molecular orbital.

<b> What are the individual atomic wavefunctions?</b>

These represent electron densityand are best represented by Slater functions.

Slater functions have the form <math>R(r) = N r^{n-1} e^{-\zeta r}\,</math><ref name="Slater"></ref>

This, however, is too computationally costly to solve, so we use an approximation by using Gaussians.

Gaussian functions have the form <math>ae^{-ar^2}</math> An example of thhe form of one of these is shown below.

[[File:SJ1815_Gaussian.jpg]]

As these don't represent the orbitals as well as Slater functions, several of them are often summed to better represent these orbitals. This sum adds computational complexity, as there are more integrals to compute, yet this is still faster than using Slater functions. Combining three Gaussians gives a basis set of STO-3G (<b>S</b>later-<b>T</b>ype <b>O</b>rbitals-<b>3</b> functions <b>G</b>aussians)<ref name="Basis"></ref>.

<h2>Optimisation methods</h2>

PM6 is a semi-empirical optimisation method. It takes into account the valence electrons for the species and then solves the integrals in relation to them, employing code already on the Gaussian programme <ref name="PM6Gauss"></ref>. It also uses fixed numbers as approximations for the integrals in the Hessian. This makes it much faster at doing calculations, yet more imprecise in the answers obtained.

B3LYP is a DFT (density functional theory) method, which takes advantage of density fitting (expansion of atomic density rather than computing all of the 2-electron integrals individually)<ref name="DensityGauss"></ref>. B3LYP differs from other DFT calculations insofar as it optimises the nuclear wavefunctions, then adds on some electron interactions to see how things change (most DFT calculations just use the nuclei) <ref name="DFTGauss"></ref>. However, these are not easily calculated by Gaussian, causing approximations to be formed.

<h2>Tutorial</h2>

<h3>Tutorial 1- Cope rearrangement of hexa-1,5-diene</h3>
[[File:Cope_rearrangementSJ1815.png|500px]]

The first method for finding a transition state is to guess and then optimise using Opt+Freq, Optimise to a TS (Berny) and calculate the force constants once. There should be 1 negative frequency at the output, which confirms that a transition state has been found and animation of said transition state should make it look like you go from reactants to products.
There are 2 different transition states (boat and chair), both of which have been accounted for below
{| class="wikitable"
!
!Boat
!Chair
|-
|
|[[File:SJ1815Boat.jpg|100px]]
|[[File:SJ1815Chair.jpg|100px]]
|-
|'''PM6'''
|[[File:SJ1815TRIAL COPE TS 2 RADICALS PM6.LOG]]
|[[File:SJ1815TRIAL COPE TS RADICAL CHAIRTS.LOG]]
|-
|'''B3LYP'''
|[[File:SJ1815COPEBOATTSB3LYP.LOG]]
|[[File:SJ1815COPECHAIRTSB3LYP.LOG]]
|}

<b>IRC</b>

[[File:SJ1815 BOAT COPE TS IRC PM6.LOG]]

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815 BOAT COPE TS IRC PM6.LOG </uploadedFileContents></jmolApplet></jmol>
<h3>Tutorial 2- Dimerisation of Cyclopentadiene</h3>
[[File:SJ1815Cyclopentadiene dimerisation.jpg|500px]]

The second method relies on generating a guess transition state, freezing the atoms in space and then uses method 1 to find exactly where the transition state lies. The keyword opt=modredundant will appear in the submission window, but submit the job as normal, optimising to a minimum. Then, unfreeze the bonds and optimise to a TS, as in method 1. To distinguish between endo and exo conformers, run IRC calculations.

<b>Optimisation:</b>

<b>PM6:</b> [[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS OPT+FREQ PM6.LOG]]

<b>B3LYP:</b>[[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS B3LYP.LOG]]

<h3>Tutorial 3-Xylylene SO2 Diels-Alder</h3>
The third method uses the reactants or products, alters the bond lengths and/or angles (normally of those involved in the reaction, but can be of neighbouring atoms too) and then runs the same way as method 2.

<b>Opt+Freq of Diels-Alder</b>

[[File:SJ1815_SO2_DIELS-ALDER_PM6_MIN.LOG]]

<h2>Exercise 1- Cis-butadiene and ethene Diels-Alder ([4+2]-cycloaddition)</h2>
[[File:Diels-Alder cyclohexene product.jpg|500px]]

This reaction is often seen as the classic Diels-Alder reaction, due to the fact that the diene and dienophile are as simple as they can be. However, this reaction is purely hypothetical as neither fragment is particularly electron rich or poor (we need this disparity in energies for both normal electron demand and inverse electron demand Diels-Alder reactions).

<h3>Optimisation</h3>

{| class="wikitable"
!
! style="background: #8b0c0c; color: white;" | Butadiene
! style="background: #8b0c0c; color: white;" | Ethene
! style="background: #8b0c0c; color: white;" | Cyclohexene
! style="background: #8b0c0c; color: white;"|Transition state
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> BUTADIENE_SJ1815.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 ETHENE_OPT+FREQ_PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXENE PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:BUTADIENE_SJ1815.LOG]]
|[[File:SJ1815 ETHENE_OPT+FREQ_PM6.LOG]]
|[[File:SJ1815 CYCLOHEXENE PM6.LOG]]
|[[File:SJ1815_DIELS-ALDER_TS10.LOG]]
|-
|'''C-C bond Lengths/Å'''
|1.33343
|1.32742
|1.33698
|1.37977 (original C=C of butadiene)
|-
|
|1.47077
|X
|1.50068
|1.41111 (original C-C of butadiene)
|-
|
|1.33343
|X
|1.53703
|1.37977 (original C=C of butadiene)
|-
|
|X
|X
|1.53491
|1.38176 (original C=C of ethene)
|-
|
|X
|X
|1.53736
|X
|-
|
|X
|X
|1.50077
|X
|}
The bond length for a C-C bond is 1.54Å <ref name="C-C"></ref> while the C=C bond length is 1.34Å <ref name="C=C"></ref>
This matches fairly well with the bond lengths in the table above, with the transition state having bond lengths partway between the two lengths. The van der Waals radius of carbon is 1.77Å <ref name="CvdW"></ref> and all C-C lengths are closer than this, so they are interacting (the van der Waals radius tells us how close atoms have to be for some interaction to take place).

<h3>MO analysis</h3>

The MO diagram for the reaction is as depicted below

[[File:SJ1815Diels-Alder2.jpg]]

We can see that only orbitals of the same symmetry can interact and have non-zero integrals. This means only fully symmetric or fully antisymmetric combinations are allowed.

The actual, calculated MOs are depicted here:

{| class="wikitable"
!MO label
!MOs
!Corresponding diagram
|-
|LUMO
|[[File:SJ1815_DA_LUMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw.jpg|150px]]
|-
|HOMO
|[[File:SJ1815_DA_HOMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw1.jpg|150px]]
|-
|HOMO-1
|[[File:SJ1815_DA_HOMO-1.png|150px]]
|[[File:SJ1815_DA_HOMO-1chemdraw.jpg|150px]]
|-
|HOMO-2
|[[File:SJ1815_DA_HOMO-2.png|150px]]
|[[File:SJ1815_DA_HOMO-2chemdraw.jpg|150px]]
|-
|HOMO-3
|[[File:SJ1815_DA_HOMO-3.png|150px]]
|[[File:SJ1815_DA_HOMO-3chemdraw.jpg|150px]]
|}

<b>The transition state</b>

[[File:SJ1815 DIELS-ALDER TS10.LOG]]

[[File:TS_DA_SJ1815.gif|thumb|none|alt=A depiction of the transition state|A depiction of the transition state (click to animate)]]

<jmol><jmolApplet><size>200</size><script>frame 15; vibration 2;rotate x -20; </script><uploadedFileContents>SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>

We can see that this is a transition state as it has a vibration at -948.72 cm<sup>-1</sup> in the log file.

Two IRC calculations were run, as the first only showed progression from products to reactants, even though the graph showed entire reaction coordinates.

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ1815_DA_IRC1.jpg|caption=The IRC path going backwards in the reaction]]
|[[File:SJ1815_DA_IRC2.jpg|caption=The IRC path going forwards in the reaction]]
|-
|'''IRC LOG files'''
|[[File:SJ1815 DIELS-ALDER IRC.LOG]]
|[[File:SJ1815_DIELS_ALDERIRCFORWARDS.LOG]]
|-
|'''IRC animations'''
|[[File:SJ1815_TS_IRC_DA.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|[[File:SJ1815_TS_IRC_DAforwards.gif|caption=The IRC path going forwards in the reaction (click to animate)]]
|}

The IRC shows synchronous bond formation between cis-butadiene and ethene.

<h2>Exercise 2- Reaction of Cyclohexa-1,3-diene and 1,3-Dioxole ([4+2] cycloaddition)</h2>
[[File:SJ18151,3-dioxole endo and exo.jpg|500px]]

{| class="wikitable"
!
!Dioxole
!Cyclohexa-1,3-diene
!Endo product
!Exo product
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 DIOXOLEPM6OPT+FREQ.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG </uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:SJ1815 DIOXOLEPM6OPT+FREQ.LOG]]
|[[File:SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG]]
|[[File:SJ1815_OPT+FREQPM6_2NDPRODUCT.LOG]]
|[[File:SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG]]
|-
|'''B3LYP'''
|[[File:DIOXOLEB3LYPOPT+FREQ_SJ1815(1).LOG]]
|[[File:SJ1815_CYCLOHEXADIENEB3LYPOPT+FREQ(1).LOG]]
|[[File:SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG]]
|[[File:SJ1815_B3LYP1STPRODUCT.LOG]]
|}

<h3>Thermochemistry</h3>

{|class= "wikitable"
!
!Energy
!Energy difference from Reactants
|-
|'''1,3-dioxole'''
||-267.068138 Hartrees/particle
|X
|-
|'''Cyclohexa-1,3-diene'''
||-233.321307 Hartrees/particle
|X
|-
|'''Total Reactants'''
||-500.389175 Hartrees/particle
|X
|-
|'''Exo TS'''
||-500.329165 Hartrees/particle
||+0.06001 Hartrees/particle = +157.556255 kJ/mol
|-
|'''Exo Product'''
||-500.418691 Hartrees/particle
||-0.029516 Hartree/particle = -77.494258.8973 kJ/mol
|-
|'''Endo TS'''
||-500.332149 Hartrees/particle
||+0.057026 Hartrees/particle = +149.7218 kJ/mol
|-
|'''Endo Product'''
||-500.417315 Hartrees/particle
||-0.02814 Hartrees/particle = -73.88157 kJ/mol
|-
|}

[[File:SJ1815DioxoleEnergydiagram.jpg]]

The thermodynamic product is therefore the exo product (the endo product has a higher energy due to steric clash within the molecule) while the kinetic product is the endo product, as the transition state is lower in energy, due to the fact that secondary orbital interactions are greater for the endo transition state.

<h4>MO diagrams</h4>

<b>Endo</b>

[[File:Diels-AlderdioxoleSJ1815exo1.jpg]]

<b>Exo</b>

[[File:Diels-AlderdioxoleSJ1815endo1.jpg]]

It can't be obtained directly from these MO diagrams as to whether the reaction proceeds via normal or inverse electron demand, as all optimisations were done on different potential energy surfaces. We can, however, say it is likely to be inverse electron demand due to the oxygen atoms of 1,3-dioxole donating electron density into the dienophile C=C.

<h3> The Transition State</h3>

The transition state for this reaction is depicted below, optimised to the B3LYP level.

<b>Endo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815EndoTSvibration.gif]]

[[File:SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG]]

Vibration occurs at -523.01cm<sup>-1</sup>.

<b>Exo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>2NDPRODUCTB3LYPTS_SJ1815.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:2NDPRODUCTB3LYPTS_SJ1815.LOG]]

[[File:ExoTSvibrationSJ1815.gif]]

Vibration occurs at -528.84cm<sup>-1</sup>.

<h4>Molecular orbitals</h4>

<b>Exo HOMO:</b>

[[File:SJ1815HOMO calledEndo product.jpg]]

Energy: -0.19052 Hartrees/particle

<b>Exo LUMO</b>

[[File:Sj1815LUMO_calledEndo_product.jpg]]

Energy:-0.00462 Hartrees/particle

<b>Endo HOMO</b>

[[File:SJ1815HOMO_TS_2nd_product.jpg]]

Energy: -0.18560 Hartrees/particle

<b>Endo LUMO</b>

[[File:SJ1815LUMO_TS_2nd_product.jpg]]

Energy:-0.00699 Hartrees/particle

There is obvious, visible secondary orbital interaction between orbitals on the oxygen atoms and those on the cyclohexa-1,3-diene's cis-butadiene fragment. This lowers the endo transition state's energy, yet both exo and endo benefit from these interactions (the overlap is just greater for the endo transition state).

<h2>Exercise 3-Diels-Alder ([4+2]) vs Cheleotropic ([4+1])</h2>
[[File:Diels-Alder SO2.jpg|500px]]

[[File:SJ1815Cheleotropic SO2 (1).jpg|500px]]

[[File:SJ1815Diels-Alder_SO2_(1)(endo).jpg|500px]]

[[File:2ndC=C-C=C_Diels-Alder_SJ1815.jpg|500px]]

{| class="wikitable"
!
!Cheleotropic
!Outer fragment Endo
!Inner fragment Endo
!Outer fragment Exo
!Inner fragment Exo
|-
|'''Products'''
|Cheleo stuff needed
|<jmol><jmolApplet><uploadedFileContents>SJ1815OUTERC=CPRODUCTENDO.LOG </uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815OUTERC=CPRODUCTENDO.LOG]]
|<jmol><jmolApplet><uploadedFileContents>DA1STotherC=CSJ1815PRODUCT(Exo).LOG </uploadedFileContents></jmolApplet></jmol>

[[File:DA1STotherC=CSJ1815PRODUCT(Exo).LOG]] (This has, in fact, been named incorrectly and is endo, as stated in the table).
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG]]
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG</uploadedFileContents></jmolApplet></jmol>
[[File:SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).
|-
|'''Transition states'''
|[[File:SJ1815_PM6CHELEOTS3.LOG]]

[[File:SJ1815_PM6CheleoTS3.gif]]

Vibration occurs at -484.77cm<sup>-1</sup>.
|[[File:DA2NDTSFROMFROZENSJ1815(endo)(1stC=C).LOG]]

[[File:SJ1815EndoTSfromfrozen(1stC=C).gif]]

Vibration occurs at -333.62cm<sup>-1</sup>.
|[[File:SJ1815EXODA2NDC=C-C=CTS(3).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:Exo_TS_Sj1815_innerC-C(real_exo).gif]]

Vibration occurs at -453.52cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(1stC=C)(exo).LOG]]

[[File:SJ1815_SO2_DA_TS_PM6.gif]]

Vibration occurs at -351.55cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(2NDC=C)(ENDO)(REALPM6).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:SJ1815_endoDAinnerC-CTS(real_endo).gif]]

Vibration occurs at -482.80cm<sup>-1</sup>.
|-
|'''IRC graphs'''
|[[File:SJ1815_Cheleo_IRC.jpg]]
|[[File:DA2ndTSfromfrozenSJ1815Endo(1stC=C).jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|[[File:SJ1815_IRCexo1stC=C.jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|-
|'''IRC animations'''
|[[File:SJ1815_Cheleo_Both_IRCPM6.gif]]

[[File:SJ1815_CHELEO_BOTH_IRCPM6.LOG]]
|[[File:SJ1815_endoIRC1stC=C.gif]]

[[File:DA2NDTSFROMFROZENSJ1815(ENDO)(1STC=C)IRC.LOG]]
|[[File:SJ1815otherC=CExoIRC.gif]]

[[File:DA2NDOTHERC=CSJ1815FROZENIRC.LOG]]
|[[File:SJ1815_outerC=CEndoIRC.gif]]

[[File:SJ1815_DA_1ST_SO2_IRCPM6(exo)(1stC=C).LOG]]

|[[File:SJ1815_innerC-C_endoDAIRC.gif]]

[[File:SJ1815INNERC=C-C=CENDOIRCPM6.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

|}

Xylylene is highly unstable as the bonding changes from 4 distinct double bonds to an aromatic ring and 2 single bonds pointing out of the ring. Due to the stability of the aromatic ring, xylylene may form a 4 membered ring to establish aromaticity or may polymerise.

<h4> Thermochemistry</h4>

[[File:SJ1815_Ex3Energydiagram.jpg]]

<h5>Outer fragment thermochemistry</h5>

<b>Cheleotropic</b>

<b>Reaction barrier</b>= +0.036864 Hartrees/particle or +96.786432 kJ/mol

<b>Reaction energy</b>= -0.062913 Hartrees/particle or -163.2877215 kJ/mol

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.028369 Hartrees/particle or +74.4828095 kJ/mol

<b>Reaction energy</b>= -0.040484 Hartrees/particle or -106.290742 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.029887 Hartrees/particle or +78.4683185 kJ/mol

<b>Reaction energy</b>= -0.040735 Hartrees/particle or -106.9497425 kJ/mol

The thermodynamic product is the cheleotropic product (it's lowest in energy) and the kinetic product is the endo product (the transition state is lowest in energy).

<h5>Inner fragment thermochemistry</h5>

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.042864 Hartrees/particle or +112.539432 kJ/mol

<b>Reaction energy</b>= +0.005114 Hartrees/particle or +13.426807 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.039882 Hartrees/particle or +104.710191 kJ/mol

<b>Reaction energy</b>= +0.003415 Hartrees/particle or 8.9660825 kJ/mol

Attack at the inner cis-butadiene fragment is disfavoured and doesn't occur.

<h2> Exercise 4- the ring opening of dimethyl (1R,2S)-cyclobut-3-ene-1,2-dicarboxylate</h2>

[[File:SJ1815ringopening.jpg]]

The ring opening of a 4-membered ring is only thermally allowed if the transition state is a Möbius transition state (that is, the 2 ends of the ring are conrotatory and twist in the same sense).

This can be seen when you look at the IRC for the reaction

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ18152+2IRC.jpg]]
|-
|'''IRC LOG files'''
|[[File:SJ18152+2TS4IRC.LOG]]
|-
|'''IRC animations'''
|[[File:SJ18152+2IRC.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|}

<h3>The transition state</h3>

[[File:SJ18152+2TSvib.gif]]

[[File:SJ18152+2TS4.LOG]]

This vibration occurs at -696.41cm<sup>-1</sup>. This negative vibration confirms the fact that this is a transition state.

<h2>References</h2>
<references>
<ref name="HammondPost">https://chem.libretexts.org/Reference/Organic_Chemistry_Glossary/Hammond%E2%80%99s_Postulate accessed on 8/11/2017 </ref>
<ref name="Bearparklecture"> Michael J Bearpark, 2017, <i>Calculating Molecular Geometries</i>, Lecture, Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Imperial College London, 6th November 2017 </ref>
<ref name="C-C"> Stark J.G., Wallace H.G. in <i>Chemistry Data Book</i> ed. Hodder Education, Hodder Education, 2nd edn, 1982, ch.19, pp. 27 </ref>
<ref name="C=C"> http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html accessed on 5/2/2018 </ref>
<ref name="PE surface">https://www.nrl.navy.mil/mstd/branches/6390/surfaces-and-interfaces accessed on 6/2/2018</ref>
<ref name="Slater">adapted from F. Jensen in <i>Introduction to Computational Chemistry </i> ed. Wiley, Wiley, Indianapolis, 1st edn., 1999, ch. 5. Adaptation obtained from https://lcbc.epfl.ch/files/content/users/232236/files/lecture_2016_2.pdf accessed on 12/2/2018</ref>
<ref name="PM6Gauss">http://gaussian.com/semiempirical/ accessed on 8/2/2108 </ref>
<ref name="DFTGauss">http://gaussian.com/dft/ accessed on 8/2/2018 </ref>
<ref name="DensityGauss">http://gaussian.com/basissets/?tabid=2 accessed on 8/2/2018</ref>
<ref name= "CvdW">https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf accessed on 11/2/2018 </ref>
<ref name="Basis"> A. Szabo, N. Oatlands in <i>Modern Quantum Chemistry </i> ed. Dover Publications Inc., Dover Publications Inc., Mineola, 1st edn., 1996, ch. 3, pp. 156 </ref>
</references>

Rep:SJ1815 Transition States

2018-02-12T13:36:15Z

Sj1815:

<h1>Investigating Transition States of Various Pericyclic Reaction</h1>
<h2>Introduction</h2>
<h3>Transition States: What do we mean?</h3>
Transition states are energy maxima along the path of a reaction and the dynamic bottleneck through which a reaction must proceed. Real energy profiles are dependent on multiple variables and you can move the reactants along the energy profile diagram in any direction, so you can encounter many maxima. However, only the one that occurs on your reaction pathway is considered a transition state. To put this in another way, I could take a flask of but-1,3-diene and ethene and expect a Diels-Alder reaction to occur. The transition state would be somewhere where the C-C bonds are being made from the C=Cs in the substrates. I could, given enough energy, stretch one of the C-C bonds to the moon (admittedly, probably breaking it in the process) and you'd have an energy maximum but it wouldn't be a transition state as it isn't part of the reaction in question.
Normally for a C-C bond forming process, we take the transition state to be somewhere between the van der Waals radii of the 2 atoms and the C-C bond length.

<h3>Locating a transition state</h3>
<h4>Use Hammond's Postulate</h4>
Take a guess at where the Transition State is and optimise using Gaussian. Use Hammond's postulate for where to guess. This is fast, but unreliable, as you have to be a very good guesser.

<b>N.B. Hammond's Postulate: 'The structure of the transition states resembles either the reactants or products (whichever is closest in energy)'</b><ref name="HammondPost" />

For C-C bond forming reactions, a guess of 2.2 for the bond length is a good place to start.

To actually run the job, use Opt+Freq (geometry optimisation via 'solving' the Schrödinger equation, which is ĤΨ=EΨ, and then moving along in small steps of energy, scaled using the second derivative d<sup>2</sup>E/dq<sup>2</sup>, where q is the reaction coordinate and frequency calculation using k=d<sup>2</sup>E/dq<sup>2</sup> and [[File:Spring frequency1.png|100px]]<ref name="Bearparklecture" />

The computer uses variational theorem to run calculations and solve the Schrödinger equation. Variational theorem takes a guess at the wavefunction of a system and then minimises the energy. This means that it hits the potential energy surface after a number of iterations. Depending on where it hits, the optimised .log file can look like a range of different things. A potential energy surface has a lot of local minima- it's 'bumpy'. If the guess wavefunction hits any of these bumps, Gaussview may tell you that it's found a transition state when it hasn't. This is why we need to analyse the results by checking the imaginary vibration and seeing if it matches with our idea of what 'going towards the products' looks like.

<table class="image">
<tr><td>[[File:PE_surface_SJ1815.gif]]</td></tr>
<tr><td class="caption"><i><span style="color:gray">Figure 1: A depiction of a 3D potential energy surface taken from reference 3 <ref name="PE surface"></ref>. We can only represent energy surfaces in 3D, yet they actually have many more dimensions than this (there are 3N-6 dimensions to consider, where N is the number of atoms in the molecule).</span></i></td></tr>
</table>

One approximation to make calculations easier is that we assume that molecular orbitals can be constructed from a linear combination of atomic orbitals. These all have different weightings called <b> orbital coefficients</b>. The wavefunction can therefore be broken down into <math>|\psi\rangle</math>=Σ<sup>N</sup><sub>i</sub>c<sub>i</sub><math>|\ \phi_i\rangle</math>

As <math>\langle\psi|</math>H<math>|\psi\rangle</math>=E<math>\psi</math>, we then have Σ<sup>N</sup><sub>m</sub>Σ<sup>N</sup><sub>n</sub>c<sub>m</sub><math>\langle\phi_m|</math>H<math>|\phi_n\rangle</math>c<sub>n</sub>

This can be written as a set of matrices with the first being a 1xn matrix of the c<sub>n</sub> coefficients, then a Hessian matrix of all of the different atomic orbital integrals and then an mx1 matrix of the c<sub>m</sub> coefficients or, more succinctly, c<sup>T</sup>Hc, where H is the Hessian here. This equals the energy and from this you can get the eigenvalue equation of Hc=Ec, which the computer solves

Each eigenvector of the eigenvalue equation yields 1 molecular orbital.

<b> What are the individual atomic wavefunctions?</b>

These represent electron densityand are best represented by Slater functions.

Slater functions have the form <math>R(r) = N r^{n-1} e^{-\zeta r}\,</math><ref name="Slater"></ref>

This, however, is too computationally costly to solve, so we use an approximation by using Gaussians.

Gaussian functions have the form <math>ae^{-ar^2}</math> An example of thhe form of one of these is shown below.

[[File:SJ1815_Gaussian.jpg]]

As these don't represent the orbitals as well as Slater functions, several of them are often summed to better represent these orbitals. This sum adds computational complexity, as there are more integrals to compute, yet this is still faster than using Slater functions. Combining three Gaussians gives a basis set of STO-3G (<b>S</b>later-<b>T</b>ype <b>O</b>rbitals-<b>3</b> functions <b>G</b>aussians)<ref name="Basis"></ref>.

<h2>Optimisation methods</h2>

PM6 is a semi-empirical optimisation method. It takes into account the valence electrons for the species and then solves the integrals in relation to them, employing code already on the Gaussian programme <ref name="PM6Gauss"></ref>. It also uses fixed numbers as approximations for the integrals in the Hessian. This makes it much faster at doing calculations, yet more imprecise in the answers obtained.

B3LYP is a DFT (density functional theory) method, which takes advantage of density fitting (expansion of atomic density rather than computing all of the 2-electron integrals individually)<ref name="DensityGauss"></ref>. B3LYP differs from other DFT calculations insofar as it optimises the nuclear wavefunctions, then adds on some electron interactions to see how things change (most DFT calculations just use the nuclei) <ref name="DFTGauss"></ref>. However, these are not easily calculated by Gaussian, causing approximations to be formed.

<h2>Tutorial</h2>

<h3>Tutorial 1- Cope rearrangement of hexa-1,5-diene</h3>
[[File:Cope_rearrangementSJ1815.png|500px]]

The first method for finding a transition state is to guess and then optimise using Opt+Freq, Optimise to a TS (Berny) and calculate the force constants once. There should be 1 negative frequency at the output, which confirms that a transition state has been found and animation of said transition state should make it look like you go from reactants to products.
There are 2 different transition states (boat and chair), both of which have been accounted for below
{| class="wikitable"
!
!Boat
!Chair
|-
|
|[[File:SJ1815Boat.jpg|100px]]
|[[File:SJ1815Chair.jpg|100px]]
|-
|'''PM6'''
|[[File:SJ1815TRIAL COPE TS 2 RADICALS PM6.LOG]]
|[[File:SJ1815TRIAL COPE TS RADICAL CHAIRTS.LOG]]
|-
|'''B3LYP'''
|[[File:SJ1815COPEBOATTSB3LYP.LOG]]
|[[File:SJ1815COPECHAIRTSB3LYP.LOG]]
|}

<b>IRC</b>

[[File:SJ1815 BOAT COPE TS IRC PM6.LOG]]

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815 BOAT COPE TS IRC PM6.LOG </uploadedFileContents></jmolApplet></jmol>
<h3>Tutorial 2- Dimerisation of Cyclopentadiene</h3>
[[File:SJ1815Cyclopentadiene dimerisation.jpg|500px]]

The second method relies on generating a guess transition state, freezing the atoms in space and then uses method 1 to find exactly where the transition state lies. The keyword opt=modredundant will appear in the submission window, but submit the job as normal, optimising to a minimum. Then, unfreeze the bonds and optimise to a TS, as in method 1. To distinguish between endo and exo conformers, run IRC calculations.

<b>Optimisation:</b>

<b>PM6:</b> [[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS OPT+FREQ PM6.LOG]]

<b>B3LYP:</b>[[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS B3LYP.LOG]]

<h3>Tutorial 3-Xylylene SO2 Diels-Alder</h3>
The third method uses the reactants or products, alters the bond lengths and/or angles (normally of those involved in the reaction, but can be of neighbouring atoms too) and then runs the same way as method 2.

<b>Opt+Freq of Diels-Alder</b>

[[File:SJ1815_SO2_DIELS-ALDER_PM6_MIN.LOG]]

<h2>Exercise 1- Cis-butadiene and ethene Diels-Alder ([4+2]-cycloaddition)</h2>
[[File:Diels-Alder cyclohexene product.jpg|500px]]

This reaction is often seen as the classic Diels-Alder reaction, due to the fact that the diene and dienophile are as simple as they can be. However, this reaction is purely hypothetical as neither fragment is particularly electron rich or poor (we need this disparity in energies for both normal electron demand and inverse electron demand Diels-Alder reactions).

<h3>Optimisation</h3>

{| class="wikitable"
!
! style="background: #8b0c0c; color: white;" | Butadiene
! style="background: #8b0c0c; color: white;" | Ethene
! style="background: #8b0c0c; color: white;" | Cyclohexene
! style="background: #8b0c0c; color: white;"|Transition state
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> BUTADIENE_SJ1815.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 ETHENE_OPT+FREQ_PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXENE PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:BUTADIENE_SJ1815.LOG]]
|[[File:SJ1815 ETHENE_OPT+FREQ_PM6.LOG]]
|[[File:SJ1815 CYCLOHEXENE PM6.LOG]]
|[[File:SJ1815_DIELS-ALDER_TS10.LOG]]
|-
|'''C-C bond Lengths/Å'''
|1.33343
|1.32742
|1.33698
|1.37977 (original C=C of butadiene)
|-
|
|1.47077
|X
|1.50068
|1.41111 (original C-C of butadiene)
|-
|
|1.33343
|X
|1.53703
|1.37977 (original C=C of butadiene)
|-
|
|X
|X
|1.53491
|1.38176 (original C=C of ethene)
|-
|
|X
|X
|1.53736
|X
|-
|
|X
|X
|1.50077
|X
|}
The bond length for a C-C bond is 1.54Å <ref name="C-C"></ref> while the C=C bond length is 1.34Å <ref name="C=C"></ref>
This matches fairly well with the bond lengths in the table above, with the transition state having bond lengths partway between the two lengths. The van der Waals radius of carbon is 1.77Å <ref name="CvdW"></ref> and all C-C lengths are closer than this, so they are interacting (the van der Waals radius tells us how close atoms have to be for some interaction to take place).

<h3>MO analysis</h3>

The MO diagram for the reaction is as depicted below

[[File:SJ1815Diels-Alder2.jpg]]

We can see that only orbitals of the same symmetry can interact and have non-zero integrals. This means only fully symmetric or fully antisymmetric combinations are allowed.

The actual, calculated MOs are depicted here:

{| class="wikitable"
!MO label
!MOs
!Corresponding diagram
|-
|LUMO
|[[File:SJ1815_DA_LUMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw.jpg|150px]]
|-
|HOMO
|[[File:SJ1815_DA_HOMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw1.jpg|150px]]
|-
|HOMO-1
|[[File:SJ1815_DA_HOMO-1.png|150px]]
|[[File:SJ1815_DA_HOMO-1chemdraw.jpg|150px]]
|-
|HOMO-2
|[[File:SJ1815_DA_HOMO-2.png|150px]]
|[[File:SJ1815_DA_HOMO-2chemdraw.jpg|150px]]
|-
|HOMO-3
|[[File:SJ1815_DA_HOMO-3.png|150px]]
|[[File:SJ1815_DA_HOMO-3chemdraw.jpg|150px]]
|}

<b>The transition state</b>

[[File:SJ1815 DIELS-ALDER TS10.LOG]]

[[File:TS_DA_SJ1815.gif|thumb|none|alt=A depiction of the transition state|A depiction of the transition state (click to animate)]]

<jmol><jmolApplet><size>200</size><script>frame 15; vibration 2;rotate x -20; </script><uploadedFileContents>SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>

We can see that this is a transition state as it has a vibration at -948.72 cm<sup>-1</sup> in the log file.

Two IRC calculations were run, as the first only showed progression from products to reactants, even though the graph showed entire reaction coordinates.

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ1815_DA_IRC1.jpg|caption=The IRC path going backwards in the reaction]]
|[[File:SJ1815_DA_IRC2.jpg|caption=The IRC path going forwards in the reaction]]
|-
|'''IRC LOG files'''
|[[File:SJ1815 DIELS-ALDER IRC.LOG]]
|[[File:SJ1815_DIELS_ALDERIRCFORWARDS.LOG]]
|-
|'''IRC animations'''
|[[File:SJ1815_TS_IRC_DA.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|[[File:SJ1815_TS_IRC_DAforwards.gif|caption=The IRC path going forwards in the reaction (click to animate)]]
|}

The IRC shows synchronous bond formation between cis-butadiene and ethene.

<h2>Exercise 2- Reaction of Cyclohexa-1,3-diene and 1,3-Dioxole ([4+2] cycloaddition)</h2>
[[File:SJ18151,3-dioxole endo and exo.jpg|500px]]

{| class="wikitable"
!
!Dioxole
!Cyclohexa-1,3-diene
!Endo product
!Exo product
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 DIOXOLEPM6OPT+FREQ.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG </uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:SJ1815 DIOXOLEPM6OPT+FREQ.LOG]]
|[[File:SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG]]
|[[File:SJ1815_OPT+FREQPM6_2NDPRODUCT.LOG]]
|[[File:SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG]]
|-
|'''B3LYP'''
|[[File:DIOXOLEB3LYPOPT+FREQ_SJ1815(1).LOG]]
|[[File:SJ1815_CYCLOHEXADIENEB3LYPOPT+FREQ(1).LOG]]
|[[File:SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG]]
|[[File:SJ1815_B3LYP1STPRODUCT.LOG]]
|}

<h3>Thermochemistry</h3>

{|class= "wikitable"
!
!Energy
!Energy difference from Reactants
|-
|'''1,3-dioxole'''
||-267.068138 Hartrees/particle
|X
|-
|'''Cyclohexa-1,3-diene'''
||-233.321307 Hartrees/particle
|X
|-
|'''Total Reactants'''
||-500.389175 Hartrees/particle
|X
|-
|'''Exo TS'''
||-500.329165 Hartrees/particle
||+0.06001 Hartrees/particle = +157.556255 kJ/mol
|-
|'''Exo Product'''
||-500.418691 Hartrees/particle
||-0.029516 Hartree/particle = -77.494258.8973 kJ/mol
|-
|'''Endo TS'''
||-500.332149 Hartrees/particle
||+0.057026 Hartrees/particle = +149.7218 kJ/mol
|-
|'''Endo Product'''
||-500.417315 Hartrees/particle
||-0.02814 Hartrees/particle = -73.88157 kJ/mol
|-
|}

[[File:SJ1815DioxoleEnergydiagram.jpg]]

The thermodynamic product is therefore the exo product (the endo product has a higher energy due to steric clash within the molecule) while the kinetic product is the endo product, as the transition state is lower in energy, due to the fact that secondary orbital interactions are greater for the endo transition state.

<h4>MO diagrams</h4>

<b>Endo</b>

[[File:Diels-AlderdioxoleSJ1815exo1.jpg]]

<b>Exo</b>

[[File:Diels-AlderdioxoleSJ1815endo1.jpg]]

It can't be obtained directly from these MO diagrams as to whether the reaction proceeds via normal or inverse electron demand, as all optimisations were done on different potential energy surfaces. We can, however, say it is likely to be inverse electron demand due to the oxygen atoms of 1,3-dioxole donating electron density into the dienophile C=C.

<h3> The Transition State</h3>

The transition state for this reaction is depicted below, optimised to the B3LYP level.

<b>Endo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815EndoTSvibration.gif]]

[[File:SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG]]

Vibration occurs at -523.01cm<sup>-1</sup>.

<b>Exo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>2NDPRODUCTB3LYPTS_SJ1815.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:2NDPRODUCTB3LYPTS_SJ1815.LOG]]

[[File:ExoTSvibrationSJ1815.gif]]

Vibration occurs at -528.84cm<sup>-1</sup>.

<h4>Molecular orbitals</h4>

<b>Exo HOMO:</b>

[[File:SJ1815HOMO calledEndo product.jpg]]

Energy: -0.19052 Hartrees/particle

<b>Exo LUMO</b>

[[File:Sj1815LUMO_calledEndo_product.jpg]]

Energy:-0.00462 Hartrees/particle

<b>Endo HOMO</b>

[[File:SJ1815HOMO_TS_2nd_product.jpg]]

Energy: -0.18560 Hartrees/particle

<b>Endo LUMO</b>

[[File:SJ1815LUMO_TS_2nd_product.jpg]]

Energy:-0.00699 Hartrees/particle

There is obvious, visible secondary orbital interaction between orbitals on the oxygen atoms and those on the cyclohexa-1,3-diene's cis-butadiene fragment. This lowers the endo transition state's energy, yet both exo and endo benefit from these interactions (the overlap is just greater for the endo transition state).

<h2>Exercise 3-Diels-Alder ([4+2]) vs Cheleotropic ([4+1])</h2>
[[File:Diels-Alder SO2.jpg|500px]]

[[File:SJ1815Cheleotropic SO2 (1).jpg|500px]]

[[File:SJ1815Diels-Alder_SO2_(1)(endo).jpg|500px]]

[[File:2ndC=C-C=C_Diels-Alder_SJ1815.jpg|500px]]

{| class="wikitable"
!
!Cheleotropic
!Outer fragment Endo
!Inner fragment Endo
!Outer fragment Exo
!Inner fragment Exo
|-
|'''Products'''
|Cheleo stuff needed
|<jmol><jmolApplet><uploadedFileContents>SJ1815OUTERC=CPRODUCTENDO.LOG </uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815OUTERC=CPRODUCTENDO.LOG]]
|<jmol><jmolApplet><uploadedFileContents>DA1STotherC=CSJ1815PRODUCT(Exo).LOG </uploadedFileContents></jmolApplet></jmol>

[[File:DA1STotherC=CSJ1815PRODUCT(Exo).LOG]] (This has, in fact, been named incorrectly and is endo, as stated in the table).
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG]]
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG</uploadedFileContents></jmolApplet></jmol>
[[File:SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).
|-
|'''Transition states'''
|Cheleo stuff needed
|[[File:DA2NDTSFROMFROZENSJ1815(endo)(1stC=C).LOG]]

[[File:SJ1815EndoTSfromfrozen(1stC=C).gif]]

Vibration occurs at -333.62cm<sup>-1</sup>.
|[[File:SJ1815EXODA2NDC=C-C=CTS(3).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:Exo_TS_Sj1815_innerC-C(real_exo).gif]]

Vibration occurs at -453.52cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(1stC=C)(exo).LOG]]

[[File:SJ1815_SO2_DA_TS_PM6.gif]]

Vibration occurs at -351.55cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(2NDC=C)(ENDO)(REALPM6).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:SJ1815_endoDAinnerC-CTS(real_endo).gif]]

Vibration occurs at -482.80cm<sup>-1</sup>.
|-
|'''IRC graphs'''
|[[File:SJ1815_Cheleo_IRC.jpg]]
|[[File:DA2ndTSfromfrozenSJ1815Endo(1stC=C).jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|[[File:SJ1815_IRCexo1stC=C.jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|-
|'''IRC animations'''
|[[File:SJ1815_Cheleo_Both_IRCPM6.gif]]

[[File:SJ1815_CHELEO_BOTH_IRCPM6.LOG]]
|[[File:SJ1815_endoIRC1stC=C.gif]]

[[File:DA2NDTSFROMFROZENSJ1815(ENDO)(1STC=C)IRC.LOG]]
|[[File:SJ1815otherC=CExoIRC.gif]]

[[File:DA2NDOTHERC=CSJ1815FROZENIRC.LOG]]
|[[File:SJ1815_outerC=CEndoIRC.gif]]

[[File:SJ1815_DA_1ST_SO2_IRCPM6(exo)(1stC=C).LOG]]

|[[File:SJ1815_innerC-C_endoDAIRC.gif]]

[[File:SJ1815INNERC=C-C=CENDOIRCPM6.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

|}

Xylylene is highly unstable as the bonding changes from 4 distinct double bonds to an aromatic ring and 2 single bonds pointing out of the ring. Due to the stability of the aromatic ring, xylylene may form a 4 membered ring to establish aromaticity or may polymerise.

<h4> Thermochemistry</h4>

[[File:SJ1815_Ex3Energydiagram.jpg]]

<h5>Outer fragment thermochemistry</h5>

<b>Cheleotropic</b>

<b>Reaction barrier</b>= +0.036864 Hartrees/particle or +96.786432 kJ/mol

<b>Reaction energy</b>= -0.062913 Hartrees/particle or -163.2877215 kJ/mol

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.028369 Hartrees/particle or +74.4828095 kJ/mol

<b>Reaction energy</b>= -0.040484 Hartrees/particle or -106.290742 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.029887 Hartrees/particle or +78.4683185 kJ/mol

<b>Reaction energy</b>= -0.040735 Hartrees/particle or -106.9497425 kJ/mol

The thermodynamic product is the cheleotropic product (it's lowest in energy) and the kinetic product is the endo product (the transition state is lowest in energy).

<h5>Inner fragment thermochemistry</h5>

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.042864 Hartrees/particle or +112.539432 kJ/mol

<b>Reaction energy</b>= +0.005114 Hartrees/particle or +13.426807 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.039882 Hartrees/particle or +104.710191 kJ/mol

<b>Reaction energy</b>= +0.003415 Hartrees/particle or 8.9660825 kJ/mol

Attack at the inner cis-butadiene fragment is disfavoured and doesn't occur.

<h2> Exercise 4- the ring opening of dimethyl (1R,2S)-cyclobut-3-ene-1,2-dicarboxylate</h2>

[[File:SJ1815ringopening.jpg]]

The ring opening of a 4-membered ring is only thermally allowed if the transition state is a Möbius transition state (that is, the 2 ends of the ring are conrotatory and twist in the same sense).

This can be seen when you look at the IRC for the reaction

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ18152+2IRC.jpg]]
|-
|'''IRC LOG files'''
|[[File:SJ18152+2TS4IRC.LOG]]
|-
|'''IRC animations'''
|[[File:SJ18152+2IRC.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|}

<h3>The transition state</h3>

[[File:SJ18152+2TSvib.gif]]

[[File:SJ18152+2TS4.LOG]]

This vibration occurs at -696.41cm<sup>-1</sup>. This negative vibration confirms the fact that this is a transition state.

<h2>References</h2>
<references>
<ref name="HammondPost">https://chem.libretexts.org/Reference/Organic_Chemistry_Glossary/Hammond%E2%80%99s_Postulate accessed on 8/11/2017 </ref>
<ref name="Bearparklecture"> Michael J Bearpark, 2017, <i>Calculating Molecular Geometries</i>, Lecture, Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Imperial College London, 6th November 2017 </ref>
<ref name="C-C"> Stark J.G., Wallace H.G. in <i>Chemistry Data Book</i> ed. Hodder Education, Hodder Education, 2nd edn, 1982, ch.19, pp. 27 </ref>
<ref name="C=C"> http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html accessed on 5/2/2018 </ref>
<ref name="PE surface">https://www.nrl.navy.mil/mstd/branches/6390/surfaces-and-interfaces accessed on 6/2/2018</ref>
<ref name="Slater">adapted from F. Jensen in <i>Introduction to Computational Chemistry </i> ed. Wiley, Wiley, Indianapolis, 1st edn., 1999, ch. 5. Adaptation obtained from https://lcbc.epfl.ch/files/content/users/232236/files/lecture_2016_2.pdf accessed on 12/2/2018</ref>
<ref name="PM6Gauss">http://gaussian.com/semiempirical/ accessed on 8/2/2108 </ref>
<ref name="DFTGauss">http://gaussian.com/dft/ accessed on 8/2/2018 </ref>
<ref name="DensityGauss">http://gaussian.com/basissets/?tabid=2 accessed on 8/2/2018</ref>
<ref name= "CvdW">https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf accessed on 11/2/2018 </ref>
<ref name="Basis"> A. Szabo, N. Oatlands in <i>Modern Quantum Chemistry </i> ed. Dover Publications Inc., Dover Publications Inc., Mineola, 1st edn., 1996, ch. 3, pp. 156 </ref>
</references>

Rep:SJ1815 Transition States

2018-02-12T13:32:59Z

Sj1815:

<h1>Investigating Transition States of Various Pericyclic Reaction</h1>
<h2>Introduction</h2>
<h3>Transition States: What do we mean?</h3>
Transition states are energy maxima along the path of a reaction and the dynamic bottleneck through which a reaction must proceed. Real energy profiles are dependent on multiple variables and you can move the reactants along the energy profile diagram in any direction, so you can encounter many maxima. However, only the one that occurs on your reaction pathway is considered a transition state. To put this in another way, I could take a flask of but-1,3-diene and ethene and expect a Diels-Alder reaction to occur. The transition state would be somewhere where the C-C bonds are being made from the C=Cs in the substrates. I could, given enough energy, stretch one of the C-C bonds to the moon (admittedly, probably breaking it in the process) and you'd have an energy maximum but it wouldn't be a transition state as it isn't part of the reaction in question.
Normally for a C-C bond forming process, we take the transition state to be somewhere between the van der Waals radii of the 2 atoms and the C-C bond length.

<h3>Locating a transition state</h3>
<h4>Use Hammond's Postulate</h4>
Take a guess at where the Transition State is and optimise using Gaussian. Use Hammond's postulate for where to guess. This is fast, but unreliable, as you have to be a very good guesser.

<b>N.B. Hammond's Postulate: 'The structure of the transition states resembles either the reactants or products (whichever is closest in energy)'</b><ref name="HammondPost" />

For C-C bond forming reactions, a guess of 2.2 for the bond length is a good place to start.

To actually run the job, use Opt+Freq (geometry optimisation via 'solving' the Schrödinger equation, which is ĤΨ=EΨ, and then moving along in small steps of energy, scaled using the second derivative d<sup>2</sup>E/dq<sup>2</sup>, where q is the reaction coordinate and frequency calculation using k=d<sup>2</sup>E/dq<sup>2</sup> and [[File:Spring frequency1.png|100px]]<ref name="Bearparklecture" />

The computer uses variational theorem to run calculations and solve the Schrödinger equation. Variational theorem takes a guess at the wavefunction of a system and then minimises the energy. This means that it hits the potential energy surface after a number of iterations. Depending on where it hits, the optimised .log file can look like a range of different things. A potential energy surface has a lot of local minima- it's 'bumpy'. If the guess wavefunction hits any of these bumps, Gaussview may tell you that it's found a transition state when it hasn't. This is why we need to analyse the results by checking the imaginary vibration and seeing if it matches with our idea of what 'going towards the products' looks like.

<table class="image">
<tr><td>[[File:PE_surface_SJ1815.gif]]</td></tr>
<tr><td class="caption"><i><span style="color:gray">Figure 1: A depiction of a 3D potential energy surface taken from reference 3 <ref name="PE surface"></ref>. We can only represent energy surfaces in 3D, yet they actually have many more dimensions than this (there are 3N-6 dimensions to consider, where N is the number of atoms in the molecule).</span></i></td></tr>
</table>

One approximation to make calculations easier is that we assume that molecular orbitals can be constructed from a linear combination of atomic orbitals. These all have different weightings called <b> orbital coefficients</b>. The wavefunction can therefore be broken down into <math>|\psi\rangle</math>=Σ<sup>N</sup><sub>i</sub>c<sub>i</sub><math>|\ \phi_i\rangle</math>

As <math>\langle\psi|</math>H<math>|\psi\rangle</math>=E<math>\psi</math>, we then have Σ<sup>N</sup><sub>m</sub>Σ<sup>N</sup><sub>n</sub>c<sub>m</sub><math>\langle\phi_m|</math>H<math>|\phi_n\rangle</math>c<sub>n</sub>

This can be written as a set of matrices with the first being a 1xn matrix of the c<sub>n</sub> coefficients, then a Hessian matrix of all of the different atomic orbital integrals and then an mx1 matrix of the c<sub>m</sub> coefficients or, more succinctly, c<sup>T</sup>Hc, where H is the Hessian here. This equals the energy and from this you can get the eigenvalue equation of Hc=Ec, which the computer solves

Each eigenvector of the eigenvalue equation yields 1 molecular orbital.

<b> What are the individual atomic wavefunctions?</b>

These represent electron densityand are best represented by Slater functions.

Slater functions have the form <math>R(r) = N r^{n-1} e^{-\zeta r}\,</math><ref name="Slater"></ref>

This, however, is too computationally costly to solve, so we use an approximation by using Gaussians.

Gaussian functions have the form <math>ae^{-ar^2}</math> An example of thhe form of one of these is shown below.

[[File:SJ1815_Gaussian.jpg]]

As these don't represent the orbitals as well as Slater functions, several of them are often summed to better represent these orbitals. This sum adds computational complexity, as there are more integrals to compute, yet this is still faster than using Slater functions. Combining three Gaussians gives a basis set of STO-3G (<b>S</b>later-<b>T</b>ype <b>O</b>rbitals-<b>3</b> functions <b>G</b>aussians)<ref name="Basis"></ref>.

<h2>Optimisation methods</h2>

PM6 is a semi-empirical optimisation method. It takes into account the valence electrons for the species and then solves the integrals in relation to them, employing code already on the Gaussian programme <ref name="PM6Gauss"></ref>. It also uses fixed numbers as approximations for the integrals in the Hessian. This makes it much faster at doing calculations, yet more imprecise in the answers obtained.

B3LYP is a DFT (density functional theory) method, which takes advantage of density fitting (expansion of atomic density rather than computing all of the 2-electron integrals individually)<ref name="DensityGauss"></ref>. B3LYP differs from other DFT calculations insofar as it optimises the nuclear wavefunctions, then adds on some electron interactions to see how things change (most DFT calculations just use the nuclei) <ref name="DFTGauss"></ref>. However, these are not easily calculated by Gaussian, causing approximations to be formed.

<h2>Tutorial</h2>

<h3>Tutorial 1- Cope rearrangement of hexa-1,5-diene</h3>
[[File:Cope_rearrangementSJ1815.png|500px]]

The first method for finding a transition state is to guess and then optimise using Opt+Freq, Optimise to a TS (Berny) and calculate the force constants once. There should be 1 negative frequency at the output, which confirms that a transition state has been found and animation of said transition state should make it look like you go from reactants to products.
There are 2 different transition states (boat and chair), both of which have been accounted for below
{| class="wikitable"
!
!Boat
!Chair
|-
|
|[[File:SJ1815Boat.jpg|100px]]
|[[File:SJ1815Chair.jpg|100px]]
|-
|'''PM6'''
|[[File:SJ1815TRIAL COPE TS 2 RADICALS PM6.LOG]]
|[[File:SJ1815TRIAL COPE TS RADICAL CHAIRTS.LOG]]
|-
|'''B3LYP'''
|[[File:SJ1815COPEBOATTSB3LYP.LOG]]
|[[File:SJ1815COPECHAIRTSB3LYP.LOG]]
|}

<b>IRC</b>

[[File:SJ1815 BOAT COPE TS IRC PM6.LOG]]

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815 BOAT COPE TS IRC PM6.LOG </uploadedFileContents></jmolApplet></jmol>
<h3>Tutorial 2- Dimerisation of Cyclopentadiene</h3>
[[File:SJ1815Cyclopentadiene dimerisation.jpg|500px]]

The second method relies on generating a guess transition state, freezing the atoms in space and then uses method 1 to find exactly where the transition state lies. The keyword opt=modredundant will appear in the submission window, but submit the job as normal, optimising to a minimum. Then, unfreeze the bonds and optimise to a TS, as in method 1. To distinguish between endo and exo conformers, run IRC calculations.

<b>Optimisation:</b>

<b>PM6:</b> [[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS OPT+FREQ PM6.LOG]]

<b>B3LYP:</b>[[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS B3LYP.LOG]]

<h3>Tutorial 3-Xylylene SO2 Diels-Alder</h3>
The third method uses the reactants or products, alters the bond lengths and/or angles (normally of those involved in the reaction, but can be of neighbouring atoms too) and then runs the same way as method 2.

<b>Opt+Freq of Diels-Alder</b>

[[File:SJ1815_SO2_DIELS-ALDER_PM6_MIN.LOG]]

<h2>Exercise 1- Cis-butadiene and ethene Diels-Alder ([4+2]-cycloaddition)</h2>
[[File:Diels-Alder cyclohexene product.jpg|500px]]

This reaction is often seen as the classic Diels-Alder reaction, due to the fact that the diene and dienophile are as simple as they can be. However, this reaction is purely hypothetical as neither fragment is particularly electron rich or poor (we need this disparity in energies for both normal electron demand and inverse electron demand Diels-Alder reactions).

<h3>Optimisation</h3>

{| class="wikitable"
!
! style="background: #8b0c0c; color: white;" | Butadiene
! style="background: #8b0c0c; color: white;" | Ethene
! style="background: #8b0c0c; color: white;" | Cyclohexene
! style="background: #8b0c0c; color: white;"|Transition state
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> BUTADIENE_SJ1815.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 ETHENE_OPT+FREQ_PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXENE PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:BUTADIENE_SJ1815.LOG]]
|[[File:SJ1815 ETHENE_OPT+FREQ_PM6.LOG]]
|[[File:SJ1815 CYCLOHEXENE PM6.LOG]]
|[[File:SJ1815_DIELS-ALDER_TS10.LOG]]
|-
|'''C-C bond Lengths/Å'''
|1.33343
|1.32742
|1.33698
|1.37977 (original C=C of butadiene)
|-
|
|1.47077
|X
|1.50068
|1.41111 (original C-C of butadiene)
|-
|
|1.33343
|X
|1.53703
|1.37977 (original C=C of butadiene)
|-
|
|X
|X
|1.53491
|1.38176 (original C=C of ethene)
|-
|
|X
|X
|1.53736
|X
|-
|
|X
|X
|1.50077
|X
|}
The bond length for a C-C bond is 1.54Å <ref name="C-C"></ref> while the C=C bond length is 1.34Å <ref name="C=C"></ref>
This matches fairly well with the bond lengths in the table above, with the transition state having bond lengths partway between the two lengths. The van der Waals radius of carbon is 1.77Å <ref name="CvdW"></ref> and all C-C lengths are closer than this, so they are interacting (the van der Waals radius tells us how close atoms have to be for some interaction to take place).

<h3>MO analysis</h3>

The MO diagram for the reaction is as depicted below

[[File:SJ1815Diels-Alder2.jpg]]

We can see that only orbitals of the same symmetry can interact and have non-zero integrals. This means only fully symmetric or fully antisymmetric combinations are allowed.

The actual, calculated MOs are depicted here:

{| class="wikitable"
!MO label
!MOs
!Corresponding diagram
|-
|LUMO
|[[File:SJ1815_DA_LUMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw.jpg|150px]]
|-
|HOMO
|[[File:SJ1815_DA_HOMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw1.jpg|150px]]
|-
|HOMO-1
|[[File:SJ1815_DA_HOMO-1.png|150px]]
|[[File:SJ1815_DA_HOMO-1chemdraw.jpg|150px]]
|-
|HOMO-2
|[[File:SJ1815_DA_HOMO-2.png|150px]]
|[[File:SJ1815_DA_HOMO-2chemdraw.jpg|150px]]
|-
|HOMO-3
|[[File:SJ1815_DA_HOMO-3.png|150px]]
|[[File:SJ1815_DA_HOMO-3chemdraw.jpg|150px]]
|}

<b>The transition state</b>

[[File:SJ1815 DIELS-ALDER TS10.LOG]]

[[File:TS_DA_SJ1815.gif|thumb|none|alt=A depiction of the transition state|A depiction of the transition state (click to animate)]]

<jmol><jmolApplet><size>200</size><script>frame 15; vibration 2;rotate x -20; </script><uploadedFileContents>SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>

We can see that this is a transition state as it has a vibration at -948.72 cm<sup>-1</sup> in the log file.

Two IRC calculations were run, as the first only showed progression from products to reactants, even though the graph showed entire reaction coordinates.

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ1815_DA_IRC1.jpg|caption=The IRC path going backwards in the reaction]]
|[[File:SJ1815_DA_IRC2.jpg|caption=The IRC path going forwards in the reaction]]
|-
|'''IRC LOG files'''
|[[File:SJ1815 DIELS-ALDER IRC.LOG]]
|[[File:SJ1815_DIELS_ALDERIRCFORWARDS.LOG]]
|-
|'''IRC animations'''
|[[File:SJ1815_TS_IRC_DA.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|[[File:SJ1815_TS_IRC_DAforwards.gif|caption=The IRC path going forwards in the reaction (click to animate)]]
|}

The IRC shows synchronous bond formation between cis-butadiene and ethene.

<h2>Exercise 2- Reaction of Cyclohexa-1,3-diene and 1,3-Dioxole ([4+2] cycloaddition)</h2>
[[File:SJ18151,3-dioxole endo and exo.jpg|500px]]

{| class="wikitable"
!
!Dioxole
!Cyclohexa-1,3-diene
!Endo product
!Exo product
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 DIOXOLEPM6OPT+FREQ.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG </uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:SJ1815 DIOXOLEPM6OPT+FREQ.LOG]]
|[[File:SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG]]
|[[File:SJ1815_OPT+FREQPM6_2NDPRODUCT.LOG]]
|[[File:SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG]]
|-
|'''B3LYP'''
|[[File:DIOXOLEB3LYPOPT+FREQ_SJ1815(1).LOG]]
|[[File:SJ1815_CYCLOHEXADIENEB3LYPOPT+FREQ(1).LOG]]
|[[File:SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG]]
|[[File:SJ1815_B3LYP1STPRODUCT.LOG]]
|}

<h3>Thermochemistry</h3>

{|class= "wikitable"
!
!Energy
!Energy difference from Reactants
|-
|'''1,3-dioxole'''
||-267.068138 Hartrees/particle
|X
|-
|'''Cyclohexa-1,3-diene'''
||-233.321307 Hartrees/particle
|X
|-
|'''Total Reactants'''
||-500.389175 Hartrees/particle
|X
|-
|'''Exo TS'''
||-500.329165 Hartrees/particle
||+0.06001 Hartrees/particle = +157.556255 kJ/mol
|-
|'''Exo Product'''
||-500.418691 Hartrees/particle
||-0.029516 Hartree/particle = -77.494258.8973 kJ/mol
|-
|'''Endo TS'''
||-500.332149 Hartrees/particle
||+0.057026 Hartrees/particle = +149.7218 kJ/mol
|-
|'''Endo Product'''
||-500.417315 Hartrees/particle
||-0.02814 Hartrees/particle = -73.88157 kJ/mol
|-
|}

[[File:SJ1815DioxoleEnergydiagram.jpg]]

The thermodynamic product is therefore the exo product (the endo product has a higher energy due to steric clash within the molecule) while the kinetic product is the endo product, as the transition state is lower in energy, due to the fact that secondary orbital interactions are greater for the endo transition state.

<h4>MO diagrams</h4>

<b>Endo</b>

[[File:Diels-AlderdioxoleSJ1815exo1.jpg]]

<b>Exo</b>

[[File:Diels-AlderdioxoleSJ1815endo1.jpg]]

It can't be obtained directly from these MO diagrams as to whether the reaction proceeds via normal or inverse electron demand, as all optimisations were done on different potential energy surfaces. We can, however, say it is likely to be inverse electron demand due to the oxygen atoms of 1,3-dioxole donating electron density into the dienophile C=C.

<h3> The Transition State</h3>

The transition state for this reaction is depicted below, optimised to the B3LYP level.

<b>Endo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815EndoTSvibration.gif]]

[[File:SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG]]

Vibration occurs at -523.01cm<sup>-1</sup>.

<b>Exo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>2NDPRODUCTB3LYPTS_SJ1815.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:2NDPRODUCTB3LYPTS_SJ1815.LOG]]

[[File:ExoTSvibrationSJ1815.gif]]

Vibration occurs at -528.84cm<sup>-1</sup>.

<h4>Molecular orbitals</h4>

<b>Exo HOMO:</b>

[[File:SJ1815HOMO calledEndo product.jpg]]

Energy: -0.19052 Hartrees/particle

<b>Exo LUMO</b>

[[File:Sj1815LUMO_calledEndo_product.jpg]]

Energy:-0.00462 Hartrees/particle

<b>Endo HOMO</b>

[[File:SJ1815HOMO_TS_2nd_product.jpg]]

Energy: -0.18560 Hartrees/particle

<b>Endo LUMO</b>

[[File:SJ1815LUMO_TS_2nd_product.jpg]]

Energy:-0.00699 Hartrees/particle

There is obvious, visible secondary orbital interaction between orbitals on the oxygen atoms and those on the cyclohexa-1,3-diene's cis-butadiene fragment. This lowers the endo transition state's energy, yet both exo and endo benefit from these interactions (the overlap is just greater for the endo transition state).

<h2>Exercise 3-Diels-Alder ([4+2]) vs Cheleotropic ([4+1])</h2>
[[File:Diels-Alder SO2.jpg|500px]]

[[File:SJ1815Cheleotropic SO2 (1).jpg|500px]]

[[File:SJ1815Diels-Alder_SO2_(1)(endo).jpg|500px]]

[[File:2ndC=C-C=C_Diels-Alder_SJ1815.jpg|500px]]

{| class="wikitable"
!
!Cheleotropic
!Outer fragment Endo
!Inner fragment Endo
!Outer fragment Exo
!Inner fragment Exo
|-
|'''Products'''
|Cheleo stuff needed
|<jmol><jmolApplet><uploadedFileContents>SJ1815OUTERC=CPRODUCTENDO.LOG </uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815OUTERC=CPRODUCTENDO.LOG]]
|<jmol><jmolApplet><uploadedFileContents>DA1STotherC=CSJ1815PRODUCT(Exo).LOG </uploadedFileContents></jmolApplet></jmol>

[[File:DA1STotherC=CSJ1815PRODUCT(Exo).LOG]] (This has, in fact, been named incorrectly and is endo, as stated in the table).
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG]]
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG</uploadedFileContents></jmolApplet></jmol>
[[File:SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).
|-
|'''Transition states'''
|Cheleo stuff needed
|[[File:DA2NDTSFROMFROZENSJ1815(endo)(1stC=C).LOG]]

[[File:SJ1815EndoTSfromfrozen(1stC=C).gif]]

Vibration occurs at -333.62cm<sup>-1</sup>.
|[[File:SJ1815EXODA2NDC=C-C=CTS(3).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:Exo_TS_Sj1815_innerC-C(real_exo).gif]]

Vibration occurs at -453.52cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(1stC=C)(exo).LOG]]

[[File:SJ1815_SO2_DA_TS_PM6.gif]]

Vibration occurs at -351.55cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(2NDC=C)(ENDO)(REALPM6).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:SJ1815_endoDAinnerC-CTS(real_endo).gif]]

Vibration occurs at -482.80cm<sup>-1</sup>.
|-
|'''IRC graphs'''
|Cheleo stuff needed
|[[File:DA2ndTSfromfrozenSJ1815Endo(1stC=C).jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|[[File:SJ1815_IRCexo1stC=C.jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|-
|'''IRC animations'''
|Cheleo stuff needed
|[[File:SJ1815_endoIRC1stC=C.gif]]

[[File:DA2NDTSFROMFROZENSJ1815(ENDO)(1STC=C)IRC.LOG]]
|[[File:SJ1815otherC=CExoIRC.gif]]

[[File:DA2NDOTHERC=CSJ1815FROZENIRC.LOG]]
|[[File:SJ1815_outerC=CEndoIRC.gif]]

[[File:SJ1815_DA_1ST_SO2_IRCPM6(exo)(1stC=C).LOG]]

|[[File:SJ1815_innerC-C_endoDAIRC.gif]]

[[File:SJ1815INNERC=C-C=CENDOIRCPM6.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

|}

Xylylene is highly unstable as the bonding changes from 4 distinct double bonds to an aromatic ring and 2 single bonds pointing out of the ring. Due to the stability of the aromatic ring, xylylene may form a 4 membered ring to establish aromaticity or may polymerise.

<h4> Thermochemistry</h4>

[[File:SJ1815_Ex3Energydiagram.jpg]]

<h5>Outer fragment thermochemistry</h5>

<b>Cheleotropic</b>

<b>Reaction barrier</b>= +0.036864 Hartrees/particle or +96.786432 kJ/mol

<b>Reaction energy</b>= -0.062913 Hartrees/particle or -163.2877215 kJ/mol

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.028369 Hartrees/particle or +74.4828095 kJ/mol

<b>Reaction energy</b>= -0.040484 Hartrees/particle or -106.290742 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.029887 Hartrees/particle or +78.4683185 kJ/mol

<b>Reaction energy</b>= -0.040735 Hartrees/particle or -106.9497425 kJ/mol

The thermodynamic product is the cheleotropic product (it's lowest in energy) and the kinetic product is the endo product (the transition state is lowest in energy).

<h5>Inner fragment thermochemistry</h5>

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.042864 Hartrees/particle or +112.539432 kJ/mol

<b>Reaction energy</b>= +0.005114 Hartrees/particle or +13.426807 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.039882 Hartrees/particle or +104.710191 kJ/mol

<b>Reaction energy</b>= +0.003415 Hartrees/particle or 8.9660825 kJ/mol

Attack at the inner cis-butadiene fragment is disfavoured and doesn't occur.

<h2> Exercise 4- the ring opening of dimethyl (1R,2S)-cyclobut-3-ene-1,2-dicarboxylate</h2>

[[File:SJ1815ringopening.jpg]]

The ring opening of a 4-membered ring is only thermally allowed if the transition state is a Möbius transition state (that is, the 2 ends of the ring are conrotatory and twist in the same sense).

This can be seen when you look at the IRC for the reaction

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ18152+2IRC.jpg]]
|-
|'''IRC LOG files'''
|[[File:SJ18152+2TS4IRC.LOG]]
|-
|'''IRC animations'''
|[[File:SJ18152+2IRC.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|}

<h3>The transition state</h3>

[[File:SJ18152+2TSvib.gif]]

[[File:SJ18152+2TS4.LOG]]

This vibration occurs at -696.41cm<sup>-1</sup>. This negative vibration confirms the fact that this is a transition state.

<h2>References</h2>
<references>
<ref name="HammondPost">https://chem.libretexts.org/Reference/Organic_Chemistry_Glossary/Hammond%E2%80%99s_Postulate accessed on 8/11/2017 </ref>
<ref name="Bearparklecture"> Michael J Bearpark, 2017, <i>Calculating Molecular Geometries</i>, Lecture, Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Imperial College London, 6th November 2017 </ref>
<ref name="C-C"> Stark J.G., Wallace H.G. in <i>Chemistry Data Book</i> ed. Hodder Education, Hodder Education, 2nd edn, 1982, ch.19, pp. 27 </ref>
<ref name="C=C"> http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html accessed on 5/2/2018 </ref>
<ref name="PE surface">https://www.nrl.navy.mil/mstd/branches/6390/surfaces-and-interfaces accessed on 6/2/2018</ref>
<ref name="Slater">adapted from F. Jensen in <i>Introduction to Computational Chemistry </i> ed. Wiley, Wiley, Indianapolis, 1st edn., 1999, ch. 5. Adaptation obtained from https://lcbc.epfl.ch/files/content/users/232236/files/lecture_2016_2.pdf accessed on 12/2/2018</ref>
<ref name="PM6Gauss">http://gaussian.com/semiempirical/ accessed on 8/2/2108 </ref>
<ref name="DFTGauss">http://gaussian.com/dft/ accessed on 8/2/2018 </ref>
<ref name="DensityGauss">http://gaussian.com/basissets/?tabid=2 accessed on 8/2/2018</ref>
<ref name= "CvdW">https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf accessed on 11/2/2018 </ref>
<ref name="Basis"> A. Szabo, N. Oatlands in <i>Modern Quantum Chemistry </i> ed. Dover Publications Inc., Dover Publications Inc., Mineola, 1st edn., 1996, ch. 3, pp. 156 </ref>
</references>

File:SJ1815 SO2 DA TS PM6 2(2NDC=C)(ENDO)(REALPM6).LOG

2018-02-12T13:30:29Z

Sj1815: Sj1815 uploaded a new version of File:SJ1815 SO2 DA TS PM6 2(2NDC=C)(ENDO)(REALPM6).LOG

Rep:SJ1815 Transition States

2018-02-12T13:29:47Z

Sj1815:

<h1>Investigating Transition States of Various Pericyclic Reaction</h1>
<h2>Introduction</h2>
<h3>Transition States: What do we mean?</h3>
Transition states are energy maxima along the path of a reaction and the dynamic bottleneck through which a reaction must proceed. Real energy profiles are dependent on multiple variables and you can move the reactants along the energy profile diagram in any direction, so you can encounter many maxima. However, only the one that occurs on your reaction pathway is considered a transition state. To put this in another way, I could take a flask of but-1,3-diene and ethene and expect a Diels-Alder reaction to occur. The transition state would be somewhere where the C-C bonds are being made from the C=Cs in the substrates. I could, given enough energy, stretch one of the C-C bonds to the moon (admittedly, probably breaking it in the process) and you'd have an energy maximum but it wouldn't be a transition state as it isn't part of the reaction in question.
Normally for a C-C bond forming process, we take the transition state to be somewhere between the van der Waals radii of the 2 atoms and the C-C bond length.

<h3>Locating a transition state</h3>
<h4>Use Hammond's Postulate</h4>
Take a guess at where the Transition State is and optimise using Gaussian. Use Hammond's postulate for where to guess. This is fast, but unreliable, as you have to be a very good guesser.

<b>N.B. Hammond's Postulate: 'The structure of the transition states resembles either the reactants or products (whichever is closest in energy)'</b><ref name="HammondPost" />

For C-C bond forming reactions, a guess of 2.2 for the bond length is a good place to start.

To actually run the job, use Opt+Freq (geometry optimisation via 'solving' the Schrödinger equation, which is ĤΨ=EΨ, and then moving along in small steps of energy, scaled using the second derivative d<sup>2</sup>E/dq<sup>2</sup>, where q is the reaction coordinate and frequency calculation using k=d<sup>2</sup>E/dq<sup>2</sup> and [[File:Spring frequency1.png|100px]]<ref name="Bearparklecture" />

The computer uses variational theorem to run calculations and solve the Schrödinger equation. Variational theorem takes a guess at the wavefunction of a system and then minimises the energy. This means that it hits the potential energy surface after a number of iterations. Depending on where it hits, the optimised .log file can look like a range of different things. A potential energy surface has a lot of local minima- it's 'bumpy'. If the guess wavefunction hits any of these bumps, Gaussview may tell you that it's found a transition state when it hasn't. This is why we need to analyse the results by checking the imaginary vibration and seeing if it matches with our idea of what 'going towards the products' looks like.

<table class="image">
<tr><td>[[File:PE_surface_SJ1815.gif]]</td></tr>
<tr><td class="caption"><i><span style="color:gray">Figure 1: A depiction of a 3D potential energy surface taken from reference 3 <ref name="PE surface"></ref>. We can only represent energy surfaces in 3D, yet they actually have many more dimensions than this (there are 3N-6 dimensions to consider, where N is the number of atoms in the molecule).</span></i></td></tr>
</table>

One approximation to make calculations easier is that we assume that molecular orbitals can be constructed from a linear combination of atomic orbitals. These all have different weightings called <b> orbital coefficients</b>. The wavefunction can therefore be broken down into <math>|\psi\rangle</math>=Σ<sup>N</sup><sub>i</sub>c<sub>i</sub><math>|\ \phi_i\rangle</math>

As <math>\langle\psi|</math>H<math>|\psi\rangle</math>=E<math>\psi</math>, we then have Σ<sup>N</sup><sub>m</sub>Σ<sup>N</sup><sub>n</sub>c<sub>m</sub><math>\langle\phi_m|</math>H<math>|\phi_n\rangle</math>c<sub>n</sub>

This can be written as a set of matrices with the first being a 1xn matrix of the c<sub>n</sub> coefficients, then a Hessian matrix of all of the different atomic orbital integrals and then an mx1 matrix of the c<sub>m</sub> coefficients or, more succinctly, c<sup>T</sup>Hc, where H is the Hessian here. This equals the energy and from this you can get the eigenvalue equation of Hc=Ec, which the computer solves

Each eigenvector of the eigenvalue equation yields 1 molecular orbital.

<b> What are the individual atomic wavefunctions?</b>

These represent electron densityand are best represented by Slater functions.

Slater functions have the form <math>R(r) = N r^{n-1} e^{-\zeta r}\,</math><ref name="Slater"></ref>

This, however, is too computationally costly to solve, so we use an approximation by using Gaussians.

Gaussian functions have the form <math>ae^{-ar^2}</math> An example of thhe form of one of these is shown below.

[[File:SJ1815_Gaussian.jpg]]

As these don't represent the orbitals as well as Slater functions, several of them are often summed to better represent these orbitals. This sum adds computational complexity, as there are more integrals to compute, yet this is still faster than using Slater functions. Combining three Gaussians gives a basis set of STO-3G (<b>S</b>later-<b>T</b>ype <b>O</b>rbitals-<b>3</b> functions <b>G</b>aussians)<ref name="Basis"></ref>.

<h2>Optimisation methods</h2>

PM6 is a semi-empirical optimisation method. It takes into account the valence electrons for the species and then solves the integrals in relation to them, employing code already on the Gaussian programme <ref name="PM6Gauss"></ref>. It also uses fixed numbers as approximations for the integrals in the Hessian. This makes it much faster at doing calculations, yet more imprecise in the answers obtained.

B3LYP is a DFT (density functional theory) method, which takes advantage of density fitting (expansion of atomic density rather than computing all of the 2-electron integrals individually)<ref name="DensityGauss"></ref>. B3LYP differs from other DFT calculations insofar as it optimises the nuclear wavefunctions, then adds on some electron interactions to see how things change (most DFT calculations just use the nuclei) <ref name="DFTGauss"></ref>. However, these are not easily calculated by Gaussian, causing approximations to be formed.

<h2>Tutorial</h2>

<h3>Tutorial 1- Cope rearrangement of hexa-1,5-diene</h3>
[[File:Cope_rearrangementSJ1815.png|500px]]

The first method for finding a transition state is to guess and then optimise using Opt+Freq, Optimise to a TS (Berny) and calculate the force constants once. There should be 1 negative frequency at the output, which confirms that a transition state has been found and animation of said transition state should make it look like you go from reactants to products.
There are 2 different transition states (boat and chair), both of which have been accounted for below
{| class="wikitable"
!
!Boat
!Chair
|-
|
|[[File:SJ1815Boat.jpg|100px]]
|[[File:SJ1815Chair.jpg|100px]]
|-
|'''PM6'''
|[[File:SJ1815TRIAL COPE TS 2 RADICALS PM6.LOG]]
|[[File:SJ1815TRIAL COPE TS RADICAL CHAIRTS.LOG]]
|-
|'''B3LYP'''
|[[File:SJ1815COPEBOATTSB3LYP.LOG]]
|[[File:SJ1815COPECHAIRTSB3LYP.LOG]]
|}

<b>IRC</b>

[[File:SJ1815 BOAT COPE TS IRC PM6.LOG]]

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815 BOAT COPE TS IRC PM6.LOG </uploadedFileContents></jmolApplet></jmol>
<h3>Tutorial 2- Dimerisation of Cyclopentadiene</h3>
[[File:SJ1815Cyclopentadiene dimerisation.jpg|500px]]

The second method relies on generating a guess transition state, freezing the atoms in space and then uses method 1 to find exactly where the transition state lies. The keyword opt=modredundant will appear in the submission window, but submit the job as normal, optimising to a minimum. Then, unfreeze the bonds and optimise to a TS, as in method 1. To distinguish between endo and exo conformers, run IRC calculations.

<b>Optimisation:</b>

<b>PM6:</b> [[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS OPT+FREQ PM6.LOG]]

<b>B3LYP:</b>[[File:SJ1815 CYCLOPENTADIENE TRIAL FIXED COORDS B3LYP.LOG]]

<h3>Tutorial 3-Xylylene SO2 Diels-Alder</h3>
The third method uses the reactants or products, alters the bond lengths and/or angles (normally of those involved in the reaction, but can be of neighbouring atoms too) and then runs the same way as method 2.

<b>Opt+Freq of Diels-Alder</b>

[[File:SJ1815_SO2_DIELS-ALDER_PM6_MIN.LOG]]

<h2>Exercise 1- Cis-butadiene and ethene Diels-Alder ([4+2]-cycloaddition)</h2>
[[File:Diels-Alder cyclohexene product.jpg|500px]]

This reaction is often seen as the classic Diels-Alder reaction, due to the fact that the diene and dienophile are as simple as they can be. However, this reaction is purely hypothetical as neither fragment is particularly electron rich or poor (we need this disparity in energies for both normal electron demand and inverse electron demand Diels-Alder reactions).

<h3>Optimisation</h3>

{| class="wikitable"
!
! style="background: #8b0c0c; color: white;" | Butadiene
! style="background: #8b0c0c; color: white;" | Ethene
! style="background: #8b0c0c; color: white;" | Cyclohexene
! style="background: #8b0c0c; color: white;"|Transition state
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> BUTADIENE_SJ1815.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 ETHENE_OPT+FREQ_PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXENE PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:BUTADIENE_SJ1815.LOG]]
|[[File:SJ1815 ETHENE_OPT+FREQ_PM6.LOG]]
|[[File:SJ1815 CYCLOHEXENE PM6.LOG]]
|[[File:SJ1815_DIELS-ALDER_TS10.LOG]]
|-
|'''C-C bond Lengths/Å'''
|1.33343
|1.32742
|1.33698
|1.37977 (original C=C of butadiene)
|-
|
|1.47077
|X
|1.50068
|1.41111 (original C-C of butadiene)
|-
|
|1.33343
|X
|1.53703
|1.37977 (original C=C of butadiene)
|-
|
|X
|X
|1.53491
|1.38176 (original C=C of ethene)
|-
|
|X
|X
|1.53736
|X
|-
|
|X
|X
|1.50077
|X
|}
The bond length for a C-C bond is 1.54Å <ref name="C-C"></ref> while the C=C bond length is 1.34Å <ref name="C=C"></ref>
This matches fairly well with the bond lengths in the table above, with the transition state having bond lengths partway between the two lengths. The van der Waals radius of carbon is 1.77Å <ref name="CvdW"></ref> and all C-C lengths are closer than this, so they are interacting (the van der Waals radius tells us how close atoms have to be for some interaction to take place).

<h3>MO analysis</h3>

The MO diagram for the reaction is as depicted below

[[File:SJ1815Diels-Alder2.jpg]]

We can see that only orbitals of the same symmetry can interact and have non-zero integrals. This means only fully symmetric or fully antisymmetric combinations are allowed.

The actual, calculated MOs are depicted here:

{| class="wikitable"
!MO label
!MOs
!Corresponding diagram
|-
|LUMO
|[[File:SJ1815_DA_LUMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw.jpg|150px]]
|-
|HOMO
|[[File:SJ1815_DA_HOMO.png|150px]]
|[[File:SJ1815_DA_HOMOchemdraw1.jpg|150px]]
|-
|HOMO-1
|[[File:SJ1815_DA_HOMO-1.png|150px]]
|[[File:SJ1815_DA_HOMO-1chemdraw.jpg|150px]]
|-
|HOMO-2
|[[File:SJ1815_DA_HOMO-2.png|150px]]
|[[File:SJ1815_DA_HOMO-2chemdraw.jpg|150px]]
|-
|HOMO-3
|[[File:SJ1815_DA_HOMO-3.png|150px]]
|[[File:SJ1815_DA_HOMO-3chemdraw.jpg|150px]]
|}

<b>The transition state</b>

[[File:SJ1815 DIELS-ALDER TS10.LOG]]

[[File:TS_DA_SJ1815.gif|thumb|none|alt=A depiction of the transition state|A depiction of the transition state (click to animate)]]

<jmol><jmolApplet><size>200</size><script>frame 15; vibration 2;rotate x -20; </script><uploadedFileContents>SJ1815_DIELS-ALDER_TS10.LOG</uploadedFileContents></jmolApplet></jmol>

We can see that this is a transition state as it has a vibration at -948.72 cm<sup>-1</sup> in the log file.

Two IRC calculations were run, as the first only showed progression from products to reactants, even though the graph showed entire reaction coordinates.

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ1815_DA_IRC1.jpg|caption=The IRC path going backwards in the reaction]]
|[[File:SJ1815_DA_IRC2.jpg|caption=The IRC path going forwards in the reaction]]
|-
|'''IRC LOG files'''
|[[File:SJ1815 DIELS-ALDER IRC.LOG]]
|[[File:SJ1815_DIELS_ALDERIRCFORWARDS.LOG]]
|-
|'''IRC animations'''
|[[File:SJ1815_TS_IRC_DA.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|[[File:SJ1815_TS_IRC_DAforwards.gif|caption=The IRC path going forwards in the reaction (click to animate)]]
|}

The IRC shows synchronous bond formation between cis-butadiene and ethene.

<h2>Exercise 2- Reaction of Cyclohexa-1,3-diene and 1,3-Dioxole ([4+2] cycloaddition)</h2>
[[File:SJ18151,3-dioxole endo and exo.jpg|500px]]

{| class="wikitable"
!
!Dioxole
!Cyclohexa-1,3-diene
!Endo product
!Exo product
|-
|
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 DIOXOLEPM6OPT+FREQ.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG </uploadedFileContents></jmolApplet></jmol>
|<jmol><jmolApplet><size>200</size><uploadedFileContents> SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG </uploadedFileContents></jmolApplet></jmol>
|-
|'''PM6'''
|[[File:SJ1815 DIOXOLEPM6OPT+FREQ.LOG]]
|[[File:SJ1815 CYCLOHEXADIENE OPT+FREQ PM6.LOG]]
|[[File:SJ1815_OPT+FREQPM6_2NDPRODUCT.LOG]]
|[[File:SJ1815 PRODUCT1PM6OPT+FREQENDO.LOG]]
|-
|'''B3LYP'''
|[[File:DIOXOLEB3LYPOPT+FREQ_SJ1815(1).LOG]]
|[[File:SJ1815_CYCLOHEXADIENEB3LYPOPT+FREQ(1).LOG]]
|[[File:SJ1815_OPT+FREQB3LYP_2NDPRODUCT2.LOG]]
|[[File:SJ1815_B3LYP1STPRODUCT.LOG]]
|}

<h3>Thermochemistry</h3>

{|class= "wikitable"
!
!Energy
!Energy difference from Reactants
|-
|'''1,3-dioxole'''
||-267.068138 Hartrees/particle
|X
|-
|'''Cyclohexa-1,3-diene'''
||-233.321307 Hartrees/particle
|X
|-
|'''Total Reactants'''
||-500.389175 Hartrees/particle
|X
|-
|'''Exo TS'''
||-500.329165 Hartrees/particle
||+0.06001 Hartrees/particle = +157.556255 kJ/mol
|-
|'''Exo Product'''
||-500.418691 Hartrees/particle
||-0.029516 Hartree/particle = -77.494258.8973 kJ/mol
|-
|'''Endo TS'''
||-500.332149 Hartrees/particle
||+0.057026 Hartrees/particle = +149.7218 kJ/mol
|-
|'''Endo Product'''
||-500.417315 Hartrees/particle
||-0.02814 Hartrees/particle = -73.88157 kJ/mol
|-
|}

[[File:SJ1815DioxoleEnergydiagram.jpg]]

The thermodynamic product is therefore the exo product (the endo product has a higher energy due to steric clash within the molecule) while the kinetic product is the endo product, as the transition state is lower in energy, due to the fact that secondary orbital interactions are greater for the endo transition state.

<h4>MO diagrams</h4>

<b>Endo</b>

[[File:Diels-AlderdioxoleSJ1815exo1.jpg]]

<b>Exo</b>

[[File:Diels-AlderdioxoleSJ1815endo1.jpg]]

It can't be obtained directly from these MO diagrams as to whether the reaction proceeds via normal or inverse electron demand, as all optimisations were done on different potential energy surfaces. We can, however, say it is likely to be inverse electron demand due to the oxygen atoms of 1,3-dioxole donating electron density into the dienophile C=C.

<h3> The Transition State</h3>

The transition state for this reaction is depicted below, optimised to the B3LYP level.

<b>Endo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815EndoTSvibration.gif]]

[[File:SJ1815_DIOXOLE_ENDOTS_B3LYP.LOG]]

Vibration occurs at -523.01cm<sup>-1</sup>.

<b>Exo</b>

<jmol><jmolApplet><size>200</size><uploadedFileContents>2NDPRODUCTB3LYPTS_SJ1815.LOG</uploadedFileContents></jmolApplet></jmol>

[[File:2NDPRODUCTB3LYPTS_SJ1815.LOG]]

[[File:ExoTSvibrationSJ1815.gif]]

Vibration occurs at -528.84cm<sup>-1</sup>.

<h4>Molecular orbitals</h4>

<b>Exo HOMO:</b>

[[File:SJ1815HOMO calledEndo product.jpg]]

Energy: -0.19052 Hartrees/particle

<b>Exo LUMO</b>

[[File:Sj1815LUMO_calledEndo_product.jpg]]

Energy:-0.00462 Hartrees/particle

<b>Endo HOMO</b>

[[File:SJ1815HOMO_TS_2nd_product.jpg]]

Energy: -0.18560 Hartrees/particle

<b>Endo LUMO</b>

[[File:SJ1815LUMO_TS_2nd_product.jpg]]

Energy:-0.00699 Hartrees/particle

There is obvious, visible secondary orbital interaction between orbitals on the oxygen atoms and those on the cyclohexa-1,3-diene's cis-butadiene fragment. This lowers the endo transition state's energy, yet both exo and endo benefit from these interactions (the overlap is just greater for the endo transition state).

<h2>Exercise 3-Diels-Alder ([4+2]) vs Cheleotropic ([4+1])</h2>
[[File:Diels-Alder SO2.jpg|500px]]

[[File:SJ1815Cheleotropic SO2 (1).jpg|500px]]

[[File:SJ1815Diels-Alder_SO2_(1)(endo).jpg|500px]]

[[File:2ndC=C-C=C_Diels-Alder_SJ1815.jpg|500px]]

{| class="wikitable"
!
!Cheleotropic
!Outer fragment Endo
!Inner fragment Endo
!Outer fragment Exo
!Inner fragment Exo
|-
|'''Products'''
|<jmol><jmolApplet><uploadedFileContents>SJ1815OUTERC=CPRODUCTENDO.LOG </uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815OUTERC=CPRODUCTENDO.LOG]]
|<jmol><jmolApplet><uploadedFileContents>DA1STotherC=CSJ1815PRODUCT(Exo).LOG </uploadedFileContents></jmolApplet></jmol>

[[File:DA1STotherC=CSJ1815PRODUCT(Exo).LOG]] (This has, in fact, been named incorrectly and is endo, as stated in the table).
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG</uploadedFileContents></jmolApplet></jmol>

[[File:SJ1815_PM6_DA2NDPRODUCT(exo)(1stC=C).LOG]]
|<jmol><jmolApplet><uploadedFileContents>SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG</uploadedFileContents></jmolApplet></jmol>
[[File:SJ1815_PM6INNERC=C-C=CENDOPRODUCT.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).
|
|-
|'''Transition states'''
|[[File:DA2NDTSFROMFROZENSJ1815(endo)(1stC=C).LOG]]

[[File:SJ1815EndoTSfromfrozen(1stC=C).gif]]

Vibration occurs at -333.62cm<sup>-1</sup>.
|[[File:SJ1815EXODA2NDC=C-C=CTS(3).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:Exo_TS_Sj1815_innerC-C(real_exo).gif]]

Vibration occurs at -453.52cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(1stC=C)(exo).LOG]]

[[File:SJ1815_SO2_DA_TS_PM6.gif]]

Vibration occurs at -351.55cm<sup>-1</sup>.

|[[File:SJ1815_SO2_DA_TS_PM6_2(2NDC=C)(ENDO)(REALPM6).LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

[[File:SJ1815_endoDAinnerC-CTS(real_endo).gif]]

Vibration occurs at -482.80cm<sup>-1</sup>.
|-
|'''IRC graphs'''
|[[File:DA2ndTSfromfrozenSJ1815Endo(1stC=C).jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|[[File:SJ1815_IRCexo1stC=C.jpg]]
|[[File:SJ1815DA2ndotherC-CIRCfromfrozen.jpg]]
|-
|'''IRC animations'''
|[[File:SJ1815_endoIRC1stC=C.gif]]

[[File:DA2NDTSFROMFROZENSJ1815(ENDO)(1STC=C)IRC.LOG]]
|[[File:SJ1815otherC=CExoIRC.gif]]

[[File:DA2NDOTHERC=CSJ1815FROZENIRC.LOG]]
|[[File:SJ1815_outerC=CEndoIRC.gif]]

[[File:SJ1815_DA_1ST_SO2_IRCPM6(exo)(1stC=C).LOG]]

|[[File:SJ1815_innerC-C_endoDAIRC.gif]]

[[File:SJ1815INNERC=C-C=CENDOIRCPM6.LOG]](This has, in fact, been named incorrectly and is exo, as stated in the table).

|}

Xylylene is highly unstable as the bonding changes from 4 distinct double bonds to an aromatic ring and 2 single bonds pointing out of the ring. Due to the stability of the aromatic ring, xylylene may form a 4 membered ring to establish aromaticity or may polymerise.

<h4> Thermochemistry</h4>

[[File:SJ1815_Ex3Energydiagram.jpg]]

<h5>Outer fragment thermochemistry</h5>

<b>Cheleotropic</b>

<b>Reaction barrier</b>= +0.036864 Hartrees/particle or +96.786432 kJ/mol

<b>Reaction energy</b>= -0.062913 Hartrees/particle or -163.2877215 kJ/mol

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.028369 Hartrees/particle or +74.4828095 kJ/mol

<b>Reaction energy</b>= -0.040484 Hartrees/particle or -106.290742 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.029887 Hartrees/particle or +78.4683185 kJ/mol

<b>Reaction energy</b>= -0.040735 Hartrees/particle or -106.9497425 kJ/mol

The thermodynamic product is the cheleotropic product (it's lowest in energy) and the kinetic product is the endo product (the transition state is lowest in energy).

<h5>Inner fragment thermochemistry</h5>

<b>Endo Diels-Alder</b>

<b>Reaction barrier</b>= +0.042864 Hartrees/particle or +112.539432 kJ/mol

<b>Reaction energy</b>= +0.005114 Hartrees/particle or +13.426807 kJ/mol

<b> Exo Diels-Alder</b>

<b>Reaction barrier</b>= +0.039882 Hartrees/particle or +104.710191 kJ/mol

<b>Reaction energy</b>= +0.003415 Hartrees/particle or 8.9660825 kJ/mol

Attack at the inner cis-butadiene fragment is disfavoured and doesn't occur.

<h2> Exercise 4- the ring opening of dimethyl (1R,2S)-cyclobut-3-ene-1,2-dicarboxylate</h2>

[[File:SJ1815ringopening.jpg]]

The ring opening of a 4-membered ring is only thermally allowed if the transition state is a Möbius transition state (that is, the 2 ends of the ring are conrotatory and twist in the same sense).

This can be seen when you look at the IRC for the reaction

{| class="wikitable"
|
!IRC
|-
|'''IRC graphs'''
|[[File:SJ18152+2IRC.jpg]]
|-
|'''IRC LOG files'''
|[[File:SJ18152+2TS4IRC.LOG]]
|-
|'''IRC animations'''
|[[File:SJ18152+2IRC.gif|caption=The IRC path going backwards in the reaction (click to animate)]]
|}

<h3>The transition state</h3>

[[File:SJ18152+2TSvib.gif]]

[[File:SJ18152+2TS4.LOG]]

This vibration occurs at -696.41cm<sup>-1</sup>. This negative vibration confirms the fact that this is a transition state.

<h2>References</h2>
<references>
<ref name="HammondPost">https://chem.libretexts.org/Reference/Organic_Chemistry_Glossary/Hammond%E2%80%99s_Postulate accessed on 8/11/2017 </ref>
<ref name="Bearparklecture"> Michael J Bearpark, 2017, <i>Calculating Molecular Geometries</i>, Lecture, Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Imperial College London, 6th November 2017 </ref>
<ref name="C-C"> Stark J.G., Wallace H.G. in <i>Chemistry Data Book</i> ed. Hodder Education, Hodder Education, 2nd edn, 1982, ch.19, pp. 27 </ref>
<ref name="C=C"> http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html accessed on 5/2/2018 </ref>
<ref name="PE surface">https://www.nrl.navy.mil/mstd/branches/6390/surfaces-and-interfaces accessed on 6/2/2018</ref>
<ref name="Slater">adapted from F. Jensen in <i>Introduction to Computational Chemistry </i> ed. Wiley, Wiley, Indianapolis, 1st edn., 1999, ch. 5. Adaptation obtained from https://lcbc.epfl.ch/files/content/users/232236/files/lecture_2016_2.pdf accessed on 12/2/2018</ref>
<ref name="PM6Gauss">http://gaussian.com/semiempirical/ accessed on 8/2/2108 </ref>
<ref name="DFTGauss">http://gaussian.com/dft/ accessed on 8/2/2018 </ref>
<ref name="DensityGauss">http://gaussian.com/basissets/?tabid=2 accessed on 8/2/2018</ref>
<ref name= "CvdW">https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf accessed on 11/2/2018 </ref>
<ref name="Basis"> A. Szabo, N. Oatlands in <i>Modern Quantum Chemistry </i> ed. Dover Publications Inc., Dover Publications Inc., Mineola, 1st edn., 1996, ch. 3, pp. 156 </ref>
</references>

File:Exo iso 0.05 LUMOSJ1815.jpg

2018-02-12T13:27:46Z

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