ChemWiki - User contributions [en]

Mod:Hunt Research Group:troublesome smd

2018-04-21T21:43:58Z

Sl7514:

SMD calculations with large imaginary frequencies

During your SMD calculations, you may run into a situation where the Gaussian optimisation has terminated normally but still contains large imaginary frequencies. For example, take a look at the two files below:

[[File:Troublesome smd freq.log]]

[[File:Troublesome smd opt.log]]

Looking at the frequency file:

[[File:Frequency example1.png|600px|thumb|center]]

In general, the optimisation is terminated if one of the two criteria is met:
- When the force and the displacement have converged
- When the maximum force and RMS force are two orders of magnitude smaller than the threshold shown, regardless of displacement

First check your optimisation log file to see if the energy has been converging. The following is taken directly from the example log file above:

[[File:troublesome_smd_optimisation_figure.png|500px|thumb|center]]

Check in your log file whether the force and the displacement have converged. The following is taken directly from the example log file above.

[[File:Convergence example1.png|400px|thumb|center]]

In this situation, it is likely that your optimisation has run into an area of potential energy surface which is quite flat and hence the optimisation will terminate since the force constant is below the threshold. However, the displacement is far from converging. It is possible to tighten the cutoffs on forces and step size that are used to determine convergence. Copy and paste the optimised structure with large imaginary frequency to new gaussian window and change the optimisation keyword from opt to opt=verytight.

Rerun your optimisation calculation with this keyword. In the four example files below, I have rerun the troublesome smd optimisation I have included earlier in this document.

[[File:Verytight troublesome smd freq.log]]

[[File:Verytight troublesome smd freq.txt]]

[[File:Verytight troublesome smd opt.log]]

[[File:Verytight troublesome smd opt.txt]]

Check your new optimisation log file at the end of the calculation for convergence. In the example above, I get

[[File:Convergence example2.png|400px|thumb|center]]

You can now see that the threshold for force and displacement has tightened and all four values have converged. In the subsequent frequency file, the imaginary frequencies have now disappeared:

[[File:Frequency example2.png|600px|thumb|center]]

Mod:Hunt Research Group:troublesome smd

2018-04-21T21:37:48Z

Sl7514:

SMD calculations with large imaginary frequencies

During your SMD calculations, you may run into a situation where the Gaussian optimisation has terminated normally but still contains large imaginary frequencies. For example, take a look at the two files below:

[[File:Troublesome smd freq.log]]

[[File:Troublesome smd opt.log]]

Looking at the frequency file:<gallery>
File:Frequency example1.png
</gallery>In general, the optimisation is terminated if one of the two criteria is met:
- When the force and the displacement have converged
- When the maximum force and RMS force are two orders of magnitude smaller than the threshold shown, regardless of displacement

First check your optimisation log file to see if the energy has been converging. The following is taken directly from the example log file above:<gallery>
File:troublesome_smd_optimisation_figure.png
</gallery>
Check in your log file whether the force and the displacement have converged. The following is taken directly from the example log file above.<gallery>
File:Convergence example1.png
</gallery>In this situation, it is likely that your optimisation has run into an area of potential energy surface which is quite flat and hence the optimisation will terminate since the force constant is below the threshold. However, the displacement is far from converging. It is possible to tighten the cutoffs on forces and step size that are used to determine convergence. Copy and paste the optimised structure with large imaginary frequency to new gaussian window and change the optimisation keyword from opt to opt=verytight.

Rerun your optimisation calculation with this keyword. In the four example files below, I have rerun the troublesome smd optimisation I have included earlier in this document.

[[File:Verytight troublesome smd freq.log]]

[[File:Verytight troublesome smd freq.txt]]

[[File:Verytight troublesome smd opt.log]]

[[File:Verytight troublesome smd opt.txt]]

Check your new optimisation log file at the end of the calculation for convergence. In the example above, I get<gallery>
File:Convergence example2.png
</gallery>You can now see that the threshold for force and displacement has tightened and all four values have converged. In the subsequent frequency file, the imaginary frequencies have now disappeared:<gallery>
File:Frequency example2.png
</gallery>

File:Frequency example2.png

2018-04-21T21:37:33Z

Sl7514:

File:Convergence example2.png

2018-04-21T21:36:57Z

Sl7514:

File:Convergence example1.png

2018-04-21T21:36:08Z

Sl7514:

File:Frequency example1.png

2018-04-21T21:35:16Z

Sl7514:

Mod:Hunt Research Group:troublesome smd

2018-04-21T21:30:38Z

Sl7514:

SMD calculations with large imaginary frequencies

During your SMD calculations, you may run into a situation where the Gaussian optimisation has terminated normally but still contains large imaginary frequencies. For example, take a look at the two files below:

[[File:Troublesome smd freq.log]]

[[File:Troublesome smd opt.log]]

Looking at the frequency file:

In general, the optimisation is terminated if one of the two criteria is met:
- When the force and the displacement have converged
- When the maximum force and RMS force are two orders of magnitude smaller than the threshold shown, regardless of displacement

First check your optimisation log file to see if the energy has been converging. The following is taken directly from the example log file above:

[[Troublesome smd optimisation figure.png]]

Check in your log file whether the force and the displacement have converged. The following is taken directly from the example log file above.

In this situation, it is likely that your optimisation has run into an area of potential energy surface which is quite flat and hence the optimisation will terminate since the force constant is below the threshold. However, the displacement is far from converging. It is possible to tighten the cutoffs on forces and step size that are used to determine convergence. Copy and paste the optimised structure with large imaginary frequency to new gaussian window and change the optimisation keyword from opt to opt=verytight.

Rerun your optimisation calculation with this keyword. In the four example files below, I have rerun the troublesome smd optimisation I have included earlier in this document.

[[File:Verytight troublesome smd freq.log]]

[[File:Verytight troublesome smd freq.txt]]

[[File:Verytight troublesome smd opt.log]]

[[File:Verytight troublesome smd opt.txt]]

Check your new optimisation log file at the end of the calculation for convergence. In the example above, I get

You can now see that the threshold for force and displacement has tightened and all four values have converged. In the subsequent frequency file, the imaginary frequencies have now disappeared:

Mod:Hunt Research Group:troublesome smd

2018-04-21T21:29:35Z

Sl7514:

SMD calculations with large imaginary frequencies

During your SMD calculations, you may run into a situation where the Gaussian optimisation has terminated normally but still contains large imaginary frequencies. For example, take a look at the two files below:

[[File:Troublesome smd freq.log]]

[[File:Troublesome smd opt.log]]

Looking at the frequency file:

In general, the optimisation is terminated if one of the two criteria is met:
- When the force and the displacement have converged
- When the maximum force and RMS force are two orders of magnitude smaller than the threshold shown, regardless of displacement

First check your optimisation log file to see if the energy has been converging. The following is taken directly from the example log file above:

[[Troublesome smd optimisation figure.png|700px|thumb|center]]

Check in your log file whether the force and the displacement have converged. The following is taken directly from the example log file above.

In this situation, it is likely that your optimisation has run into an area of potential energy surface which is quite flat and hence the optimisation will terminate since the force constant is below the threshold. However, the displacement is far from converging. It is possible to tighten the cutoffs on forces and step size that are used to determine convergence. Copy and paste the optimised structure with large imaginary frequency to new gaussian window and change the optimisation keyword from opt to opt=verytight.

Rerun your optimisation calculation with this keyword. In the four example files below, I have rerun the troublesome smd optimisation I have included earlier in this document.

[[File:Verytight troublesome smd freq.log]]
[[File:Verytight troublesome smd freq.txt]]
[[File:Verytight troublesome smd opt.log]]
[[File:Verytight troublesome smd opt.txt]]

Check your new optimisation log file at the end of the calculation for convergence. In the example above, I get

You can now see that the threshold for force and displacement has tightened and all four values have converged. In the subsequent frequency file, the imaginary frequencies have now disappeared:

Mod:Hunt Research Group:troublesome smd

2018-04-21T21:28:16Z

Sl7514:

SMD calculations with large imaginary frequencies

During your SMD calculations, you may run into a situation where the Gaussian optimisation has terminated normally but still contains large imaginary frequencies. For example, take a look at the two files below:

[[File:Troublesome smd freq.log]]
[[File:Troublesome smd opt.log]]

Looking at the frequency file:

In general, the optimisation is terminated if one of the two criteria is met:
- When the force and the displacement have converged
- When the maximum force and RMS force are two orders of magnitude smaller than the threshold shown, regardless of displacement

First check your optimisation log file to see if the energy has been converging. The following is taken directly from the example log file above:

[[Troublesome smd optimisation figure.png]]

Check in your log file whether the force and the displacement have converged. The following is taken directly from the example log file above.

In this situation, it is likely that your optimisation has run into an area of potential energy surface which is quite flat and hence the optimisation will terminate since the force constant is below the threshold. However, the displacement is far from converging. It is possible to tighten the cutoffs on forces and step size that are used to determine convergence. Copy and paste the optimised structure with large imaginary frequency to new gaussian window and change the optimisation keyword from opt to opt=verytight.

Rerun your optimisation calculation with this keyword. In the four example files below, I have rerun the troublesome smd optimisation I have included earlier in this document.

[[File:Verytight troublesome smd freq.log]]
[[File:Verytight troublesome smd freq.txt]]
[[File:Verytight troublesome smd opt.log]]
[[File:Verytight troublesome smd opt.txt]]

Check your new optimisation log file at the end of the calculation for convergence. In the example above, I get

You can now see that the threshold for force and displacement has tightened and all four values have converged. In the subsequent frequency file, the imaginary frequencies have now disappeared:

Mod:Hunt Research Group:troublesome smd

2018-04-21T21:27:44Z

Sl7514:

SMD calculations with large imaginary frequencies

During your SMD calculations, you may run into a situation where the Gaussian optimisation has terminated normally but still contains large imaginary frequencies. For example, take a look at the two files below:

[[File:Troublesome smd freq.log]]

[[File:Troublesome smd opt.log]]

Looking at the frequency file:

In general, the optimisation is terminated if one of the two criteria is met:
- When the force and the displacement have converged
- When the maximum force and RMS force are two orders of magnitude smaller than the threshold shown, regardless of displacement

First check your optimisation log file to see if the energy has been converging. The following is taken directly from the example log file above:

[[Troublesome smd optimisation figure.png]]

Check in your log file whether the force and the displacement have converged. The following is taken directly from the example log file above.

In this situation, it is likely that your optimisation has run into an area of potential energy surface which is quite flat and hence the optimisation will terminate since the force constant is below the threshold. However, the displacement is far from converging. It is possible to tighten the cutoffs on forces and step size that are used to determine convergence. Copy and paste the optimised structure with large imaginary frequency to new gaussian window and change the optimisation keyword from opt to opt=verytight.

Rerun your optimisation calculation with this keyword. In the four example files below, I have rerun the troublesome smd optimisation I have included earlier in this document.

[[File:Verytight troublesome smd freq.log]]
[[File:Verytight troublesome smd freq.txt]]
[[File:Verytight troublesome smd opt.log]]
[[File:Verytight troublesome smd opt.txt]]

Check your new optimisation log file at the end of the calculation for convergence. In the example above, I get

You can now see that the threshold for force and displacement has tightened and all four values have converged. In the subsequent frequency file, the imaginary frequencies have now disappeared:

Mod:Hunt Research Group:troublesome smd

2018-04-21T21:26:52Z

Sl7514: Created page with "SMD calculations with large imaginary frequencies During your SMD calculations, you may run into a situation where the Gaussian optimisation has terminated normally but still..."

SMD calculations with large imaginary frequencies

During your SMD calculations, you may run into a situation where the Gaussian optimisation has terminated normally but still contains large imaginary frequencies. For example, take a look at the two files below:
[[File:Troublesome smd freq.log]]
[[File:Troublesome smd opt.log]]

Looking at the frequency file:

In general, the optimisation is terminated if one of the two criteria is met:
- When the force and the displacement have converged
- When the maximum force and RMS force are two orders of magnitude smaller than the threshold shown, regardless of displacement

First check your optimisation log file to see if the energy has been converging. The following is taken directly from the example log file above:
[[Troublesome smd optimisation figure.png]]

Check in your log file whether the force and the displacement have converged. The following is taken directly from the example log file above.

In this situation, it is likely that your optimisation has run into an area of potential energy surface which is quite flat and hence the optimisation will terminate since the force constant is below the threshold. However, the displacement is far from converging. It is possible to tighten the cutoffs on forces and step size that are used to determine convergence. Copy and paste the optimised structure with large imaginary frequency to new gaussian window and change the optimisation keyword from opt to opt=verytight.

Rerun your optimisation calculation with this keyword. In the four example files below, I have rerun the troublesome smd optimisation I have included earlier in this document.

[[File:Verytight troublesome smd freq.log]]
[[File:Verytight troublesome smd freq.txt]]
[[File:Verytight troublesome smd opt.log]]
[[File:Verytight troublesome smd opt.txt]]

Check your new optimisation log file at the end of the calculation for convergence. In the example above, I get

You can now see that the threshold for force and displacement has tightened and all four values have converged. In the subsequent frequency file, the imaginary frequencies have now disappeared:

File:Verytight troublesome smd opt.txt

2018-04-21T21:26:37Z

Sl7514:

File:Verytight troublesome smd opt.log

2018-04-21T21:26:14Z

Sl7514:

File:Verytight troublesome smd freq.txt

2018-04-21T21:25:44Z

Sl7514:

File:Verytight troublesome smd freq.log

2018-04-21T21:25:21Z

Sl7514:

File:Troublesome smd optimisation figure.png

2018-04-21T21:22:52Z

Sl7514:

File:Troublesome smd opt.log

2018-04-21T21:19:56Z

Sl7514:

File:Troublesome smd freq.log

2018-04-21T21:18:59Z

Sl7514:

Mod:Hunt Research Group

2018-04-21T18:24:03Z

Sl7514: /* Gaussian General */

==Hunt Group Wiki==

Back to the main [http://www.ch.ic.ac.uk/hunt web-page]
===Report and Paper Writing===
#procedures [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_procedures link]
#instructions [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_writing link]
#report components [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_components link]
#files to provide when writing a paper [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/paper link]

===Group Admin===
#Which files to store on the database and database template [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/database link]
#[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/calendar Calendar]

===HPC Resources===
#'''Hunt group HPC servers and run scripts''' [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc link]
#Computing resources available in the chemistry department [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/computing_resources link]
#How to set up cx2 [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cx2 link]
#Setting up a connection to HPC if you have a PC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc_connections link]
#How to fix Windows files under UNIX [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Windowsfiles link]
#How to make ssh more comfortable [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/pimpSSH link]
#How to make qsub more comfortable (gfunc) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/pimpQSUB link]
#Tired of entering your password all the time: set up a SSH keypair [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/SSHkeyfile link]
#Use Imperial Software Hub to access gaussview and gaussian [http://www.imperial.ac.uk/admin-services/ict/store/software/software-hub/ link]
#How to use gaussview directly on the HPC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/gview link]
#How to comfortably search through old BASH commands [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/searchbash link]
#Using VPN from home, for Sierra follow the college instructions [[link]]
#How to connect to HPC directory on desktop for file transfers - MacFusion [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc_Directory_on_desktop link]
#How to set-up remote desktop [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/mac_remote link]

===Key Papers, References and Resources===
#Meta study on DFT functionals [https://pubs.acs.org/doi/abs/10.1021/ct401111c doi]
#M06 suite of DFT functionals [https://link.springer.com/article/10.1007/s00214-007-0310-x doi]
#SMD for ILs [https://pubs.acs.org/doi/abs/10.1021/jp304365v doi]

===Gaussian General===
#We are starting a database of common errors encountered when running Gaussian jobs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/gaussian_errors link]
# Here is an already existing database of common errors [https://www.ace-net.ca/wiki/Gaussian_Error_Messages link]
# [http://www.ch.ic.ac.uk/hunt/g03_man/index.htm G03 Manual]
#How to run NBO5.9 on the HPC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/NBO5.9 link]
#How to include dispersion [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/dispersion link]
#Basic ONIOM (Mechanical Embedding) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/basiconiom link]
#M0n and DFT-D [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/DFTD link]
#IL ONIOM clusters [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/oniomclusers link]
#Molecular volume calculations [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/molecular_volume link]
#problems with scf convergence [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/scf_convergence link]
#partial optimisations and scans [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/z-matrix link]
#generating natural transition orbitals [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/nto link]
#Using solvent models [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/solvent link]
#Using SMD on ILs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_Using_SMD_on_ILs link]
#computing excited state polarisabilities [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_ES_alpha link]
#computing deuterated and/or anharmonic spectra [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_Danharm link]
#manipulating checkpoint files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:usingchkfiles link]
#for NMR calculations look here: [http://cheshirenmr.info/index.htm Chemical Shift Repository]
#Script to pull thermodynamic data and low frequencies from log files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:freq_script link]
#General procedure for locating transition state structures [[link]]
#Troublesome optimisations in SMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:troublesome_smd link]

===Codes to Help Gaussian Analysis===
# Extract E2 Values (From NBO Calculations) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/NBO_Matlab_Code link]
# Extract last Standard Orientation structure of gaussian log file [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/extract_single_geom link]
# Extract geometry and charges (ESP) into a .pdb file for visualising in VMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ESP_charges_for_VMD link]
# Extract ESP and NBO charges [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/extract_ESP_charges link]
# Calculate pDoS/XP spectra code (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Calc_XPS_Code link]
# Codes to extract frequency data from gaussian .log files and generate vibrational spectra [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:frequency_spectrum_script link]
# Optimally Tuned Range Seperated Hybrid Functionals [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/OTRSH_Funct link]
# Some G09 Parsers [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Some_G09_Parsers link]
# Codes to extract CHELPG and NBO charge values to excel [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/chelpg_extract link]

===QC Visualisation===
*'''Using AIMALL: density based visualisation'''
#download [http://aim.tkgristmill.com AIMALL]
#basic instructions [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:aim_basics link]
#AimAll with pseudo potentials [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:aim_pseudopotentials link]

*'''ESPs and manipulating gaussian cube files'''
#Instructions for visualizing electrostatic potentials (Gaussview)[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/electrostatic_potentials link]
#Electrostatic Potentials II (Molden) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/electrostatic_potentials_2 link]
#Manipulating cube files [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/cube_files link]
#Format of cube files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/cube_format link]
#Using A. Stone's distributed multipole analysis [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/GDMA link]

*'''NCI plots'''
#get the program here: [http://www.lct.jussieu.fr/pagesperso/contrera/nciplot.html link]
#How to install NCIPlot on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/InstallNCIPlot link]
#Using NCIPlot [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/UseNCIPlot link]

*'''GeomView'''
#How to download and use GeomView to visualise solvation cavities [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/geomview link]

===Other Visualisation===
*'''JMol'''
#Visualising MOs using Jmol [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:basic_jmol_instructions link]
#Surfaces (Solvent-Accessible and Connolly) in Jmol [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/jmolsurfaces link]

*'''PyGauss'''
#Python API for analysis of Gaussian compuations [https://pygauss.readthedocs.org - Documentation]

===Setup and Running Classical MD Simulations===
#DLPOLY a MD simulation package, Installation on an IMac (old needs to be updated) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/dlpoly_install link]
#DL_POLY FAQs [http://www.stfc.ac.uk/cse/DL_POLY/ccp1gui/38621.aspx] from DL_POLY webpage.
#Installing Packmol
#Getting started: generating a solvated structure and "relaxing" it [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Starting_MD link]
#Equilibration and production simulations [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/EquilibrationandProduction link]
#How to equilibrate an MD run[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/equilibration link]
#Getting the Force Field [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Wheretostart link]
#Choosing an Ensemble [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Ensembles link]
#Molten Salt Simulations [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/MoltenSaltSimulation link]
#Common Errors [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/CommonErrors link]
#Voids in ILs[https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/voids link]
#Equilibration of [bmim][BF4] and [bmim][NO3][https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/BmimBF4_equilibration link]
#Summary of discussions with Ruth[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Aug09QtoRuth link]

===MD Visualisation===
*'''VMD: a molecular dynamics visualisation package'''
#Download VMD [//wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/download_vmd link]
#Quick reminder [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VMDReminder link]
#Tricks and tips [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VMDTips link]
#Changing the graphical representation of your structures [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/vmd link]
#Basic visualisation of a trajectory [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VisualisingyourSimulation link]
#How to turn a Gaussian optimization into a VMD movie [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/VMDmovie link]
#Using scripts in VMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdScripts link]
#Dealing with periodic boundaries and bonding (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdScriptsPeriodic link]
#Dealing with bonding (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdBonding link]
#Overlapping two structures [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdVisual link]

*'''SDFs'''
#How to generate SDFs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/sdfs_generate link]

===MD Post processing===
#Code to Recentre DL_PLOY HISTORY file [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/recentre_xyz.py link]
#Link to the code to convert the DL_POLY HISTORY file to the multi-frame XYZ file[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/his2xyz.py link]
#Convert a HISTORY file into an xyz file ('''needs fixing''') [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/hist_to_xyz link]
#Center the trajectory at a particular atom ('''needs fixing''') [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Recenter link]
#How to generate SDFs with TRAVIS [[Talk:Mod:Hunt Research Group/How to draw SDFs with TRAVIS|link]]

===Coding===
*'''installing Xcode and other programming environments'''
#to use many programs you will need a compiler, this is not installed by default on your mac
#How to install Xcode on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/InstallXcode link]
#using MacPorts as code for managing other codes on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/MacPorts link]
#HomeBrew and Fink are other options (HomeBrew is not advised for us)
#gfortran on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Gfortran link]
#using python on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/python link]

*'''EMO Code'''
#How to use Ling's emo plot code[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emoplot link]
#How to plot EMOs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emo link]

*'''Jan's charge based analysis Code'''
#charge analysis [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Jan_charges link]

*'''Oxana's visualisation of ESPs Code'''
#Scripts for reading, saving, manipulating and visualising data from cube files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Python_scripts_for_cube_files link]

===Other Codes===
#ADF Submission script [http://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/ADF_sricpt link]
#How to install POLYRATE [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/polyrate link]
#XMGRACE, gfortran, c compilers for Lion [http://hpc.sourceforge.net/]

===Setup and Running Ab-Initio MD Simulations===
#CPMD: Car-Parrinello Molecular Dynamics [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/cpmd link]
#How to run CPMD to study aqueous solutions [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/cpmd_water link]
#How to run CP2K [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cp2k_how link]
#[bmim]Cl using CPMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/bmimCl_cpmd link]
#[bmim]Cl using CP2K [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/bmimCl_cp2k link]
#mman using CPMD and Gaussian [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/mman link]
#[emim]SCN using CP2K[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emimscn link]
#CP2K Donts [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cp2k link]

===Running QM/MM Simulations in ChemShell===
#ChemShell official website which contains the manual and a tutorial [http://www.stfc.ac.uk/CSE/randd/ccg/36254.aspx link]
#Introduction to ChemShell - Copper in water [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_Introduction link]
#Defining the system: Cu<sup>2+</sup> and its first 2 solvation shells [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_System_Aqeuous_Cu(II) link]
#Defining the force field parameters [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_Force_Field_Parameters_Aqueous_Cu(II) link]
#Single point QM/MM energy calculation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_SP_Aqeuous_Cu(II) link]
#QM/MM Optimisation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_OPT_Aqeuous_Cu(II) link]
#QM/MM Molecular Dynamics [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_MD_Aqeuous_Cu(II) link]
#Using MolCluster [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/MolCluster link]
#Running ChemShell [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell link]
#Explaining ChemShell files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_files link]
#Step By Step [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Chemshell_Step_By_Step link]

===Research Notes===
#Cl- in water [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/wannier_centre link]
#The use of Legendre time correlation functions to study reorientational dynamics in liquids[https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/legendre link]
#Functional for ILs using CPMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/IL_cpmd_functional link]
#Solving the angular part of the Schrödinger equation for a hydrogen atom [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/angular_schrodinger link] (notes by Vincent)
#Systematic conformational scan for ion-pair dimers [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ion_pair_scan link]
#Obtaining NBO, ESP, and RESP charges [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Charges link]
#DFT Workshop Notes [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/DFT_Workshop]

===Admin Stuff===
#Not used to writing a wiki, make your test runs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/testing on this page]
#How to set-up new macs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/mac_setup link]
#How to switch the printer HP CP3525dn duplex on and off [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/printing link]

Mod:Hunt Research Group

2018-03-13T16:41:33Z

Sl7514:

==Hunt Group Wiki==

Back to the main [http://www.ch.ic.ac.uk/hunt web-page]
===Report and Paper Writing===
#procedures [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_procedures link]
#instructions [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_writing link]
#report components [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_components link]
#files to provide when writing a paper [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/paper link]

===Group Admin===
#Which files to store on the database and database template [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/database link]
#[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/calendar Calendar]

===HPC Resources===
#'''Hunt group HPC servers and run scripts''' [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc link]
#Computing resources available in the chemistry department [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/computing_resources link]
#How to set up cx2 [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cx2 link]
#Setting up a connection to HPC if you have a PC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc_connections link]
#How to fix Windows files under UNIX [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Windowsfiles link]
#How to make ssh more comfortable [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/pimpSSH link]
#How to make qsub more comfortable (gfunc) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/pimpQSUB link]
#Tired of entering your password all the time: set up a SSH keypair [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/SSHkeyfile link]
#Use Imperial Software Hub to access gaussview and gaussian [http://www.imperial.ac.uk/admin-services/ict/store/software/software-hub/ link]
#How to use gaussview directly on the HPC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/gview link]
#How to comfortably search through old BASH commands [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/searchbash link]
#Using VPN from home, for Sierra follow the college instructions [[link]]
#How to connect to HPC directory on desktop for file transfers - MacFusion [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc_Directory_on_desktop link]
#How to set-up remote desktop [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/mac_remote link]

===Key Papers, References and Resources===
#Meta study on DFT functionals [https://pubs.acs.org/doi/abs/10.1021/ct401111c doi]
#M06 suite of DFT functionals [https://link.springer.com/article/10.1007/s00214-007-0310-x doi]
#SMD for ILs [https://pubs.acs.org/doi/abs/10.1021/jp304365v doi]

===Gaussian General===
#We are starting a database of common errors encountered when running Gaussian jobs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/gaussian_errors link]
# Here is an already existing database of common errors [https://www.ace-net.ca/wiki/Gaussian_Error_Messages link]
# [http://www.ch.ic.ac.uk/hunt/g03_man/index.htm G03 Manual]
#How to run NBO5.9 on the HPC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/NBO5.9 link]
#How to include dispersion [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/dispersion link]
#Basic ONIOM (Mechanical Embedding) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/basiconiom link]
#M0n and DFT-D [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/DFTD link]
#IL ONIOM clusters [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/oniomclusers link]
#Molecular volume calculations [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/molecular_volume link]
#problems with scf convergence [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/scf_convergence link]
#partial optimisations and scans [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/z-matrix link]
#generating natural transition orbitals [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/nto link]
#Using solvent models [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/solvent link]
#Using SMD on ILs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_Using_SMD_on_ILs link]
#computing excited state polarisabilities [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_ES_alpha link]
#computing deuterated and/or anharmonic spectra [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_Danharm link]
#manipulating checkpoint files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:usingchkfiles link]
#for NMR calculations look here: [http://cheshirenmr.info/index.htm Chemical Shift Repository]
#Script to pull thermodynamic data and low frequencies from log files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:freq_script link]
#General procedure for locating transition state structures [[link]]

===Codes to Help Gaussian Analysis===
# Extract E2 Values (From NBO Calculations) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/NBO_Matlab_Code link]
# Extract last Standard Orientation structure of gaussian log file [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/extract_single_geom link]
# Extract geometry and charges (ESP) into a .pdb file for visualising in VMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ESP_charges_for_VMD link]
# Extract ESP and NBO charges [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/extract_ESP_charges link]
# Calculate pDoS/XP spectra code (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Calc_XPS_Code link]
# Codes to extract frequency data from gaussian .log files and generate vibrational spectra [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:frequency_spectrum_script link]
# Optimally Tuned Range Seperated Hybrid Functionals [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/OTRSH_Funct link]
# Some G09 Parsers [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Some_G09_Parsers link]
# Codes to extract CHELPG and NBO charge values to excel [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/chelpg_extract link]

===QC Visualisation===
*'''Using AIMALL: density based visualisation'''
#download [http://aim.tkgristmill.com AIMALL]
#basic instructions [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:aim_basics link]
#AimAll with pseudo potentials [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:aim_pseudopotentials link]

*'''ESPs and manipulating gaussian cube files'''
#Instructions for visualizing electrostatic potentials (Gaussview)[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/electrostatic_potentials link]
#Electrostatic Potentials II (Molden) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/electrostatic_potentials_2 link]
#Manipulating cube files [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/cube_files link]
#Format of cube files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/cube_format link]
#Using A. Stone's distributed multipole analysis [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/GDMA link]

*'''NCI plots'''
#get the program here: [http://www.lct.jussieu.fr/pagesperso/contrera/nciplot.html link]
#How to install NCIPlot on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/InstallNCIPlot link]
#Using NCIPlot [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/UseNCIPlot link]

*'''GeomView'''
#How to download and use GeomView to visualise solvation cavities [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/geomview link]

===Other Visualisation===
*'''JMol'''
#Visualising MOs using Jmol [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:basic_jmol_instructions link]
#Surfaces (Solvent-Accessible and Connolly) in Jmol [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/jmolsurfaces link]

*'''PyGauss'''
#Python API for analysis of Gaussian compuations [https://pygauss.readthedocs.org - Documentation]

===Setup and Running Classical MD Simulations===
#DLPOLY a MD simulation package, Installation on an IMac (old needs to be updated) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/dlpoly_install link]
#DL_POLY FAQs [http://www.stfc.ac.uk/cse/DL_POLY/ccp1gui/38621.aspx] from DL_POLY webpage.
#Installing Packmol
#Getting started: generating a solvated structure and "relaxing" it [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Starting_MD link]
#Equilibration and production simulations [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/EquilibrationandProduction link]
#How to equilibrate an MD run[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/equilibration link]
#Getting the Force Field [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Wheretostart link]
#Choosing an Ensemble [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Ensembles link]
#Molten Salt Simulations [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/MoltenSaltSimulation link]
#Common Errors [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/CommonErrors link]
#Voids in ILs[https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/voids link]
#Equilibration of [bmim][BF4] and [bmim][NO3][https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/BmimBF4_equilibration link]
#Summary of discussions with Ruth[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Aug09QtoRuth link]

===MD Visualisation===
*'''VMD: a molecular dynamics visualisation package'''
#Download VMD [//wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/download_vmd link]
#Quick reminder [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VMDReminder link]
#Tricks and tips [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VMDTips link]
#Changing the graphical representation of your structures [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/vmd link]
#Basic visualisation of a trajectory [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VisualisingyourSimulation link]
#How to turn a Gaussian optimization into a VMD movie [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/VMDmovie link]
#Using scripts in VMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdScripts link]
#Dealing with periodic boundaries and bonding (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdScriptsPeriodic link]
#Dealing with bonding (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdBonding link]
#Overlapping two structures [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdVisual link]

*'''SDFs'''
#How to generate SDFs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/sdfs_generate link]

===MD Post processing===
#Code to Recentre DL_PLOY HISTORY file [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/recentre_xyz.py link]
#Link to the code to convert the DL_POLY HISTORY file to the multi-frame XYZ file[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/his2xyz.py link]
#Convert a HISTORY file into an xyz file ('''needs fixing''') [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/hist_to_xyz link]
#Center the trajectory at a particular atom ('''needs fixing''') [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Recenter link]
#How to generate SDFs with TRAVIS [[Talk:Mod:Hunt Research Group/How to draw SDFs with TRAVIS|link]]

===Coding===
*'''installing Xcode and other programming environments'''
#to use many programs you will need a compiler, this is not installed by default on your mac
#How to install Xcode on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/InstallXcode link]
#using MacPorts as code for managing other codes on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/MacPorts link]
#HomeBrew and Fink are other options (HomeBrew is not advised for us)
#gfortran on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Gfortran link]
#using python on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/python link]

*'''EMO Code'''
#How to use Ling's emo plot code[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emoplot link]
#How to plot EMOs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emo link]

===Other Codes===
#ADF Submission script [http://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/ADF_sricpt link]
#How to install POLYRATE [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/polyrate link]
#XMGRACE, gfortran, c compilers for Lion [http://hpc.sourceforge.net/]

===Setup and Running Ab-Initio MD Simulations===
#CPMD: Car-Parrinello Molecular Dynamics [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/cpmd link]
#How to run CPMD to study aqueous solutions [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/cpmd_water link]
#How to run CP2K [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cp2k_how link]
#[bmim]Cl using CPMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/bmimCl_cpmd link]
#[bmim]Cl using CP2K [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/bmimCl_cp2k link]
#mman using CPMD and Gaussian [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/mman link]
#[emim]SCN using CP2K[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emimscn link]
#CP2K Donts [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cp2k link]

===Running QM/MM Simulations in ChemShell===
#ChemShell official website which contains the manual and a tutorial [http://www.stfc.ac.uk/CSE/randd/ccg/36254.aspx link]
#Introduction to ChemShell - Copper in water [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_Introduction link]
#Defining the system: Cu<sup>2+</sup> and its first 2 solvation shells [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_System_Aqeuous_Cu(II) link]
#Defining the force field parameters [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_Force_Field_Parameters_Aqueous_Cu(II) link]
#Single point QM/MM energy calculation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_SP_Aqeuous_Cu(II) link]
#QM/MM Optimisation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_OPT_Aqeuous_Cu(II) link]
#QM/MM Molecular Dynamics [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_MD_Aqeuous_Cu(II) link]
#Using MolCluster [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/MolCluster link]
#Running ChemShell [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell link]
#Explaining ChemShell files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_files link]
#Step By Step [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Chemshell_Step_By_Step link]

===Research Notes===
#Cl- in water [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/wannier_centre link]
#The use of Legendre time correlation functions to study reorientational dynamics in liquids[https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/legendre link]
#Functional for ILs using CPMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/IL_cpmd_functional link]
#Solving the angular part of the Schrödinger equation for a hydrogen atom [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/angular_schrodinger link] (notes by Vincent)
#Systematic conformational scan for ion-pair dimers [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ion_pair_scan link]
#Obtaining NBO, ESP, and RESP charges [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Charges link]
#DFT Workshop Notes [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/DFT_Workshop]

===Admin Stuff===
#Not used to writing a wiki, make your test runs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/testing on this page]
#How to set-up new macs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/mac_setup link]
#How to switch the printer HP CP3525dn duplex on and off [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/printing link]

File:Nbo charge script.txt

2018-03-08T12:39:41Z

Sl7514: Sl7514 uploaded a new version of File:Nbo charge script.txt

Mod:Hunt Research Group/chelpg extract

2018-03-08T12:10:33Z

Sl7514:

Before running the code please ensure you have XlsxWriter python module and python version later than 3.5.

Python code to extract charge values from CHELPG calculation log file: [[File:Chelpg.txt]]

Here is an example log file to test the code: [[File:Test chelpg.log]]

Here is the correct excel file the code should generate: [[File:Test chelpg.xlsx]]

Python code to extract charge values from NBO calculation log file: [[File:Nbo charge script.txt]]

Here is an example log file to test the code: [[File:Test nbo.log]]

Here is the correct excel file the code should generate: [[File:Test nbo.xlsx]]

'''Instructions to run the python code from the same directory:'''

1. Download the code, change the extension to .py and place the code at the same directory as the .log file from CHELPG or NBO calculation you want to extract the charge values

2. Type either
python chelpg.py
or
python nbo_charge_script.py
to run the code

3. The code will ask
Enter filename:
type the name of the .log file exactly as it is, e.g.
test_chelpg.log
4. If the code has run successfully, it should generate an excel file with the title same as the log file and return
Generated your_file_name.xlsx file

'''Instructions to run the python code with alias:'''

If you need to do CHELPG or NBO analysis on many log files, it may be more convenient to create an alias rather than copying the code to the directory each time you need to run the code. Here are the instructions:

1. Download the code, change the extension to .py and place the code at the desired directory. I would recommend creating a folder dedicated to python scripts at your home directory.

2. Go to your home directory and type:
vim .bash_profile
3. Enter following texts to .bash_profile file where the alias are:
alias nbo_charge="python ~/path/to/directory/where/you/placed/python/scripts/nbo_charge_script.py"

alias chelpg_charge="python ~/path/to/directory/where/you/placed/python/scripts/chelp.py"
4. Now go to the directory where you have the .log files you want to extract charge values from NBO or CHELPG calculation. You can now run the code by simply typing the commands below to the terminal:
nbo_charge
or
chelpg_charge

Mod:Hunt Research Group/chelpg extract

2018-03-08T12:10:13Z

Sl7514:

Before running the code please ensure you have XlsxWriter python module and python version later than 3.5.

Python code to extract charge values from CHELPG calculation log file: [[File:Chelpg.txt]]

Here is an example log file to test the code: [[File:Test chelpg.log]]

Here is the correct excel file the code should generate: [[File:Test chelpg.xlsx]]

Python code to extract charge values from NBO calculation log file: [[File:Nbo charge script.txt]]

Here is an example log file to test the code: [[File:Test nbo.log]]

Here is the correct excel file the code should generate: [[File:Test nbo.xlsx]]

'''Instructions to run the python code from the same directory:'''

1. Download the code, change the extension to .py and place the code at the same directory as the .log file from CHELPG or NBO calculation you want to extract the charge values

2. Type either
python chelpg.py
or
python nbo_charge_script.py
to run the code

3. The code will ask
Enter filename:
type the name of the .log file exactly as it is, e.g.
test_chelpg.log
4. If the code has run successfully, it should generate an excel file with the title same as the log file and return
Generated your_file_name.xlsx file

'''Instructions to run the python code with alias:'''
If you need to do CHELPG or NBO analysis on many log files, it may be more convenient to create an alias rather than copying the code to the directory each time you need to run the code. Here are the instructions:

1. Download the code, change the extension to .py and place the code at the desired directory. I would recommend creating a folder dedicated to python scripts at your home directory.

2. Go to your home directory and type:
vim .bash_profile
3. Enter following texts to .bash_profile file where the alias are:
alias nbo_charge="python ~/path/to/directory/where/you/placed/python/scripts/nbo_charge_script.py"

alias chelpg_charge="python ~/path/to/directory/where/you/placed/python/scripts/chelp.py"
4. Now go to the directory where you have the .log files you want to extract charge values from NBO or CHELPG calculation. You can now run the code by simply typing the commands below to the terminal:
nbo_charge
or
chelpg_charge

Mod:Hunt Research Group/chelpg extract

2018-03-08T12:00:03Z

Sl7514:

Before running the code please ensure you have XlsxWriter python module.

Python code to extract charge values from CHELPG calculation log file: [[File:Chelpg.txt]]

Here is an example log file to test the code: [[File:Test chelpg.log]]

Here is the correct excel file the code should generate: [[File:Test chelpg.xlsx]]

Python code to extract charge values from NBO calculation log file: [[File:Nbo charge script.txt]]

Here is an example log file to test the code: [[File:Test nbo.log]]

Here is the correct excel file the code should generate: [[File:Test nbo.xlsx]]

'''Instructions to run the python code from the same directory:'''

'''Instructions to run the python code with alias:'''

If you need to do CHELPG or NBO analysis on many log files, it may be more convenient to create an alias rather than copying the code to the directory each time you need to run the code. Here are the instructions:

1. Download the code, change the extension to .py and place the code at the desired directory. I would recommend creating a folder dedicated to python scripts at your home directory.

2. Go to your home directory and type:

3. Enter following texts to

Mod:Hunt Research Group/chelpg extract

2018-03-08T11:54:32Z

Sl7514:

Mod:Hunt Research Group/chelpg extract

2018-03-08T11:54:15Z

Sl7514:

File:Test nbo.xlsx

2018-03-08T11:54:00Z

Sl7514:

File:Test nbo.log

2018-03-08T11:53:40Z

Sl7514:

File:Nbo charge script.txt

2018-03-08T11:53:19Z

Sl7514:

File:Test chelpg.xlsx

2018-03-08T11:52:38Z

Sl7514:

File:Test chelpg.log

2018-03-08T11:52:06Z

Sl7514:

File:Chelpg.txt

2018-03-08T11:48:30Z

Sl7514: Python code to extract charge values from CHLEPG calculation

Python code to extract charge values from CHLEPG calculation

Mod:Hunt Research Group/chelpg extract

2018-03-08T11:41:40Z

Sl7514: Created page with "Before running the code please ensure you have XlsxWriter python module:"

Before running the code please ensure you have XlsxWriter python module:

Mod:Hunt Research Group

2018-03-08T11:40:20Z

Sl7514: /* Codes to Help Gaussian Analysis */

==Hunt Group Wiki==

Back to the main [http://www.ch.ic.ac.uk/hunt web-page]
===Report and Paper Writing===
#procedures [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_procedures link]
#instructions [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_writing link]
#report components [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_components link]
#files to provide when writing a paper [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/paper link]

===Group Admin===
#Which files to store on the database and database template [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/database link]
#[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/calendar Calendar]

===HPC Resources===
#'''Hunt group HPC servers and run scripts''' [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc link]
#Computing resources available in the chemistry department [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/computing_resources link]
#How to set up cx2 [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cx2 link]
#Setting up a connection to HPC if you have a PC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc_connections link]
#How to fix Windows files under UNIX [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Windowsfiles link]
#How to make ssh more comfortable [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/pimpSSH link]
#How to make qsub more comfortable (gfunc) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/pimpQSUB link]
#Tired of entering your password all the time: set up a SSH keypair [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/SSHkeyfile link]
#How to use gaussview directly on the HPC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/gview link]
#How to comfortably search through old BASH commands [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/searchbash link]
#Using VPN from home, for Sierra follow the college instructions [[link]]
#How to connect to HPC directory on desktop for file transfers - MacFusion [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc_Directory_on_desktop link]
#How to set-up remote desktop [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/mac_remote link]

===Key Papers, References and Resources===
#Meta study on DFT functionals [https://pubs.acs.org/doi/abs/10.1021/ct401111c doi]
#M06 suite of DFT functionals [https://link.springer.com/article/10.1007/s00214-007-0310-x doi]
#SMD for ILs [https://pubs.acs.org/doi/abs/10.1021/jp304365v doi]

===Gaussian General===
#We are starting a database of common errors encountered when running Gaussian jobs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/gaussian_errors link]
# Here is an already existing database of common errors [https://www.ace-net.ca/wiki/Gaussian_Error_Messages link]
# [http://www.ch.ic.ac.uk/hunt/g03_man/index.htm G03 Manual]
#How to run NBO5.9 on the HPC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/NBO5.9 link]
#How to include dispersion [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/dispersion link]
#Basic ONIOM (Mechanical Embedding) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/basiconiom link]
#M0n and DFT-D [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/DFTD link]
#IL ONIOM clusters [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/oniomclusers link]
#Molecular volume calculations [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/molecular_volume link]
#problems with scf convergence [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/scf_convergence link]
#partial optimisations and scans [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/z-matrix link]
#generating natural transition orbitals [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/nto link]
#Using solvent models [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/solvent link]
#Using SMD on ILs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_Using_SMD_on_ILs link]
#computing excited state polarisabilities [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_ES_alpha link]
#computing deuterated and/or anharmonic spectra [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_Danharm link]
#manipulating checkpoint files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:usingchkfiles link]
#for NMR calculations look here: [http://cheshirenmr.info/index.htm Chemical Shift Repository]
#Script to pull thermodynamic data and low frequencies from log files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:freq_script link]
#General procedure for locating transition state structures [[link]]

===Codes to Help Gaussian Analysis===
# Extract E2 Values (From NBO Calculations) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/NBO_Matlab_Code link]
# Extract last Standard Orientation structure of gaussian log file [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/extract_single_geom link]
# Extract geometry and charges (ESP) into a .pdb file for visualising in VMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ESP_charges_for_VMD link]
# Extract ESP and NBO charges [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/extract_ESP_charges link]
# Calculate pDoS/XP spectra code (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Calc_XPS_Code link]
# Codes to extract frequency data from gaussian .log files and generate vibrational spectra [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:frequency_spectrum_script link]
# Optimally Tuned Range Seperated Hybrid Functionals [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/OTRSH_Funct link]
# Some G09 Parsers [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Some_G09_Parsers link]
# Codes to extract chelpg and charge values to excel [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/chelpg_extract link]

===QC Visualisation===
*'''Using AIMALL: density based visualisation'''
#download [http://aim.tkgristmill.com AIMALL]
#basic instructions [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:aim_basics link]
#AimAll with pseudo potentials [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:aim_pseudopotentials link]

*'''ESPs and manipulating gaussian cube files'''
#Instructions for visualizing electrostatic potentials (Gaussview)[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/electrostatic_potentials link]
#Electrostatic Potentials II (Molden) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/electrostatic_potentials_2 link]
#Manipulating cube files [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/cube_files link]
#Format of cube files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/cube_format link]
#Using A. Stone's distributed multipole analysis [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/GDMA link]

*'''NCI plots'''
#get the program here: [http://www.lct.jussieu.fr/pagesperso/contrera/nciplot.html link]
#How to install NCIPlot on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/InstallNCIPlot link]
#Using NCIPlot [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/UseNCIPlot link]

*'''GeomView'''
#How to download and use GeomView to visualise solvation cavities [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/geomview link]

===Other Visualisation===
*'''JMol'''
#Visualising MOs using Jmol [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:basic_jmol_instructions link]
#Surfaces (Solvent-Accessible and Connolly) in Jmol [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/jmolsurfaces link]

*'''PyGauss'''
#Python API for analysis of Gaussian compuations [https://pygauss.readthedocs.org - Documentation]

===Setup and Running Classical MD Simulations===
#DLPOLY a MD simulation package, Installation on an IMac (old needs to be updated) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/dlpoly_install link]
#DL_POLY FAQs [http://www.stfc.ac.uk/cse/DL_POLY/ccp1gui/38621.aspx] from DL_POLY webpage.
#Installing Packmol
#Getting started: generating a solvated structure and "relaxing" it [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Starting_MD link]
#Equilibration and production simulations [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/EquilibrationandProduction link]
#How to equilibrate an MD run[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/equilibration link]
#Getting the Force Field [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Wheretostart link]
#Choosing an Ensemble [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Ensembles link]
#Molten Salt Simulations [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/MoltenSaltSimulation link]
#Common Errors [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/CommonErrors link]
#Voids in ILs[https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/voids link]
#Equilibration of [bmim][BF4] and [bmim][NO3][https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/BmimBF4_equilibration link]
#Summary of discussions with Ruth[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Aug09QtoRuth link]

===MD Visualisation===
*'''VMD: a molecular dynamics visualisation package'''
#Download VMD [//wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/download_vmd link]
#Quick reminder [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VMDReminder link]
#Tricks and tips [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VMDTips link]
#Changing the graphical representation of your structures [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/vmd link]
#Basic visualisation of a trajectory [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VisualisingyourSimulation link]
#How to turn a Gaussian optimization into a VMD movie [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/VMDmovie link]
#Using scripts in VMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdScripts link]
#Dealing with periodic boundaries and bonding (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdScriptsPeriodic link]
#Dealing with bonding (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdBonding link]
#Overlapping two structures [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdVisual link]

*'''SDFs'''
#How to generate SDFs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/sdfs_generate link]

===MD Post processing===
#Code to Recentre DL_PLOY HISTORY file [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/recentre_xyz.py link]
#Link to the code to convert the DL_POLY HISTORY file to the multi-frame XYZ file[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/his2xyz.py link]
#Convert a HISTORY file into an xyz file ('''needs fixing''') [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/hist_to_xyz link]
#Center the trajectory at a particular atom ('''needs fixing''') [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Recenter link]
#How to generate SDFs with TRAVIS [[Talk:Mod:Hunt Research Group/How to draw SDFs with TRAVIS|link]]

===Coding===
*'''installing Xcode and other programming environments'''
#to use many programs you will need a compiler, this is not installed by default on your mac
#How to install Xcode on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/InstallXcode link]
#using MacPorts as code for managing other codes on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/MacPorts link]
#HomeBrew and Fink are other options (HomeBrew is not advised for us)
#gfortran on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Gfortran link]
#using python on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/python link]

*'''EMO Code'''
#How to use Ling's emo plot code[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emoplot link]
#How to plot EMOs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emo link]

===Other Codes===
#ADF Submission script [http://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/ADF_sricpt link]
#How to install POLYRATE [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/polyrate link]
#XMGRACE, gfortran, c compilers for Lion [http://hpc.sourceforge.net/]

===Setup and Running Ab-Initio MD Simulations===
#CPMD: Car-Parrinello Molecular Dynamics [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/cpmd link]
#How to run CPMD to study aqueous solutions [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/cpmd_water link]
#How to run CP2K [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cp2k_how link]
#[bmim]Cl using CPMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/bmimCl_cpmd link]
#[bmim]Cl using CP2K [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/bmimCl_cp2k link]
#mman using CPMD and Gaussian [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/mman link]
#[emim]SCN using CP2K[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emimscn link]
#CP2K Donts [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cp2k link]

===Running QM/MM Simulations in ChemShell===
#ChemShell official website which contains the manual and a tutorial [http://www.stfc.ac.uk/CSE/randd/ccg/36254.aspx link]
#Introduction to ChemShell - Copper in water [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_Introduction link]
#Defining the system: Cu<sup>2+</sup> and its first 2 solvation shells [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_System_Aqeuous_Cu(II) link]
#Defining the force field parameters [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_Force_Field_Parameters_Aqueous_Cu(II) link]
#Single point QM/MM energy calculation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_SP_Aqeuous_Cu(II) link]
#QM/MM Optimisation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_OPT_Aqeuous_Cu(II) link]
#QM/MM Molecular Dynamics [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_MD_Aqeuous_Cu(II) link]
#Using MolCluster [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/MolCluster link]
#Running ChemShell [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell link]
#Explaining ChemShell files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_files link]
#Step By Step [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Chemshell_Step_By_Step link]

===Research Notes===
#Cl- in water [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/wannier_centre link]
#The use of Legendre time correlation functions to study reorientational dynamics in liquids[https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/legendre link]
#Functional for ILs using CPMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/IL_cpmd_functional link]
#Solving the angular part of the Schrödinger equation for a hydrogen atom [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/angular_schrodinger link] (notes by Vincent)
#Systematic conformational scan for ion-pair dimers [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ion_pair_scan link]
#Obtaining NBO, ESP, and RESP charges [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Charges link]
#DFT Workshop Notes [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/DFT_Workshop]

===Admin Stuff===
#Not used to writing a wiki, make your test runs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/testing on this page]
#How to set-up new macs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/mac_setup link]
#How to switch the printer HP CP3525dn duplex on and off [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/printing link]

Mod:Hunt Research Group

2018-03-08T11:39:33Z

Sl7514: /* Codes to Help Gaussian Analysis */

==Hunt Group Wiki==

Back to the main [http://www.ch.ic.ac.uk/hunt web-page]
===Report and Paper Writing===
#procedures [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_procedures link]
#instructions [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_writing link]
#report components [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/report_components link]
#files to provide when writing a paper [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/paper link]

===Group Admin===
#Which files to store on the database and database template [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/database link]
#[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/calendar Calendar]

===HPC Resources===
#'''Hunt group HPC servers and run scripts''' [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc link]
#Computing resources available in the chemistry department [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/computing_resources link]
#How to set up cx2 [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cx2 link]
#Setting up a connection to HPC if you have a PC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc_connections link]
#How to fix Windows files under UNIX [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Windowsfiles link]
#How to make ssh more comfortable [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/pimpSSH link]
#How to make qsub more comfortable (gfunc) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/pimpQSUB link]
#Tired of entering your password all the time: set up a SSH keypair [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/SSHkeyfile link]
#How to use gaussview directly on the HPC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/gview link]
#How to comfortably search through old BASH commands [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/searchbash link]
#Using VPN from home, for Sierra follow the college instructions [[link]]
#How to connect to HPC directory on desktop for file transfers - MacFusion [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/hpc_Directory_on_desktop link]
#How to set-up remote desktop [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/mac_remote link]

===Key Papers, References and Resources===
#Meta study on DFT functionals [https://pubs.acs.org/doi/abs/10.1021/ct401111c doi]
#M06 suite of DFT functionals [https://link.springer.com/article/10.1007/s00214-007-0310-x doi]
#SMD for ILs [https://pubs.acs.org/doi/abs/10.1021/jp304365v doi]

===Gaussian General===
#We are starting a database of common errors encountered when running Gaussian jobs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/gaussian_errors link]
# Here is an already existing database of common errors [https://www.ace-net.ca/wiki/Gaussian_Error_Messages link]
# [http://www.ch.ic.ac.uk/hunt/g03_man/index.htm G03 Manual]
#How to run NBO5.9 on the HPC [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/NBO5.9 link]
#How to include dispersion [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/dispersion link]
#Basic ONIOM (Mechanical Embedding) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/basiconiom link]
#M0n and DFT-D [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/DFTD link]
#IL ONIOM clusters [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/oniomclusers link]
#Molecular volume calculations [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/molecular_volume link]
#problems with scf convergence [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/scf_convergence link]
#partial optimisations and scans [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/z-matrix link]
#generating natural transition orbitals [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/nto link]
#Using solvent models [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/solvent link]
#Using SMD on ILs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_Using_SMD_on_ILs link]
#computing excited state polarisabilities [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_ES_alpha link]
#computing deuterated and/or anharmonic spectra [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:_Danharm link]
#manipulating checkpoint files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:usingchkfiles link]
#for NMR calculations look here: [http://cheshirenmr.info/index.htm Chemical Shift Repository]
#Script to pull thermodynamic data and low frequencies from log files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:freq_script link]
#General procedure for locating transition state structures [[link]]

===Codes to Help Gaussian Analysis===
# Extract E2 Values (From NBO Calculations) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/NBO_Matlab_Code link]
# Extract last Standard Orientation structure of gaussian log file [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/extract_single_geom link]
# Extract geometry and charges (ESP) into a .pdb file for visualising in VMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ESP_charges_for_VMD link]
# Extract ESP and NBO charges [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/extract_ESP_charges link]
# Calculate pDoS/XP spectra code (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Calc_XPS_Code link]
# Codes to extract frequency data from gaussian .log files and generate vibrational spectra [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:frequency_spectrum_script link]
# Optimally Tuned Range Seperated Hybrid Functionals [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/OTRSH_Funct link]
# Some G09 Parsers [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Some_G09_Parsers link]
# Code to extract chelpg charge values [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/chelpg_extract link]

===QC Visualisation===
*'''Using AIMALL: density based visualisation'''
#download [http://aim.tkgristmill.com AIMALL]
#basic instructions [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:aim_basics link]
#AimAll with pseudo potentials [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group:aim_pseudopotentials link]

*'''ESPs and manipulating gaussian cube files'''
#Instructions for visualizing electrostatic potentials (Gaussview)[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/electrostatic_potentials link]
#Electrostatic Potentials II (Molden) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/electrostatic_potentials_2 link]
#Manipulating cube files [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/cube_files link]
#Format of cube files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/cube_format link]
#Using A. Stone's distributed multipole analysis [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/GDMA link]

*'''NCI plots'''
#get the program here: [http://www.lct.jussieu.fr/pagesperso/contrera/nciplot.html link]
#How to install NCIPlot on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/InstallNCIPlot link]
#Using NCIPlot [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/UseNCIPlot link]

*'''GeomView'''
#How to download and use GeomView to visualise solvation cavities [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/geomview link]

===Other Visualisation===
*'''JMol'''
#Visualising MOs using Jmol [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:basic_jmol_instructions link]
#Surfaces (Solvent-Accessible and Connolly) in Jmol [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/jmolsurfaces link]

*'''PyGauss'''
#Python API for analysis of Gaussian compuations [https://pygauss.readthedocs.org - Documentation]

===Setup and Running Classical MD Simulations===
#DLPOLY a MD simulation package, Installation on an IMac (old needs to be updated) [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/dlpoly_install link]
#DL_POLY FAQs [http://www.stfc.ac.uk/cse/DL_POLY/ccp1gui/38621.aspx] from DL_POLY webpage.
#Installing Packmol
#Getting started: generating a solvated structure and "relaxing" it [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Starting_MD link]
#Equilibration and production simulations [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/EquilibrationandProduction link]
#How to equilibrate an MD run[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/equilibration link]
#Getting the Force Field [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Wheretostart link]
#Choosing an Ensemble [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/Ensembles link]
#Molten Salt Simulations [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/MoltenSaltSimulation link]
#Common Errors [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/CommonErrors link]
#Voids in ILs[https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/voids link]
#Equilibration of [bmim][BF4] and [bmim][NO3][https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/BmimBF4_equilibration link]
#Summary of discussions with Ruth[https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Aug09QtoRuth link]

===MD Visualisation===
*'''VMD: a molecular dynamics visualisation package'''
#Download VMD [//wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/download_vmd link]
#Quick reminder [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VMDReminder link]
#Tricks and tips [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VMDTips link]
#Changing the graphical representation of your structures [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/vmd link]
#Basic visualisation of a trajectory [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/VisualisingyourSimulation link]
#How to turn a Gaussian optimization into a VMD movie [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/VMDmovie link]
#Using scripts in VMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdScripts link]
#Dealing with periodic boundaries and bonding (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdScriptsPeriodic link]
#Dealing with bonding (under construction) [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdBonding link]
#Overlapping two structures [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/VmdVisual link]

*'''SDFs'''
#How to generate SDFs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/sdfs_generate link]

===MD Post processing===
#Code to Recentre DL_PLOY HISTORY file [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/recentre_xyz.py link]
#Link to the code to convert the DL_POLY HISTORY file to the multi-frame XYZ file[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/his2xyz.py link]
#Convert a HISTORY file into an xyz file ('''needs fixing''') [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/hist_to_xyz link]
#Center the trajectory at a particular atom ('''needs fixing''') [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Recenter link]
#How to generate SDFs with TRAVIS [[Talk:Mod:Hunt Research Group/How to draw SDFs with TRAVIS|link]]

===Coding===
*'''installing Xcode and other programming environments'''
#to use many programs you will need a compiler, this is not installed by default on your mac
#How to install Xcode on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/InstallXcode link]
#using MacPorts as code for managing other codes on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/MacPorts link]
#HomeBrew and Fink are other options (HomeBrew is not advised for us)
#gfortran on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/Gfortran link]
#using python on your mac [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/python link]

*'''EMO Code'''
#How to use Ling's emo plot code[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emoplot link]
#How to plot EMOs [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emo link]

===Other Codes===
#ADF Submission script [http://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/ADF_sricpt link]
#How to install POLYRATE [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/polyrate link]
#XMGRACE, gfortran, c compilers for Lion [http://hpc.sourceforge.net/]

===Setup and Running Ab-Initio MD Simulations===
#CPMD: Car-Parrinello Molecular Dynamics [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/cpmd link]
#How to run CPMD to study aqueous solutions [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/cpmd_water link]
#How to run CP2K [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cp2k_how link]
#[bmim]Cl using CPMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/bmimCl_cpmd link]
#[bmim]Cl using CP2K [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/bmimCl_cp2k link]
#mman using CPMD and Gaussian [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/mman link]
#[emim]SCN using CP2K[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/emimscn link]
#CP2K Donts [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/cp2k link]

===Running QM/MM Simulations in ChemShell===
#ChemShell official website which contains the manual and a tutorial [http://www.stfc.ac.uk/CSE/randd/ccg/36254.aspx link]
#Introduction to ChemShell - Copper in water [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_Introduction link]
#Defining the system: Cu<sup>2+</sup> and its first 2 solvation shells [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_System_Aqeuous_Cu(II) link]
#Defining the force field parameters [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_Force_Field_Parameters_Aqueous_Cu(II) link]
#Single point QM/MM energy calculation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_SP_Aqeuous_Cu(II) link]
#QM/MM Optimisation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_OPT_Aqeuous_Cu(II) link]
#QM/MM Molecular Dynamics [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/QMMM_MD_Aqeuous_Cu(II) link]
#Using MolCluster [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/MolCluster link]
#Running ChemShell [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell link]
#Explaining ChemShell files [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ChemShell_files link]
#Step By Step [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/Chemshell_Step_By_Step link]

===Research Notes===
#Cl- in water [https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/wannier_centre link]
#The use of Legendre time correlation functions to study reorientational dynamics in liquids[https://www.ch.ic.ac.uk/wiki/index.php/Talk:Mod:Hunt_Research_Group/legendre link]
#Functional for ILs using CPMD [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/IL_cpmd_functional link]
#Solving the angular part of the Schrödinger equation for a hydrogen atom [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/angular_schrodinger link] (notes by Vincent)
#Systematic conformational scan for ion-pair dimers [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Talk:Mod:Hunt_Research_Group/ion_pair_scan link]
#Obtaining NBO, ESP, and RESP charges [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/Charges link]
#DFT Workshop Notes [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Hunt_Research_Group/DFT_Workshop]

===Admin Stuff===
#Not used to writing a wiki, make your test runs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/testing on this page]
#How to set-up new macs [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/mac_setup link]
#How to switch the printer HP CP3525dn duplex on and off [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group/printing link]

Mod:Hunt Research Group/calendar

2017-12-18T13:16:18Z

Sl7514:

Back to the main [https://www.ch.ic.ac.uk/wiki/index.php/Mod:Hunt_Research_Group wiki-page]
== Calendar ==

{| class="wikitable"
|-
! 1
! 2
! 3
|-
| Tricia (Not Done)
| Ken (Done)
| Becky (Not Done)
|-
| Sophie (Not Done)
| Lennart (Not Done)
| Oxana (Not Done)
|-
| Sanha (Done)
| Nerissa (Not Done)
|
|-
|-)
|}
Everyone should be away during the college closure dates, so you don't need to add your name on those days

Tricia maybe: Tricia may or may-not be in college i.e. working from home
{| class="wikitable" style="width: 100%"
!Mon
!Tue
!Wed
!Thur
!Fri
!Sat
!Sun
|-
|11st
Ken Away
|12th
Ken Away
|13th
Ken Away
|14th
|15th
| style="background: grey;" |16th
| style="background: grey;" |17th
|-
|18th
Sophie Away

Lennart in South Africa

Oxana away
|19th
Sophie Away

Lennart in South Africa

Oxana away
|20th
Sophie Away

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Rep:SL7514TransitionStates

2017-03-16T10:32:40Z

Sl7514:

==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 17; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) 17:54, 15 March 2017 (UTC) Good MO diagram, but you are missing the symmetry labels on the transition state MOs.)

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) 17:54, 15 March 2017 (UTC) You are not stating that only AS/AS and S/S combinations are allowed)

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

([[User:Fv611|Fv611]] ([[User talk:Fv611|talk]]) 17:54, 15 March 2017 (UTC) Including the butadiene-ethylene bond lenghts in the reactants makes it look like they are always bonded.)

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 33; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 17; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable and the molecule is usually heavily distorted.<ref name="breslow" /> Indeed, optimised xylylene using B3LYP/6-31(d) basis set showed this distortion.

[[File: SL7514 Non-planar antiaromatic.png|500px|thumb| '''Figure 37.''' Antiaromatic distortion in Xylylene optimised at B3LYP/6-31(d) level]]

The experimental literature review showed that above 50<sup>ο</sup>C, formation of sulfolenes were highly favoured whereas below 50<sup>ο</sup>C sultines were formed.<ref name="roversi" /> This agreed very well with the reaction profile diagram in Figure 36. At high temperature, the reaction is thermodynamically controlled, and hence the cheletropic reaction and the formation of sulfolene were favoured. At lower temperatures, the reaction was kinetically controlled and the reaction pathway with lower activation energy barrier (Diels-Alder) reaction was favoured.

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 21; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 11; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 13; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 21; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 27; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

Photochemical reaction would proceed via opposite stereochemistry. The excitation of the electron from the HOMO to LUMO would produce a triplet excited state with the reaction proceeding from the LUMO. The phase of the orbital in the FOs has now been reversed and hence the electrocylic reaction of butene would proceed via disrotatory path with Hückel transition state involving suparafacial component. There were many research already performed in this field and conical interactions connecting different electronically excited states was the believed pathway in photochemical reactions. <ref name="hass" /> <ref name="santolini" />

[[File: SL7514 Disrotatory photochemistry.png|600px|thumb| '''Figure 39.''' Disrotatory path is favoured in photochemical reaction]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 78; </script>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 48; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 95; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 40.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 40.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 41.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

It was unfortunately not possible to investigate the conical intersection for the photochemical reaction. The B3LYP/6-31(d) basis set was too time consuming to model and perform IRC at the first excited state. With the lower basis set it was not possible to accurately model the MOs required for CASSCF computation.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
<ref name="roversi"> E. Roversi, F. Monnat and P. Vogel, 2002, <i> Helv. Chim. Acta </i>,<b> 85</b>, 733–760</ref>
<ref name="hass"> Y. Hass and S. Zilberg, 2000, <i> J. Photochem. Photobiol. </i>,<b> 144</b>, 221-228</ref>
<ref name="santolini"> V. Santolini, J. P. Malhado, M. A. Robb, M. Garavelli and
M. J. Bearpark, 2015, <i> Molecular Physics </i>,<b> 113</b>, 1978–1990</ref>
</references>

File:SL7514 Exo Steric Clash2.png

2017-03-16T10:29:59Z

Sl7514:

Rep:SL7514TransitionStates

2017-03-09T22:03:19Z

Sl7514:

==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 17; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 33; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 17; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable and the molecule is usually heavily distorted.<ref name="breslow" /> Indeed, optimised xylylene using B3LYP/6-31(d) basis set showed this distortion.

[[File: SL7514 Non-planar antiaromatic.png|500px|thumb| '''Figure 37.''' Antiaromatic distortion in Xylylene optimised at B3LYP/6-31(d) level]]

The experimental literature review showed that above 50<sup>ο</sup>C, formation of sulfolenes were highly favoured whereas below 50<sup>ο</sup>C sultines were formed.<ref name="roversi" /> This agreed very well with the reaction profile diagram in Figure 36. At high temperature, the reaction is thermodynamically controlled, and hence the cheletropic reaction and the formation of sulfolene were favoured. At lower temperatures, the reaction was kinetically controlled and the reaction pathway with lower activation energy barrier (Diels-Alder) reaction was favoured.

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 21; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 11; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 13; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 21; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 27; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

Photochemical reaction would proceed via opposite stereochemistry. The excitation of the electron from the HOMO to LUMO would produce a triplet excited state with the reaction proceeding from the LUMO. The phase of the orbital in the FOs has now been reversed and hence the electrocylic reaction of butene would proceed via disrotatory path with Hückel transition state involving suparafacial component. There were many research already performed in this field and conical interactions connecting different electronically excited states was the believed pathway in photochemical reactions. <ref name="hass" /> <ref name="santolini" />

[[File: SL7514 Disrotatory photochemistry.png|600px|thumb| '''Figure 39.''' Disrotatory path is favoured in photochemical reaction]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 78; </script>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 48; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 95; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 37.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 40.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 41.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

It was unfortunately not possible to investigate the conical intersection for the photochemical reaction. The B3LYP/6-31(d) basis set was too time consuming to model and perform IRC at the first excited state. With the lower basis set it was not possible to accurately model the MOs required for CASSCF computation.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
<ref name="roversi"> E. Roversi, F. Monnat and P. Vogel, 2002, <i> Helv. Chim. Acta </i>,<b> 85</b>, 733–760</ref>
<ref name="hass"> Y. Hass and S. Zilberg, 2000, <i> J. Photochem. Photobiol. </i>,<b> 144</b>, 221-228</ref>
<ref name="santolini"> V. Santolini, J. P. Malhado, M. A. Robb, M. Garavelli and
M. J. Bearpark, 2015, <i> Molecular Physics </i>,<b> 113</b>, 1978–1990</ref>
</references>

Rep:SL7514TransitionStates

2017-03-09T21:43:54Z

Sl7514:

==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 17; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 33; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 17; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable and the molecule is usually heavily distorted.<ref name="breslow" /> Indeed, optimised xylylene using B3LYP/6-31(d) basis set showed this distortion.

[[File: SL7514 Non-planar antiaromatic.png|500px|thumb| '''Figure 37.''' Antiaromatic distortion in Xylylene optimised at B3LYP/6-31(d) level]]

The experimental literature review showed that above 50<sup>ο</sup>C, formation of sulfolenes were highly favoured whereas below 50<sup>ο</sup>C sultines were formed.<ref name="roversi" /> This agreed very well with the reaction profile diagram in Figure 36. At high temperature, the reaction is thermodynamically controlled, and hence the cheletropic reaction and the formation of sulfolene were favoured. At lower temperatures, the reaction was kinetically controlled and the reaction pathway with lower activation energy barrier (Diels-Alder) reaction was favoured.

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 21; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 11; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 13; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 21; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 27; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

Photochemical reaction would proceed via opposite stereochemistry. The excitation of the electron from the HOMO to LUMO would produce a triplet excited state with the reaction proceeding from the LUMO. The phase of the orbital in the FOs has now been reversed and hence the electrocylic reaction of butene would proceed via disrotatory path with Hückel transition state involving suparafacial component. There were many research already performed in this field and conical interactions connecting different electronically excited states was the believed pathway in photochemical reactions. <ref name="hass" /> <ref name="santolini" />

[[File: SL7514 Disrotatory photochemistry.png|600px|thumb| '''Figure 39.''' Disrotatory path is favoured in photochemical reaction]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 78; </script>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 48; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 95; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 37.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 40.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 41.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

It was unfortunately not possible to investigate the conical intersection for the photochemical reaction. The B3LYP/6-31(d) basis set was too time consuming to model and perform IRC at the first excited state. With the lower basis set it was not possible to accurately model the MOs required for CASSCF computation.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
<ref name="roversi"> E. Roversi, F. Monnat and P. Vogel, 2002, <i> Helv. Chim. Acta </i>,<b> 85</b>, 733–760</ref>
<ref name="hass"> Y. Hass and S. Zilberg, 2000, <i> J. Photochem. Photobiol. </i>,<b> 144</b>, 221-228</ref>
<ref name="santolini"> V. Santolini, J. P. Malhado, M. A. Robb, M. Garavelli and
M. J. Bearpark, 2015, <i> Molecular Physics </i>,<b> 113</b>, 1978–1990</ref>
</references>

Rep:SL7514TransitionStates

2017-03-09T21:40:08Z

Sl7514:

==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 17; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable and the molecule is usually heavily distorted.<ref name="breslow" /> Indeed, optimised xylylene using B3LYP/6-31(d) basis set showed this distortion.

[[File: SL7514 Non-planar antiaromatic.png|500px|thumb| '''Figure 37.''' Antiaromatic distortion in Xylylene optimised at B3LYP/6-31(d) level]]

The experimental literature review showed that above 50<sup>ο</sup>C, formation of sulfolenes were highly favoured whereas below 50<sup>ο</sup>C sultines were formed.<ref name="roversi" /> This agreed very well with the reaction profile diagram in Figure 36. At high temperature, the reaction is thermodynamically controlled, and hence the cheletropic reaction and the formation of sulfolene were favoured. At lower temperatures, the reaction was kinetically controlled and the reaction pathway with lower activation energy barrier (Diels-Alder) reaction was favoured.

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 10; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

Photochemical reaction would proceed via opposite stereochemistry. The excitation of the electron from the HOMO to LUMO would produce a triplet excited state with the reaction proceeding from the LUMO. The phase of the orbital in the FOs has now been reversed and hence the electrocylic reaction of butene would proceed via disrotatory path with Hückel transition state involving suparafacial component. There were many research already performed in this field and conical interactions connecting different electronically excited states was the believed pathway in photochemical reactions. <ref name="hass" /> <ref name="santolini" />

[[File: SL7514 Disrotatory photochemistry.png|600px|thumb| '''Figure 39.''' Disrotatory path is favoured in photochemical reaction]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 78; </script>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 48; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 94; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 37.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 40.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 41.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

It was unfortunately not possible to investigate the conical intersection for the photochemical reaction. The B3LYP/6-31(d) basis set was too time consuming to model and perform IRC at the first excited state. With the lower basis set it was not possible to accurately model the MOs required for CASSCF computation.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
<ref name="roversi"> E. Roversi, F. Monnat and P. Vogel, 2002, <i> Helv. Chim. Acta </i>,<b> 85</b>, 733–760</ref>
<ref name="hass"> Y. Hass and S. Zilberg, 2000, <i> J. Photochem. Photobiol. </i>,<b> 144</b>, 221-228</ref>
<ref name="santolini"> V. Santolini, J. P. Malhado, M. A. Robb, M. Garavelli and
M. J. Bearpark, 2015, <i> Molecular Physics </i>,<b> 113</b>, 1978–1990</ref>
</references>

Rep:SL7514TransitionStates

2017-03-09T21:35:57Z

Sl7514:

==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable and the molecule is usually heavily distorted.<ref name="breslow" /> Indeed, optimised xylylene using B3LYP/6-31(d) basis set showed this distortion.

[[File: SL7514 Non-planar antiaromatic.png|500px|thumb| '''Figure 37.''' Antiaromatic distortion in Xylylene optimised at B3LYP/6-31(d) level]]

The experimental literature review showed that above 50<sup>ο</sup>C, formation of sulfolenes were highly favoured whereas below 50<sup>ο</sup>C sultines were formed.<ref name="roversi" /> This agreed very well with the reaction profile diagram in Figure 36. At high temperature, the reaction is thermodynamically controlled, and hence the cheletropic reaction and the formation of sulfolene were favoured. At lower temperatures, the reaction was kinetically controlled and the reaction pathway with lower activation energy barrier (Diels-Alder) reaction was favoured.

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 10; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

Photochemical reaction would proceed via opposite stereochemistry. The excitation of the electron from the HOMO to LUMO would produce a triplet excited state with the reaction proceeding from the LUMO. The phase of the orbital in the FOs has now been reversed and hence the electrocylic reaction of butene would proceed via disrotatory path with Hückel transition state involving suparafacial component. There were many research already performed in this field and conical interactions connecting different electronically excited states was the believed pathway in photochemical reactions. <ref name="hass" /> <ref name="santolini" />

[[File: SL7514 Disrotatory photochemistry.png|600px|thumb| '''Figure 39.''' Disrotatory path is favoured in photochemical reaction]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 78; </script>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 48; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 94; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 37.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 40.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 41.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

It was unfortunately not possible to investigate the conical intersection for the photochemical reaction. The B3LYP/6-31(d) basis set was too time consuming to model and perform IRC at the first excited state. With the lower basis set it was not possible to accurately model the MOs required for CASSCF computation.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
<ref name="roversi"> E. Roversi, F. Monnat and P. Vogel, 2002, <i> Helv. Chim. Acta </i>,<b> 85</b>, 733–760</ref>
<ref name="hass"> Y. Hass and S. Zilberg, 2000, <i> J. Photochem. Photobiol. </i>,<b> 144</b>, 221-228</ref>
<ref name="santolini"> V. Santolini, J. P. Malhado, M. A. Robb, M. Garavelli and
M. J. Bearpark, 2015, <i> Molecular Physics </i>,<b> 113</b>, 1978–1990</ref>
</references>

Rep:SL7514TransitionStates

2017-03-09T21:28:13Z

Sl7514:

==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable and the molecule is usually heavily distorted.<ref name="breslow" /> Indeed, optimised xylylene using B3LYP/6-31(d) basis set showed this distortion.

[[File: SL7514 Non-planar antiaromatic.png|500px|thumb| '''Figure 37.''' Antiaromatic distortion in Xylylene optimised at B3LYP/6-31(d) level]]

The experimental literature review showed that above 50<sup>ο</sup>C, formation of sulfolenes were highly favoured whereas below 50<sup>ο</sup>C sultines were formed.<ref name="roversi" /> This agreed very well with the reaction profile diagram in Figure 36. At high temperature, the reaction is thermodynamically controlled, and hence the cheletropic reaction and the formation of sulfolene were favoured. At lower temperatures, the reaction was kinetically controlled and the reaction pathway with lower activation energy barrier (Diels-Alder) reaction was favoured.

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 10; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

Photochemical reaction would proceed via opposite stereochemistry. The excitation of the electron from the HOMO to LUMO would produce a triplet excited state with the reaction proceeding from the LUMO. The phase of the orbital in the FOs has now been reversed and hence the electrocylic reaction of butene would proceed via disrotatory path with Hückel transition state involving suparafacial component. There were many research already performed in this field and conical interactions connecting different electronically excited states was the believed pathway in photochemical reactions. <ref name="hass" /> <ref name="santolini" />

[[File: SL7514 Disrotatory photochemistry.png|600px|thumb| '''Figure 39.''' Disrotatory path is favoured in photochemical reaction]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 78; </script>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 48; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 94; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 37.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 40.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 41.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

It was unfortunately not possible to investigate the conical intersection for the photochemical reaction. The B3LYP/6-31(d) basis set was too time consuming to model and perform IRC at the first excited state. With the lower basis set it was not possible to accurately model the MOs required for CASSCF computation.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
<ref name="roversi"> E. Roversi, F. Monnat and P. Vogel, 2002, <i> Helv. Chim. Acta </i>,<b> 85</b>, 733–760</ref>
<ref name="hass"> Y. Hass and S. Zilberg, 2000, <i> J. Photochem. Photobiol. </i>,<b> 144</b>, 221-228</ref>
<ref name="santolini"> V. Santolini, J. P. Malhado, M. A. Robb, M. Garavelli and
M. J. Bearpark, 2015, <i> Molecular Physics </i>,<b> 113</b>, 1978–1990</ref>
</references>

Rep:SL7514TransitionStates

2017-03-09T20:38:25Z

Sl7514:

==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable and the molecule is usually heavily distorted.<ref name="breslow" /> Indeed, optimised xylylene using B3LYP/6-31(d) basis set showed this distortion.

[[File: SL7514 Non-planar antiaromatic.png|500px|thumb| '''Figure 37.''' Antiaromatic distortion in Xylylene optimised at B3LYP/6-31(d) level]]

The experimental literature review showed that above 50<sup>ο</sup>C, formation of sulfolenes were highly favoured whereas below 50<sup>ο</sup>C sultines were formed.<ref name="roversi" /> This agreed very well with the reaction profile diagram in Figure 36. At high temperature, the reaction is thermodynamically controlled, and hence the cheletropic reaction and the formation of sulfolene were favoured. At lower temperatures, the reaction was kinetically controlled and the reaction pathway with lower activation energy barrier (Diels-Alder) reaction was favoured.

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 10; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

Photochemical reaction would proceed via opposite stereochemistry. The excitation of the electron from the HOMO to LUMO would produce a triplet excited state with the reaction proceeding from the LUMO. The phase of the orbital in the FOs has now been reversed and hence the electrocylic reaction of butene would proceed via disrotatory path with Hückel transition state involving suparafacial component. There were many research already performed in this field and conical interactions connecting different electronically excited states was the believed pathway in photochemical reactions. <ref name="hass" /> <ref name="santolini" />

[[File: SL7514 Disrotatory photochemistry.png|600px|thumb| '''Figure 39.''' Disrotatory path is favoured in photochemical reaction]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 37.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 40.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 41.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

It was unfortunately not possible to investigate the conical intersection for the photochemical reaction. The B3LYP/6-31(d) basis set was too time consuming to model and perform IRC at the first excited state. With the lower basis set it was not possible to accurately model the MOs required for CASSCF computation.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
<ref name="roversi"> E. Roversi, F. Monnat and P. Vogel, 2002, <i> Helv. Chim. Acta </i>,<b> 85</b>, 733–760</ref>
<ref name="hass"> Y. Hass and S. Zilberg, 2000, <i> J. Photochem. Photobiol. </i>,<b> 144</b>, 221-228</ref>
<ref name="santolini"> V. Santolini, J. P. Malhado, M. A. Robb, M. Garavelli and
M. J. Bearpark, 2015, <i> Molecular Physics </i>,<b> 113</b>, 1978–1990</ref>
</references>

Rep:SL7514TransitionStates

2017-03-09T20:16:53Z

Sl7514:

==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable and the molecule is usually heavily distorted.<ref name="breslow" /> Indeed, optimised xylylene using B3LYP/6-31(d) basis set showed this distortion.

[[File: SL7514 Non-planar antiaromatic.png|500px|thumb| '''Figure 37.''' Antiaromatic distortion in Xylylene optimised at B3LYP/6-31(d) level]]

The experimental literature review showed that above 50<sup>ο</sup>C, formation of sulfolenes were highly favoured whereas below 50<sup>ο</sup>C sultines were formed.<ref name="roversi" /> This agreed very well with the reaction profile diagram in Figure 36. At high temperature, the reaction is thermodynamically controlled, and hence the cheletropic reaction and the formation of sulfolene were favoured. At lower temperatures, the reaction was kinetically controlled and the reaction pathway with lower activation energy barrier (Diels-Alder) reaction was favoured.

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 10; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

Photochemical reaction would proceed via opposite stereochemistry. The excitation of the electron from the HOMO to LUMO would produce a triplet excited state with the reaction proceeding from the LUMO. The phase of the orbital in the FOs has now been reversed and hence the electrocylic reaction of butene would proceed via disrotatory path with Hückel transition state involving suparafacial component. There were many research already performed in this field and conical interactions connecting different electronically excited states was the believed pathway in photochemical reactions. <ref name="hass" /> <ref name="santolini" />

[[File: SL7514 Disrotatory photochemistry.png|600px|thumb| '''Figure 39.''' Disrotatory path is favoured in photochemical reaction]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 37.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 40.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 41.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

It was unfortunately not possible to investigate the conical intersection for the photochemical reaction. The B3LYP/6-31(d) basis set was too time consuming to model and perform IRC at the first excited state. With the lower basis set it was not possible to accurately model the MOs required for CASSCF computation.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
<ref name="roversi"> E. Roversi, F. Monnat and P. Vogel, 2002, <i> Helv. Chim. Acta </i>,<b> 85</b>, 733–760</ref>
<ref name="hass"> Y. Hass and S. Zilberg, 2000, <i> J. Photochem. Photobiol. </i>,<b> 144</b>, 221-228</ref>
<ref name="santolini"> V. Santolini, J. P. Malhado, M. A. Robb, M. Garavelli and
M. J. Bearpark, 2015, <i> Molecular Physics </i>,<b> 113</b>, 1978–1990</ref>
</references>

File:SL7514 Non-planar antiaromatic.png

2017-03-09T20:10:53Z

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File:SL7514 Disrotatory photochemistry.png

2017-03-09T20:01:20Z

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Rep:SL7514TransitionStates

2017-03-09T19:41:42Z

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==Introduction==

For a molecule consisting of N number of atoms, it is possible to assign a general set of cartesian coordinates for each atom. This would result in a total number of <math> 3N_{atoms} </math> possible coordinates. However, the global translation and rotation must be taken into account as they do not affect the energy of the molecule. Translation of the whole molecule along or rotation about any of the axes will not affect the total energy. Therefore, the molecule has total number of <math>3N_{atoms}-6</math> degrees of freedom and hence the potential energy surface is a multivariable function of <math>3N_{atoms}-6</math> variables. <ref name="mcdouall" />

[[File: Degrees of freedom.png|300px|thumb|center| '''Figure 1.''' It is possible to assign Cartesian coordinates to all atoms in the molecule.]]

By taking the Taylor expansion of the potential function, it is possible to find the Hessian matrix of function with n variables <math>f(x_1, x_2, ... , x_n) </math>:

<math> \mathbf{H} = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
\vdots & \vdots & \ddots & \vdots \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix} </math>

Local maximum and minimum can be found by equating the first order differential (gradient) of the potential function to zero. These points correspond to locations on the potential energy surface where the net force on the molecule is zero. <ref name="dill" />

<math>\frac{\partial f}{\partial x_1} = 0,\ \frac{\partial f}{\partial x_2} = 0,\ ...,\ \frac{\partial f}{\partial x_n} = 0</math>

The transition state correspond to the saddle points in the potential energy surface. The coordinates for the saddle points are found where the determinant of the Hessian matrix is less than zero (gradient = 0, curvature < 0).

<math>\det(\mathbf{H}) < 0 </math>

If the determinant is greater than zero, than the points correspond to either maximum or minimum. The minimum, or the stable equilibrium of the multivariable function is found where all the eigenvalues of the Hessian matrix is positive (gradient = 0, curvature > 0). From the Sylvester's criterion, the Hessian matrix is positive definite if all the leading principal minors are positive.

Each vibrational modes in the molecule correspond to a normal mode. The multivariable Taylor expansion of the potential shows that the second derivatives correspond to the force constant, forming the Hessian matrix.

<math>V = V(0) + \sum_i \left ( \frac{\partial V}{\partial x_i} \right )_0 x_i + \frac{1}{2} \sum_{i,j} \left ( \frac{\partial^2 V}{\partial x_ix_j} \right )_0 x_i x_j + ... </math>

let

<math>k_{i,j} = \left ( \frac{\partial^2 V}{\partial x_ix_j} \right ) </math>

If <math>k_{i,j} \ne 0</math> where <math>i\ne j</math>, then the vibrations are coupled. The vibrational modes correspond to normal coordinates which diagonalise the Hessian matrix.

<math>\begin{bmatrix}
k_{11} & k_{12}& \cdots \\
k_{21} & k_{22} & \\
\vdots & & k_{(3N-6)(3N-6}
\end{bmatrix} </math> → <math> \begin{bmatrix}
\kappa_{11} & 0& \cdots \\
0 & \kappa_{22} & \\
\vdots & & \kappa_{(3N-6)(3N-6)}
\end{bmatrix}</math>

If one of the vibrational mode is negative, then one of the direction in the normal coordinate system has a energy maximum and all other orthogonal direction has minimum. This is the reason why the vibration with the negative frequency must correspond to the reaction pathway. If all vibrational modes are positive then all orthogonal directions in the normal coordinate have energy minimum and therefore this corresponds to the local minima.

==Reaction of Butadiene with Ethylene==

All of the optimised product, reactants and transition states in this experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 1.''' Optimised diene used to <br> optimise the transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; </script>
<uploadedFileContents>SL7514 DIENE DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 2.''' Fully optimised diene <br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 ETHENE OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 3.''' Fully optimised ethene<br>
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 DIELS-ALDER FREEZE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 4.''' Freeze bond optimisation<br>for diene and ethene
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 5.''' Transition state optimisation<br>for diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER LONG.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 6.'''IRC for Diels-Alder<br>reaction betweem diene and ethene
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 7.'''Initial optimisation of the <br> final product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 72; </script>
<uploadedFileContents>SL7514 PRODUCT DISTORT + OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 8.'''Fully optimised final <br> product after distortion
|}

The MO diagram for the formation of the butadiene and ethene transition state is shown in Figure 2. The relative energies of the fragment orbitals were found using the literature.<ref name="bachrach" />. Figures 3 to 10 shows the MO surface calculations from Gaussian on PM6 level. The MOs diagrams corresponding to each MO surface from Gaussian calculations are labelled on the diagram in Figure 2 as MO16, MO17 etc. It should be noted that the HOMO and LUMO energy of the diene and ethene are expected to be similar as no electron withdrawing group or electron donating groups are present on ethene or diene.

[[File: SL7514 EX1 MODiagram.png|500px|thumb| '''Figure 2.''' The MO diagram for the reaction of butadiene with ethene]]

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Diene HOMO.png|500px|thumb| '''Figure 3.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Diene LUMO.png|500px|thumb|center| '''Figure 4.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Ethene HOMO.png|500px|thumb| '''Figure 5.''' HOMO of optimised diene]]
| colspan="3" align="center"|[[File: SL7514 Ethene LUMO.png|500px|thumb|center| '''Figure 6.''' LUMO of optimised diene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO16.png|500px|thumb| '''Figure 7.''' MO16 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO17.png|500px|thumb|center| '''Figure 8.''' MO17 of the transition state for the Diels-Alder reaction between diene and ethene]]
|-
| colspan="3" align="center"|[[File: SL7514 Transition State MO18.png|500px|thumb| '''Figure 9.''' MO18 of the transition state for the Diels-Alder reaction between diene and ethene]]
| colspan="3" align="center"|[[File: SL7514 Transition State MO19.png|500px|thumb|center| '''Figure 10.''' MO19 of the transition state for the Diels-Alder reaction between diene and ethene]]
|}

In molecular orbital theory, the molecular orbitals (MOs) are formed from linear combination of atomic orbitals (AOs) or fragment orbitals (FOs). For two AOs or FOs wavefunctions <math>\psi_1 </math> and <math>\psi_2</math> there are two possible linear combinations:

<math>\Psi_T = c_1 \psi_1 + c_2 \psi_2 </math>

<math>\Psi_T^* = c_1 \psi_1 - c_2 \psi_2 </math>

In a bonding interaction, the sign of the coefficient for each AOs or FOs are the same, leading to bonding molecular orbital <math>\Psi_T</math>. In an antibonding interaction, the sign of the coefficient for each AOs or FOs are opposite, leading to antibonding molecular orbital <math>\Psi_T^*</math>. In bonding interaction, electron density is present between the atoms or molecular fragments and hence leads to lowering of the energy of the formed MO. In antibonding interaction, the bond is weakened and hence leads to raising of the energy of the formed MO. It is therefore important to consider the interaction of AOs and MOs in bonding and antibonding pairs.

[[File:SL7514 EX1 Symmetry.png|500px|thumb|center| '''Figure 11.''' MO diagram to illustrate the possible linear combinations for symmetric-symmetric, symmetric-antisymmetric and antisymmetric-antisymmetric interactions]]

For this Diels-Alder reaction to be allowed, the plane of symmetry must be preserved as it can be seen on Figure 11, and hence the ethylene fragment should approach the diene from one face. The reaction would be disallowed if the ethene fragment approaches the diene at an angle which does not preserve the plane of symmetry. Furthermore, both HOMO-LUMO interactions are allowed by symmetry as this results in one bonding interaction since it is possible for both fragments to approach in phase.

As discussed before, to qualitatively determine the orbital overlap integral, both linear combinations must be considered where the coefficient of FOs have been swapped. As illustrated in Figure 11, for symmetric-symmetric and antisymmetric-antisymmetric interactions, there is a clear one bonding interaction and one antibonding interaction leading to one bonding orbital and one antibonding orbital. Therefore, the orbital overlap integral is expected to be non-zero. For the symmetric-antisymmetric case, there is a one bonding and one antibonding interaction within the same fragment. When the orbital coefficient is swapped, there is still one bonding and one antibonding interaction within the same fragment and therefore, orbital overlap integral is expected to be zero.

[[File: SL7514 IRC Ex1.png|500px|thumb|center| '''Figure 12.''' IRC and the gradient plot for the Diels-Alder reaction between diene and ethene]]

The IRC plot showed a successful reaction pathway as the gradient was found to be zero at the coordinates corresponding to transition state, reactant and products. The reaction barrier was found to be 26.2 kCal mol<sup>-1</sup> which agreed well with the literature calculation <ref name="rowley" />

The plot below illustrates the change in carbon-carbon bond distanced during the Diels-Alder reaction, obtained from this experiment.

[[File: SL7514 Bond Distance.png|700px|thumb|center| '''Figure 13.''' Change in C-C bond distances during the Diels-Alder reaction, obtained from this experiment]]

{| class="wikitable"
|+ Table 1. A summary of the C-C bond lengths from literature <ref name="lide" />
|-
! Bond Type
! Bond Length / Å
|-
|Sp<sup>3</sup> - Sp<sup>3</sup>
|1.54
|-
|Sp<sup>3</sup> - Sp<sup>2</sup>
|1.50
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (single)
|1.47
|-
|Sp<sup>2</sup> - Sp<sup>2</sup> (double)
|1.34
|}

{| class="wikitable"
|+ Table 2. A summary of the C-C bond lengths obtained from this experiment <ref name="lide" />
|-
! Bond Type
! Transition State Bond Length / Å
! Reactants Bond Length / Å
! Products Bond Length / Å
|-
|C1-C4
| 1.380
| 1.335
| 1.501
|-
|C4-C6
| 1.411
| 1.468
| 1.338
|-
|C6-C7
| 1.380
| 1.335
| 1.501
|-
|C11-C12
| 1.382
| 1.327
| 1.541
|-
|C1-C12
| 2.115
| 3.415
| 1.540
|-
|C11-C7
| 2.115
| 3.414
| 1.540
|}

Comparing Table 1 and Table 2, the reactant and product bond lengths obtained from the calculation matched the literature results very well. At the transition state, all the C=C double bonds (C1-C1, C6-C7 and C11-C12) elongated, and the single bond (C4-C6) was shortened compared to the reactants. The inter-molecular bonds (C1-C12 and C11-C7) remained the longest. As it can be seen from Figure 12, the electron density in these bonds are smallest in the transition state and hence was expected to be the longest. It should also be noted that the bond length C4-C6 and C11-C12 cross over each other after the reaction coordinate 0 where the transition state was optimised. This suggested that the transition state at coordinate zero resembled the reactants more than the products meaning the reaction went via early transition state from Hammond's postulate.

The van der Waals radius for carbon was found to be 1.70 Å <ref name="batsanov" />. The van der Waals radius is the half the internuclear separation of two atoms of the same element at their closest possible approach without forming a bond. Therefore, the closest possible carbon-carbon distance without forming a bond is 3.40 Å, if all atoms are modeled as hard-spheres. From Table 2, it can be seen that all carbon-carbon distances were shorter than this value which suggest there are bonding interaction between all carbons listed in the table.

The vibration with the negative frequency must correspond to the reaction pathway. This vibrational mode is illustrated in Molecule 5. The vibration was symmetrical where the two carbons at the opposite ends of the diene approached the two carbons on ethene simultaneously. The bond formation in this Diels-Alder reaction was a concerted process. This finding agreed with the literature where the study by Houk et al predicted synchronous bond formation in Diels-Alder reaction using Hartree-Fock method in favour of di-radical mechanism. <ref name="houk" />

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

All of the optimised product, reactants and transition states for the Endo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 9.''' Optimised cyclodiene <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 CYCLODIENE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 10.''' Optimised cyclodiene <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; </script>
<uploadedFileContents>SL7514 CYCLODIENE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 11.''' Cyclodiene distorted and <br> re-optimised at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 12.''' 1,3-Dioxole optimised <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; </script>
<uploadedFileContents>SL7514 DIOXOLE OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 13.''' 1,3-Dioxole optimised <br> at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 DIOXOLE DISTORT + OPTIMISATION DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 14.'''1,3-Dioxole distorted and <br> re-optimised at B3LYP(d)level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 15.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 36; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER ENDO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 16.''' Freeze coordinate minimisation for the <br> transition state of Endo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 25; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 17.''' Transition state optimisation for Endo <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER ENDO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 18.''' Transition state optimisation for Endo <br> at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 67; </script>
<uploadedFileContents>SL7514 IRC DIELS-ALDER ENDO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 19.''' IRC calculation for Endo transition <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 20.''' Optimisation of the Endo product <br> at PM6 level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION ENDO DFT 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 21.''' Optimisation of the Endo product <br> at B3LYP(d) level
|}

All of the optimised product, reactants and transition states for the Exo Diels-Alder experiment are outlined below:

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 40; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 22.''' Freeze coordinate minimisation <br> for Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 FREEZE REACTANTS DIELS-ALDER EXO DFT.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 23.''' Freeze coordinate minimisation <br> for Exo reaction at B3LYP(d) level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 24; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 24.''' Transition state optimisation for the <br> Exo reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE DIELS-ALDER EXO DFT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 25.''' Transition state optimisation for the <br> Exo reaction at B3LYP(d) level
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC DIELS-ALDER EXO PM6 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 26.''' IRC calculation for the Exo <br> reaction at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 8; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO PM6 2.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 27.''' Exo product optimisation <br> at PM6 level
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 14; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION EXO DFT 2.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 28.''' Exo product optimisation <br> at B3LYP(d) level
|}

The MOs associated with this Diels-Alder reaction are shown below. The HOMO and LUMO orbitals corresponds to Figures 16 to 19.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Endo Diels-Alder MOs.png|500px|thumb| '''Figure 14.''' Frontier Molecular Orbitals for Endo Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 Exo Diels-Alder MOs.png|500px|thumb|center| '''Figure 15.''' Frontier Molecular Orbitals for Exo Diels-Alder reaction]]
|}

The MOs calculated from Gaussian are shown below for both Endo and Exo reactions.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole HOMO.png|400px|thumb| '''Figure 16.''' HOMO of 1,3-Dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514 1,3-Dioxole LUMO.png|400px|thumb| '''Figure 17.''' LUMO of 1,3-Dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514 Cyclodiene HOMO.png|400px|thumb| '''Figure 18.''' HOMO of Cyclohexadiene (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 Cyclodiene LUMO.png|400px|thumb| '''Figure 19.''' LUMO of Cyclohexadiene (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO40.png|400px|thumb| '''Figure 20.''' MO40 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO41.png|400px|thumb| '''Figure 21.''' MO41 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514EndoMO42.png|400px|thumb| '''Figure 22.''' MO42 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514EndoMO43.png|400px|thumb| '''Figure 23.''' MO43 of the transition state for the Endo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO40.png|400px|thumb| '''Figure 24.''' MO40 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|-
| colspan="3" align="center"|[[File: SL7514 ExoMO41.png|400px|thumb|center| '''Figure 23.''' MO41 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO42.png|400px|thumb| '''Figure 24.''' MO42 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (symmetric)]]
| colspan="3" align="center"|[[File: SL7514ExoMO43.png|400px|thumb|center| '''Figure 25.''' MO43 of the transition state for the Exo Diels-Alder reaction between cyclohexadiene and 1,3-dioxole (antisymmetric)]]
|}

The transition state, reactants and products were confirmed by the frequency analysis. At the transition state, one negative frequency was observed at -529 cm<sup>-1</sup> and -521 cm<sup>-1</sup> for Exo and Endo reactions respectively.

In order to determine whether the electron demand was normal or inverse for this Diels-Alder reaction, energy optimisation was performed at B3LYP/6-31G(d) for the initial reactants. The alkene in this reaction possessed electron donating groups and qualitatively, would increase the HOMO and LUMO of the dienenophile. Therefore, intuitively inverse electron demand Diels-Alder was expected.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Normal Electron Demand MO.png|400px|thumb| '''Figure 26.''' Expected MO diagram for normal electron demand Diels-Alder reaction]]
| colspan="3" align="center"|[[File: SL7514 This simulation MO.png|400px|thumb| '''Figure 27.''' MO diagram constructed following the Gaussian calculation at B3LYP/6-31G(d) level]]
|}

Figure 26 and 27 compares the expected MO diagram for normal electron demand and the MO diagram constructed for the Exo Diels-Alder reaction. Figure 26 represents a normal electron demand since the energy matching between ethene LUMO and diene HOMO is much better than ethene HOMO and diene LUMO and hence, resulting in stronger interaction. Therefore, the ethene is expected to have greater electron accepting character and diene have greater electron donating character.

Figure 27 showed the relative energies of the HOMOs and LUMOs in Hartree for this experiment. It was clear that energy matching between the HOMO of the ethene and the LUMO of the diene was much better than the LUMO of ethene and HOMO of diene. Therefore, the ethene was expected to have greater electron donating character and diene was expected to have greater electron accepting character. As predicted by the organic chemistry intuition, the MO calculation supported the argument that the reaction was inverse electron demand. It was not possible determine the electron demand by comparing the relative energies of the MOs from the transition state. The energy difference between the HOMO and HOMO-1 and LUMO and LUMO+1 was too similar to justify the electron demand was changed.

It is worth noting that different DFT calculation can potentially lead to differing results. B3LYP method utilised the Kohn-Sham method, where it was approximated that N electrons do not interact with each other. <ref name="mcdouall" /> <ref name="sham" /> Therefore, DFT method was approximate and this was also the reason why it was not possible to quantitatively compare the energy values of the MOs.

{| class="wikitable"
|+ Table 3. A summary of the energy output from Diels-Alder reaction between cyclohexene and 1,3-dioxole <ref name="lide" />
|-
!
!Endo
!Exo
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|72.03
|79.85984
|-
|Product Free Energy Change Δ<sub>r</sub>G
| -155.18281
| -151.5885
|}

The free energy change was calculated by finding the difference in absolute free energy between sum of reactants with transition state and the product from Gaussian calculation at B3LYP/6-31(d). This experiment predicted the Endo product to be both kinetic and thermodynamic product because the activation energy barrier and the Gibbs free energy change for the reaction was lower. This was contradictory from usual Diels-Alder reaction where the Exo product was expected to be the thermodynamic product. <ref name="cooley" />. The reasoning came by studying the sterics of the ring clash within the molecule as illustrated in Figure 28 and 29. The nearest distance between the dioxole ring and cyclohexene ring in Exo was 234 pm compared to 295 pm in Endo and therefore, the Endo product was more favoured due to the steric clash.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: Sl7514EndoClash.png|400px|thumb| '''Figure 28.''' Steric interaction in Endo Diels-Alder product]]
| colspan="3" align="center"|[[File: SL7514ExoClash.png|400px|thumb| '''Figure 29.''' Steric interaction in Exo Diels-Alder product]]
|}

[[File: SL7514Secondaryorbitaloverlap.png|400px|thumb| '''Figure 30.''' Secondary orbital overlap was possible in Endo Diels-Alder reaction]]

The reason why the activation energy barrier for the endo product was because of the secondary orbital overlap. The oxygen atoms in 1,3-Dioxole was Sp<sup>3</sup> hybridised and hence the lone pair electrons were in the p orbital. Figure 30 below illustrated how these p orbital could favourably overlap with the MO in the cyclohexadiene in Endo, lowering the transition state energy. This interaction was not possible for the Exo transition state leading to higher activation energy barrier. MO 41 and MO 43 in the Endo transition state (Figure 21 and 23) clearly illustrated this interaction as mixing was observed between the p orbitals from the oxygen with the diene. Steric effects were also analysed for both transition states. The closest distance between other atoms (other than the carbon atoms involved in the transition states) was longer than the distance between the carbon atoms directly involved in the reaction. Therefore, steric had a negligible effect on the reaction energy barrier and the secondary orbital interactions were the main contributor for the Endo product being the kinetic product.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 Exo Steric Clash2.png|450px|thumb| '''Figure 30.''' Illustration of possible steric clash in Exo transition state]]
| colspan="3" align="center"|[[File: SL7514 Endo Steric Clash.png|300px|thumb| '''Figure 31.''' Illustration of possible steric clash in Exo transition state]]
|}

==Diels-Alder and Cheletropic Reaction==

The IRC plot for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514EndoExoChel.png|700px|thumb| '''Figure 32.''' IRC and gradient plot for Cheletropic, Endo and Exo Diels-Alder reaction between xylylene and SO<sub>2</sub>. The primary orbital interactions are shown by the solid line and the secondary by the dashed line.]]
|}

The IRC movie for Endo, Exo and Cheletropic reaction between Xylylene and SO<sub>2</sub> are shown below.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 Chel Movie.gif|300px|thumb| '''Figure 33.''' Cheletropic reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 ENDO Movie.gif|300px|thumb| '''Figure 34.''' Endo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
| colspan="3" align="center"|[[File: SL7514 IRC XylyleneSO2 EXO Movie.gif|300px|thumb| '''Figure 35.''' Exo Diels-Alder reaction between xylylene and SO<sub>2</sub> visualisation]]
|}

The reaction profile diagram for this experiment is shown in Figure 36.

{| class="wikitable" border="1"
| colspan="3" align="center"|[[File: SL7514 EX3 Reaction Profile2.png|800px|thumb| '''Figure 36.''' The reaction profile diagram for the Endo, Exo Diels-Alder reaction and Cheletropic reaction between Xylylene and SO<sub>2</sub>]]
|}

Following the reaction, the 6-membered ring becomes aromatic as it satisfy the Huckel's rule 4n+2 electrons in continuous p orbitals on a flat surface in a ring. Xylylene is very unstable molecule since it is antiaromatic. Antiaromatic compounds possess 4n π electron system and since Xylylene has 8 π electrons, the electron interactions in the π system is highly unfavourable.<ref name="breslow" />

{| class="wikitable"
|+ Table 4. A summary of the activation energy and the change in free energy for the Diels-Alder reaction at the cyclohexadiene part of the molecule compared to the end diene part
|-
!
!Endo Cyclohexadiene Part
!Exo Cyclohexadiene Part
!Endo End Part
!Exo End Part
|-
|Activation Barrier ΔG<sup>ǂ</sup>
|103.0
|110.8
|72.8
|76.8
|-
|Product Free Energy Change Δ<sub>r</sub>G
| 7.3
| 11.7
| -108.0
| -108.7
|}

Table 4 summarised the free energy changes that occurred during the reaction for the Diels-Alder at the end diene and cyclohexadiene. The reaction at the cyclohexadiene part of the molecule was kinetically unfavoured due to much higher activation energy barrier. Furthermore, the free energy change for the product formation was positive and hence it was unfavourable for the reaction to proceed. The formed product was more likely to split back to its reactant form under thermodynamic conditions.

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 70; </script>
<uploadedFileContents> SL7514 XYLYLENESO2 OPTIMISATION Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 29.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 30.''' Freeze coordinate energy minimisation for the Endo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 XYLYLENESO2 OPTIMISATION FREEZE Exo.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 31.''' Freeze coordinate energy minimisation for the Exo product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 54; </script>
<uploadedFileContents>SL7514 FREEZE CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 32.''' Freeze coordinate energy minimisation for the cheletropic reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 33.''' Transition state optimisation for the Endo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 10; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 EXO.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 34.''' Transition state optimisation for the Exo reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 12; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 35.''' Transition state optimisation for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 36.''' IRC for the Endo Diels-Alder reaction
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 37.''' IRC for the Exo Diels-Alder reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC XYLYLENESO2 CHELETROPIC.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 38.''' IRC for the Cheletropic reaction
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 38; </script>
<uploadedFileContents>SL7514 PRODUCT OPT ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 39.''' Endo product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 18; </script>
<uploadedFileContents>SL7514 PRODUCT OPT EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 40.''' Exo product optimisation
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPT CHEL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 41.''' Cheletropic product optimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 32; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 42.''' Endo freeze coordinate minimisation for the Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 30; </script>
<uploadedFileContents>SL7514 FREEZE NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 43.''' Exo freeze coordinate minimisation for the Diels-Alder reaction at cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE ENDO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 44.''' Initial product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 111; </script>
<uploadedFileContents>SL7514 NON AROMATIC XYLYLENE EXO OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 45.''' Initial product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 20; vibration 1; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 46.''' Transition state optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 26; vibration 1 </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 47.''' Transition state optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 48.''' Product optimisation for the Endo Diels-Alder reaction at the cyclohexadiene position
|-
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 16; </script>
<uploadedFileContents>SL7514 PRODUCT OPTIMISATION NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 49.''' Product optimisation for the Exo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 50.''' IRC calculation for Endo Diels-Alder reaction at the cyclohexadiene position
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>SL7514 IRC NON AROMATIC XYLYLENE EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 51.''' IRC calculation for Exo Diels-Alder reaction at the cyclohexadiene position
|}

==Extension==

===Introduction===

For ring closing electrocyclic reactions, the ring closure can be either conrotatory or disrotatory. From Woodward-Hoffmann rules, for thermally allowed pericyclic reactions the stereospecificity is determined by the symmetry of the HOMO.<ref name="ponec" /> In this study, the ring closing pericyclic reaction in the formation cyclobutene was investigated. The unusual stereochemical outcome was first investigated by Vogel in 1958.<ref name="vogel" /> As shown in Figure 36, due to the symmetry of the HOMO only the conrotatory reaction is allowed via Mobius transition state involving one antarafacial component.

[[File: SL7514convsdis.png|600px|thumb| '''Figure 36.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

===Methodology===

{| class="wikitable" border="1"
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents> SL7514 INITIAL STRUCTURE OPTIMISATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 52.''' Initial optimisation of the product
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents> SL7514 FREEZE CONROTATION.LOG </uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 53.''' Freeze coordinate energy minimisation
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 TRANSITION STATE OPTIMISATION CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 54.''' Conrotation transition state
| colspan="3" align="center"|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script> frame 34; </script>
<uploadedFileContents>SL7514 IRC CONROTATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol> '''Molecule 55.''' IRC for the conrotation reaction
|}

The product was initially optimised using Gaussview at PM6 level. The initial guess for the transition state was made by elongating the C-C bond which forms during the reaction to 2.2 Ǎ and manually rotating the substituents. The four bonds in the cyclobutene ring was kept constant by freezing the bond length and the angle. The transition state was found using the PM6 method, following which the IRC calculation was performed.

===Results and Discussion===

The simulation for this reaction is shown below as the gif in Figure 37.

[[File: SL7514 Conrotatory reaction.gif|300px|thumb| '''Figure 37.''' Reaction pathway for the conrotatory reaction]]

[[File: SL7514IRCplot.png|500px|thumb| '''Figure 38.''' Conrotatory vs disrotatory reaction in the formation of cyclobutene]]

IRC analysis showed the expected reaction pathway with a clear transition state and product energy higher than the reactant due to the ring strain. The activation energy barrier and the free energy change for the reaction was found to be 200.9 kJ/mol and 60.6 kJ/mol respectively.

==References==

<references>
<ref name="mcdouall"> J. W. McDouall,<i> Computational Quantum Chemistry </i>, RSC Publishing, Cambridge, 2013</ref>
<ref name="dill"> K. A. Dill and S. Bromberg,<i> Molecular Driving Forces </i>, Garland Science, New York, 2011</ref>
<ref name="bachrach"> S. M. Bachrach,<i> Computational Organic Chemistry </i>, Wiley, New Jersey, 2007</ref>
<ref name="lide"> R. Lide, 1961, <i> Elsevier </i>,<b> 17</b>, 125-134</ref>
<ref name="batsanov"> S. S. Batsanov, 2001, <i> Inorg. Mater.</i>,<b> 37</b>, 1031-1046</ref>
<ref name="rowley"> D. Rowley and H. Steiner, 1951, <i> Discuss. Faraday Soc.</i>, 'Kinetics of Diene Reactions at High Temperatures', 198-213</ref>
<ref name="houk"> K. N. Houk, Y. T. Lin and F. K. Brown, 1986, <i> J. Am. Chem. Soc. </i>,<b> 108</b>, 554-556</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="sham"> W. Kohn and L. J. Sham, 1965, <i> Phys. Rev. </i>,<b> 140</b>, 1133-1138</ref>
<ref name="cooley"> J. H. Cooley, R. V. Williams, 1997, <i> Jour. Chem. Educ. </i>,<b> 74</b>, 582-585</ref>
<ref name="ponec"> R. Ponec,<i> Overlap Determinant Method in the Theory of Pericyclic Reactions </i>, Springer, Berlin, 1995</ref>
<ref name="vogel"> E. Vogel, 1958, <i> Wiley </i>,<b> 615</b>, 14-21</ref>
<ref name="breslow"> R. Breslow, J. Brown and J. J. Gajewski, 1967, <i> Jour. Am. Chem. Soc </i>,<b> 89</b>, 4383-4390</ref>
</references>

File:Exo Steric Clash2.png

2017-03-09T19:23:10Z

Sl7514:

File:SL7514 Exo Steric Clash.png

2017-03-09T19:22:49Z

Sl7514: Sl7514 uploaded a new version of File:SL7514 Exo Steric Clash.png