ChemWiki - User contributions [en]

Third Year TS and Reactivity Lab

2019-01-08T11:10:00Z

Tam10: /* Write Up */

'''Transition States Exercises'''

''In these exercises you will locate and characterise transition states of several Diels-Alder reactions. Before starting, you should complete the '''[[Mod:ts_tutorial|tutorial]]''' and decide which method suits you best.''

<br />

== Introduction ==

In this lab, you will locate and characterise transition structures for a variety of pericyclic reactions.

The lab is split into two sections:

1) A tutorial section located '''[[Mod:ts_tutorial|here]]'''. Work through the tutorial first, while not assessed, it will introduce you to the methods and programs involved. It is highly recommended that you are familiar with all three methods before continuing to the exercises.

2) An assessed exercise section below.

In the second year physical chemistry laboratory, you may have carried out dynamics calculations using model potential energy surfaces to explore transition states. In that computational experiment, the total energy could quickly be calculated for different geometries of a triatomic system using an analytical function of the atomic coordinates (for more information, see for example [http://books.google.com/books?id=T8IZ1aa_FRkC&pg=RA1-PA36&lpg=RA1-PA36&dq=%22lake+eyring%22&source=web&ots=OXY00lSZ7D&sig=Ld_MTNwNjUDNGzB_5w1IxaMBMPU&hl=en&sa=X&oi=book_result&resnum=7&ct=result here] and [http://www.rsc.org/ejarchive/DC/1979/DC9796700007.pdf here]).

In this experiment, you will be studying transition structures in larger molecules. There are no longer fitted formulae for the energy, and the molecular mechanics/force field methods that work well for structure determination cannot be used (in general) as they do not describe bonds being made and broken, and changes in bonding type/electron distribution. Instead, we use molecular orbital-based methods, numerically solving the Schrödinger equation, and locating transition structures based on the local shape of a potential energy surface. As well as showing what transition structures look like, reaction paths and barrier heights can also be calculated.

=== Computational Methods ===

Gaussian and Gaussview will be used for the lab. You should be familiar with both from previous labs. Gaussian is a computational chemistry program which runs the calculations. Gaussview is the graphical user interface for Gaussian and can be used to visualise and build the structures.

You will be using Gaussian to calculate the minimum and transition state structures for several reactions. Quantum chemical calculations require an electronic structure method and a basis set, these define the model chemistry of the calculation.

During the lab, you will be using two electronic structure methods: <br />
: '''PM6''' - a semi-empirical method. This means that the method is parameterised using experimental data which saves computational time and resources but does result in lower accuracy than ab initio methods. <br />
: '''B3LYP''' - a Density Functional Theory (DFT) method. B3LYP is reasonably fast compared to other DFT or ''ab inito'' methods and is capable of reproducing chemical data.

In the lab, you will use PM6 to generate initial geometries where possible. The geometries will then be optimised with B3LYP to achieve a more accurate geometry.

A basis set is a set of functions that typically mimic atomic orbitals, which when combined linearly generate molecular orbitals. In a way, they are the building blocks of molecular orbitals. The higher the basis set, the more blocks are available to construct a molecular orbital, at the cost of computational effort.

You should be familiar with the theory behind the lab from last term's Quantum Mechanics 3 lectures. For further information, a really good introduction into the methods used in Gaussian and the quantum chemistry methods that you will use in the lab can be found in the first chapter of [http://pubs.rsc.org/en/content/chapter/bk9781849736084-00001/978-1-84973-608-4|Computational quantum chemistry: molecular structure and properties in silico]. This will be very helpful for your introduction.

== Assessment Information ==
=== Lab Objectives ===

The objectives of the lab are:
* Exploring advanced techniques in Gaussian (and Gaussview)
* Being able to explain what a Transition State and a Potential Energy Surface are
* Being able to use chemical intuition to help locate stationary points on a potential energy surface (i.e. relate the energy balance of a reaction to its landscape)
* Being able to discuss the role of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction

=== Mark Scheme ===

The break-down for the marks for this lab are as follows:
* '''Introduction/Summary''' (Half a page) 20%
* '''Question and answer''' (No page limit) 60%
* '''Conclusions''' (Half a page) 20%

=== Write Up ===

Generally, try to use clear and concise writing style: short sentences that follow each other logically, with a simple writing style. Label all tables, diagrams, and figures with self-contained captions. Use appropriate referencing style. Consider moving long lists of images to an SI section.

:'''Introduction / Summary''': This is where you should discuss the theory behind the computational methods you have applied in this lab. Include the mathematical definition of minima and maxima on a surface, and how they can be related to chemical events. Think about what PM6 and DFT are, and why they are the methods we are using.<br />
:'''Questions and Answers''': Follow the guidelines in the wiki. <br />
:'''Conclusion''': Summarise the key concepts of the lab. What do your results mean? Can you think of any way to obtain better descriptions of the reactions you have studied? 5% of the conclusion marks go to the overall presentation and writing style.<br />

===Lab Time and Report Submission ===

The lab is located in Room 232A (level 2 computer lab). The lab times are 10.00-17.00 Mon, Tue, Thu, Fri.

The report deadline is on Wednesday at 12.00 noon, the week after starting the lab.

'''You must submit on Blackboard:'''
* A written report as a PDF
* A zip file containing '''all''' output files from calculations which you use to answer the questions

The lab time assigned is sufficient to be able to complete the tutorial, assessed exercises and write up within the lab time. In general, it is advised that:

* The tutorial should be completed before moving on to the assessed section. It is advised that you complete the tutorial on Monday to enable enough time for the exercises. By this time you should be comfortable with methods of optimising minima and transition states.
* All calculations should be completed by the end of Friday.
* Write up as you go, it will help you keep track of results and answers.
* Submitted reports and output files will be checked for plagiarism
* Name your output files sensibly and use a unique name (e.g. your username or shortcode: hgr16_butadiene.log)
* ChemDraw is recommended to create MO diagrams and reaction coordinates

=== Demonstrators ===

The demonstrators for the lab session are Francesco, Sami, and Sophie. They will be available to answer your questions and help during the lab in the following sessions:

:'''Monday 10.00 - 12.00''': Francesco<br />
:'''Tuesday 10.00 - 12.00''': Sophie<br />
:'''Thursday 10.00 - 12.00''': Sami<br />
:'''Friday 14.00 - 16.00''': <br />

The demonstrators can also be asked for feedback on the work that you've completed so far in the lab. Outside of the above hours, please use the Year 3 Computational Labs forum, found on the 3rd Year Chemistry Laboratories and Coursework Blackboard page, to post any questions you have on the lab.

Additionally, there is a troubleshooting page [[Mod:ts_troubleshooting|here]] for common errors.

===PM6 Speed Issues===

The Windows code for PM6 calculations does not scale well. In general, increasing the number of processors usually increases performance. However, for these particular calculations, it actually slows it down. In the Calculation Setup window (CTRL+G), go to the Link 0 tab and set Shared Processors to 1. This should be done for all long jobs such as TS and IRC calculations.

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

<br />

[[File:ts_tutorial_BDE_Scheme.png|400px]]

<br />

1) Optimise the reactants and TS at the '''PM6 level'''.

2) Confirm that you have the correct TS with a '''[[Mod:ts_tutorial#Frequency_Calculation|frequency calculation]]''' and '''[[Mod:ts_tutorial#IRC|IRC]]'''.

3) Optimise the products at the PM6 level.

=== Write up and Analysis===

Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).

For each of the reactants and the TS, open the .chk (checkpoint) file. Under the '''Edit''' menu, choose '''MOs''' and visualise the MOs. Include images (or '''[[Mod:Cheatsheet#MOs_with_Jmol|Jmol objects]]''') for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.

Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.

''Alternatively, you can extract these distances from an IRC log file using the script in '''[[IRC_Internuclear_Distances|this page]]''' to create an Excel file with the measurements for each geometry in the IRC and plot the results.''

View the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?

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

<br />

[[File:CHD_Diox_Scheme.png|500px]]

<br />

1) Using any of the methods in the '''[[Mod:ts_tutorial|tutorial]]''', locate both the endo and exo TSs using '''B3LYP/6-31G(d)''' (Note that it is always fastest to optimise with a less expensive method such as PM6 first and then reoptimise with B3LYP). Confirm that you have a TS for each case using a frequency calculation.

'''''Note:''' B3LYP calculations - especially those with calcfc and/or freq - take a long time to run. You can use this time to write up your wiki.''

2) Optimise and run frequency calculations for cyclohexadiene, 1,3-dioxole, and the endo and exo products at the B3LYP/6-31G(d) level. Ensure you have the correct number of imaginary frequencies for these geometries.

=== Write up and Analysis ===

Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry). Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction? (Hint: Run an IRC calculation on the TSs. Running a single point energy calculation - ''Energy''' under '''Job Type''' - will yield an ordered list of MOs that you can use to start you off).

In the .log files for each calculation, find a section named "Thermochemistry". Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol, B3LYP/6-31G(d)) at room temperature (the corrected energies are labelled "'''Sum of electronic and thermal Free Energies'''", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? More detail regarding thermochemistry in Gaussian is given [http://web.thu.edu.tw/ghliu/www/pdf/thermo.pdf here].

Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy (Hint: in GaussView, set the isovalue to 0.01. In Jmol, change the mo cutoff to 0.01)? The Wikipedia page on [https://en.wikipedia.org/wiki/Frontier_molecular_orbital_theory#Cycloadditions Frontier Molecular Orbital Theory] has some useful information on what these secondary orbital interactions are.

== Exercise 3: Diels-Alder vs Cheletropic ==

See the '''[[Mod:ts_tutorial#Xylylene-SO2_Diels_Alder_Cycloaddition|o-Xylylene-SO2 Cycloaddition]]''' section in the tutorial as a guide.

<br />

[[File:Ts_tutorial_xylylene_so2_scheme.png|600px]]

<br />

In the tutorial, you will have ended up with either the endo or the exo TS and adduct for the Diels-Alder reaction. In this exercise, include both TSs and both adducts for each of the cheletropic and Diels-Alder reactions.

1) Optimise the TSs for the endo- and exo- Diels-Alder and the Cheletropic reactions at the '''PM6 level'''.

2) Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.

3) Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred.

4) Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.

Xylylene is highly unstable. Look at the IRCs for the reactions - what happens to the bonding of the 6-membered ring during the course of the reaction?

Third Year TS and Reactivity Lab

2018-09-19T15:29:05Z

Tam10: /* Further Work */

'''Transition States Exercises'''

''In these exercises you will locate and characterise transition states of several Diels-Alder reactions. Before starting, you should complete the '''[[Mod:ts_tutorial|tutorial]]''' and decide which method suits you best.''

<br />

== Introduction ==

In this module you will locate and characterise transition structures for a variety of pericyclic reactions. The lab is split into two sections:

1) A tutorial section located '''[[Mod:ts_tutorial|here]]'''. It is not assessed, but it will introduce you to the methods and programs involved and it is highly recommended that you are familiar with all three methods before continuing.

2) An assessed exercise section below.

<font color="#0000FF">''Don't rush the tutorial section. The exercises will become more straightforward once you have a good understanding of the techniques used in the tutorial section. In addition, the page includes solutions to common errors that are encountered along the way, and instructions for characterising transition state structures. Write up as you go along; constructing a wiki page might take longer than you expect! If you encounter any problems, talk to a demonstrator or a member of staff.''</font>

In the second year physical chemistry laboratory, you may have carried out dynamics calculations using model potential energy surfaces to explore transition states. In that computational experiment, the total energy could quickly be calculated for different geometries of a triatomic system using an analytical function of the atomic coordinates (for more information, see for example [http://books.google.com/books?id=T8IZ1aa_FRkC&pg=RA1-PA36&lpg=RA1-PA36&dq=%22lake+eyring%22&source=web&ots=OXY00lSZ7D&sig=Ld_MTNwNjUDNGzB_5w1IxaMBMPU&hl=en&sa=X&oi=book_result&resnum=7&ct=result here] and [http://www.rsc.org/ejarchive/DC/1979/DC9796700007.pdf here]).

In this experiment, you will be studying transition structures in larger molecules. There are no longer fitted formulae for the energy, and the molecular mechanics / force field methods that work well for structure determination cannot be used (in general) as they do not describe bonds being made and broken, and changes in bonding type / electron distribution. Instead, we use molecular orbital-based methods, numerically solving the Schrödinger equation, and locating transition structures based on the local shape of a potential energy surface. As well as showing what transition structures look like, reaction paths and barrier heights can also be calculated.

=== Suggested Time Frame ===

Try to complete the '''[[Mod:ts_tutorial|Tutorial]]''' on Monday to give enough time for the exercise. By this time you should be comfortable with methods of optimising minima and transition states. The tutorial is not examined, but keep the files that you have created as they might come in useful later in the exercise.

All calculations should be completed by the end of Friday. The deadline for handing in is on the following Wednesday at noon to give you time to write up and format your report.

=== Mark Scheme ===

The break-down for the marks for this lab are as follows:

{|class=wikitable
|-
|Introduction and conclusion
|10%
|-
|Presentation
|10%
|-
|Exercise 1
|20%
|-
|Exercise 2
|30%
|-
|Exercise 3
|30%
|}

Marks are awarded for presentation of data, including the use of tables, images and Jmol objects. If you're unsure what to put into your wiki report or how to structure it, ask a demonstrator.

=== Computational Methods ===

During this lab you will be using two electronic structure methods: the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP. Briefly, PM6 is a fitted method using experimental data to save resources and time during calculations. As a result, it is generally much faster than ab initio methods with reasonable results. B3LYP is a reasonably fast DFT methods that is capable of reproducing chemical data. In this lab, PM6 is used to generate initial geometries where possible, and this geometry is optimised with B3LYP.

A basis set is a set of functions that typically mimic atomic orbitals, which when combined linearly generate molecular orbitals. In a way, they are the building blocks of molecular orbitals. The higher the basis set, the more blocks are available to construct a molecular orbital, at the cost of computational effort.

A really good introduction into the methods used in Gaussian and the quantum chemistry methods that you will use in the lab can be found in the first chapter of [http://pubs.rsc.org/en/content/chapter/bk9781849736084-00001/978-1-84973-608-4|Computational quantum chemistry: molecular structure and properties in silico]. This will be very helpful for your introduction.

=== Objectives ===

By the end of this lab:

* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.

=== Write up ===

Make sure your page name is unique (eg Mod:grj13TS), and every file that you upload has your username in it to prevent it being replaced (eg grj13_butadiene.png).

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

For each of your calculations, upload the log file and include a link in the wiki (this is not necessary if you have included a JMol for that calculation).

'''If you're expecting to use JMols later on, read the section on [[Mod:Cheatsheet#Jmol_Appletsl|JMols]] first before submitting calculations'''

It is recommended to use ChemDraw to create MO diagrams and reaction coordinates.

=== Plagiarism ===

Submissions are checked for plagiarism. Do not copy text or images from other wiki pages. External images may be used if correctly cited, but it's always better to create your own.

=== Demonstrators ===

The demonstrators are Tristan (tam10), Nathan (nf710), and Francesca (fv611). If you're stuck and you can't proceed, you can send us an email and we'll try to help.

{| class="wikitable"
! Hour Beginning
! Monday
! Tuesday
! Wednesday
! Thursday
! Friday
|-
! 10
| Tristan
| Francesca
| -
| Nathan
| Tristan
|-
! 11
| -
| -
| -
| -
| -
|-
! 12
| -
| -
| -
| -
| -
|-
! 13
| -
| -
| -
| -
| -
|-
! 14
| Francesca
| Nathan
| -
| Tristan
| Francesca
|-
! 15
| -
| -
| -
| -
| -
|-
! 16
| Nathan
| Tristan
| -
| Francesca
| Nathan
|-
! 17
| -
| -
| -
| -
| -
|-
! 18
| -
| -
| -
| -
| -
|}

===PM6 Speed Issues===

The Windows code for PM6 calculations does not scale well. Usually you would hope that increasing the number of processors will increase the performance. For these particular calculations it actually slows it down. In the Calculation Setup window (CTRL+G), go to the Link 0 tab and set Shared Processors to 1. This should be done for all long jobs such as TS and IRC calculations.

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

<br />

[[File:ts_tutorial_BDE_Scheme.png|400px]]

<br />

1) Optimise the reactants and TS at the '''PM6 level'''.

2) Confirm that you have the correct TS with a '''[[Mod:ts_tutorial#Frequency_Calculation|frequency calculation]]''' and '''[[Mod:ts_tutorial#IRC|IRC]]'''.

3) Optimise the products at the PM6 level.

=== Write up and Analysis===

Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).

For each of the reactants and the TS, open the .chk (checkpoint) file. Under the '''Edit''' menu, choose '''MOs''' and visualise the MOs. Include images (or '''[[Mod:Cheatsheet#MOs_with_Jmol|Jmol objects]]''') for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.

Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.

''Alternatively, you can extract these distances from an IRC log file using the script in '''[[IRC_Internuclear_Distances|this page]]''' to create an Excel file with the measurements for each geometry in the IRC and plot the results.''

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?

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

<br />

[[File:CHD_Diox_Scheme.png|500px]]

<br />

1) Using any of the methods in the '''[[Mod:ts_tutorial|tutorial]]''', locate both the endo and exo TSs using '''B3LYP/6-31G(d)''' (Note that it is always fastest to optimise with a less expensive method such as PM6 first and then reoptimise with B3LYP). Confirm that you have a TS for each case using a frequency calculation.

'''''Note:''' B3LYP calculations - especially those with calcfc and/or freq - take a long time to run. You can use this time to write up your wiki.''

2) Optimise and run frequency calculations for cyclohexadiene, 1,3-dioxole, and the endo and exo products at the B3LYP/6-31G(d) level. Ensure you have the correct number of imaginary frequencies for these geometries.

=== Write up and Analysis ===

Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry). Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction? (Hint: Run an IRC calculation on the TSs. Running a single point energy calculation - ''Energy''' under '''Job Type''' - will yield an ordered list of MOs that you can use to start you off).

In the .log files for each calculation, find a section named "Thermochemistry". Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol, B3LYP/6-31G(d)) at room temperature (the corrected energies are labelled "'''Sum of electronic and thermal Free Energies'''", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? More detail regarding thermochemistry in Gaussian is given [http://web.thu.edu.tw/ghliu/www/pdf/thermo.pdf here].

Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy (Hint: in GaussView, set the isovalue to 0.01. In Jmol, change the mo cutoff to 0.01)? The Wikipedia page on [https://en.wikipedia.org/wiki/Frontier_molecular_orbital_theory#Cycloadditions Frontier Molecular Orbital Theory] has some useful information on what these secondary orbital interactions are.

== Exercise 3: Diels-Alder vs Cheletropic ==

See the '''[[Mod:ts_tutorial#Xylylene-SO2_Diels_Alder_Cycloaddition|o-Xylylene-SO2 Cycloaddition]]''' section in the tutorial as a guide.

<br />

[[File:Ts_tutorial_xylylene_so2_scheme.png|600px]]

<br />

In the tutorial, you will have ended up with either the endo or the exo TS and adduct for the Diels-Alder reaction. In this exercise, include both TSs and both adducts for each of the cheletropic and Diels-Alder reactions.

1) Optimise the TSs for the endo- and exo- Diels-Alder and the Cheletropic reactions at the '''PM6 level'''.

2) Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.

3) Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred.

4) Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.

Xylylene is highly unstable. Look at the IRCs for the reactions - what happens to the bonding of the 6-membered ring during the course of the reaction?

Third Year TS and Reactivity Lab

2018-09-19T15:27:58Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

'''Transition States Exercises'''

''In these exercises you will locate and characterise transition states of several Diels-Alder reactions. Before starting, you should complete the '''[[Mod:ts_tutorial|tutorial]]''' and decide which method suits you best.''

<br />

== Introduction ==

In this module you will locate and characterise transition structures for a variety of pericyclic reactions. The lab is split into two sections:

1) A tutorial section located '''[[Mod:ts_tutorial|here]]'''. It is not assessed, but it will introduce you to the methods and programs involved and it is highly recommended that you are familiar with all three methods before continuing.

2) An assessed exercise section below.

<font color="#0000FF">''Don't rush the tutorial section. The exercises will become more straightforward once you have a good understanding of the techniques used in the tutorial section. In addition, the page includes solutions to common errors that are encountered along the way, and instructions for characterising transition state structures. Write up as you go along; constructing a wiki page might take longer than you expect! If you encounter any problems, talk to a demonstrator or a member of staff.''</font>

In the second year physical chemistry laboratory, you may have carried out dynamics calculations using model potential energy surfaces to explore transition states. In that computational experiment, the total energy could quickly be calculated for different geometries of a triatomic system using an analytical function of the atomic coordinates (for more information, see for example [http://books.google.com/books?id=T8IZ1aa_FRkC&pg=RA1-PA36&lpg=RA1-PA36&dq=%22lake+eyring%22&source=web&ots=OXY00lSZ7D&sig=Ld_MTNwNjUDNGzB_5w1IxaMBMPU&hl=en&sa=X&oi=book_result&resnum=7&ct=result here] and [http://www.rsc.org/ejarchive/DC/1979/DC9796700007.pdf here]).

In this experiment, you will be studying transition structures in larger molecules. There are no longer fitted formulae for the energy, and the molecular mechanics / force field methods that work well for structure determination cannot be used (in general) as they do not describe bonds being made and broken, and changes in bonding type / electron distribution. Instead, we use molecular orbital-based methods, numerically solving the Schrödinger equation, and locating transition structures based on the local shape of a potential energy surface. As well as showing what transition structures look like, reaction paths and barrier heights can also be calculated.

=== Suggested Time Frame ===

Try to complete the '''[[Mod:ts_tutorial|Tutorial]]''' on Monday to give enough time for the exercise. By this time you should be comfortable with methods of optimising minima and transition states. The tutorial is not examined, but keep the files that you have created as they might come in useful later in the exercise.

All calculations should be completed by the end of Friday. The deadline for handing in is on the following Wednesday at noon to give you time to write up and format your report.

=== Mark Scheme ===

The break-down for the marks for this lab are as follows:

{|class=wikitable
|-
|Introduction and conclusion
|10%
|-
|Presentation
|10%
|-
|Exercise 1
|20%
|-
|Exercise 2
|30%
|-
|Exercise 3
|30%
|}

Marks are awarded for presentation of data, including the use of tables, images and Jmol objects. If you're unsure what to put into your wiki report or how to structure it, ask a demonstrator.

=== Computational Methods ===

During this lab you will be using two electronic structure methods: the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP. Briefly, PM6 is a fitted method using experimental data to save resources and time during calculations. As a result, it is generally much faster than ab initio methods with reasonable results. B3LYP is a reasonably fast DFT methods that is capable of reproducing chemical data. In this lab, PM6 is used to generate initial geometries where possible, and this geometry is optimised with B3LYP.

A basis set is a set of functions that typically mimic atomic orbitals, which when combined linearly generate molecular orbitals. In a way, they are the building blocks of molecular orbitals. The higher the basis set, the more blocks are available to construct a molecular orbital, at the cost of computational effort.

A really good introduction into the methods used in Gaussian and the quantum chemistry methods that you will use in the lab can be found in the first chapter of [http://pubs.rsc.org/en/content/chapter/bk9781849736084-00001/978-1-84973-608-4|Computational quantum chemistry: molecular structure and properties in silico]. This will be very helpful for your introduction.

=== Objectives ===

By the end of this lab:

* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.

=== Write up ===

Make sure your page name is unique (eg Mod:grj13TS), and every file that you upload has your username in it to prevent it being replaced (eg grj13_butadiene.png).

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

For each of your calculations, upload the log file and include a link in the wiki (this is not necessary if you have included a JMol for that calculation).

'''If you're expecting to use JMols later on, read the section on [[Mod:Cheatsheet#Jmol_Appletsl|JMols]] first before submitting calculations'''

It is recommended to use ChemDraw to create MO diagrams and reaction coordinates.

=== Plagiarism ===

Submissions are checked for plagiarism. Do not copy text or images from other wiki pages. External images may be used if correctly cited, but it's always better to create your own.

=== Demonstrators ===

The demonstrators are Tristan (tam10), Nathan (nf710), and Francesca (fv611). If you're stuck and you can't proceed, you can send us an email and we'll try to help.

{| class="wikitable"
! Hour Beginning
! Monday
! Tuesday
! Wednesday
! Thursday
! Friday
|-
! 10
| Tristan
| Francesca
| -
| Nathan
| Tristan
|-
! 11
| -
| -
| -
| -
| -
|-
! 12
| -
| -
| -
| -
| -
|-
! 13
| -
| -
| -
| -
| -
|-
! 14
| Francesca
| Nathan
| -
| Tristan
| Francesca
|-
! 15
| -
| -
| -
| -
| -
|-
! 16
| Nathan
| Tristan
| -
| Francesca
| Nathan
|-
! 17
| -
| -
| -
| -
| -
|-
! 18
| -
| -
| -
| -
| -
|}

===PM6 Speed Issues===

The Windows code for PM6 calculations does not scale well. Usually you would hope that increasing the number of processors will increase the performance. For these particular calculations it actually slows it down. In the Calculation Setup window (CTRL+G), go to the Link 0 tab and set Shared Processors to 1. This should be done for all long jobs such as TS and IRC calculations.

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

<br />

[[File:ts_tutorial_BDE_Scheme.png|400px]]

<br />

1) Optimise the reactants and TS at the '''PM6 level'''.

2) Confirm that you have the correct TS with a '''[[Mod:ts_tutorial#Frequency_Calculation|frequency calculation]]''' and '''[[Mod:ts_tutorial#IRC|IRC]]'''.

3) Optimise the products at the PM6 level.

=== Write up and Analysis===

Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).

For each of the reactants and the TS, open the .chk (checkpoint) file. Under the '''Edit''' menu, choose '''MOs''' and visualise the MOs. Include images (or '''[[Mod:Cheatsheet#MOs_with_Jmol|Jmol objects]]''') for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.

Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.

''Alternatively, you can extract these distances from an IRC log file using the script in '''[[IRC_Internuclear_Distances|this page]]''' to create an Excel file with the measurements for each geometry in the IRC and plot the results.''

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?

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

<br />

[[File:CHD_Diox_Scheme.png|500px]]

<br />

1) Using any of the methods in the '''[[Mod:ts_tutorial|tutorial]]''', locate both the endo and exo TSs using '''B3LYP/6-31G(d)''' (Note that it is always fastest to optimise with a less expensive method such as PM6 first and then reoptimise with B3LYP). Confirm that you have a TS for each case using a frequency calculation.

'''''Note:''' B3LYP calculations - especially those with calcfc and/or freq - take a long time to run. You can use this time to write up your wiki.''

2) Optimise and run frequency calculations for cyclohexadiene, 1,3-dioxole, and the endo and exo products at the B3LYP/6-31G(d) level. Ensure you have the correct number of imaginary frequencies for these geometries.

=== Write up and Analysis ===

Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry). Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction? (Hint: Run an IRC calculation on the TSs. Running a single point energy calculation - ''Energy''' under '''Job Type''' - will yield an ordered list of MOs that you can use to start you off).

In the .log files for each calculation, find a section named "Thermochemistry". Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol, B3LYP/6-31G(d)) at room temperature (the corrected energies are labelled "'''Sum of electronic and thermal Free Energies'''", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? More detail regarding thermochemistry in Gaussian is given [http://web.thu.edu.tw/ghliu/www/pdf/thermo.pdf here].

Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy (Hint: in GaussView, set the isovalue to 0.01. In Jmol, change the mo cutoff to 0.01)? The Wikipedia page on [https://en.wikipedia.org/wiki/Frontier_molecular_orbital_theory#Cycloadditions Frontier Molecular Orbital Theory] has some useful information on what these secondary orbital interactions are.

== Exercise 3: Diels-Alder vs Cheletropic ==

See the '''[[Mod:ts_tutorial#Xylylene-SO2_Diels_Alder_Cycloaddition|o-Xylylene-SO2 Cycloaddition]]''' section in the tutorial as a guide.

<br />

[[File:Ts_tutorial_xylylene_so2_scheme.png|600px]]

<br />

In the tutorial, you will have ended up with either the endo or the exo TS and adduct for the Diels-Alder reaction. In this exercise, include both TSs and both adducts for each of the cheletropic and Diels-Alder reactions.

1) Optimise the TSs for the endo- and exo- Diels-Alder and the Cheletropic reactions at the '''PM6 level'''.

2) Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.

3) Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred.

4) Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.

Xylylene is highly unstable. Look at the IRCs for the reactions - what happens to the bonding of the 6-membered ring during the course of the reaction?

== Further Work ==

There are examples of several electrocyclic reactions on [http://www.ch.ic.ac.uk/local/organic/pericyclic/p1_electro.html this page] that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:CP2215TransitionStructureLab

2018-04-04T14:56:51Z

Tam10:

= Transition States Lab - Calum Patel =

=== Introduction ===

'''Background'''

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

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

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

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

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

'''Computational Methods'''

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

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

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

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

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

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

'''Exploring the Potential Energy Surface'''

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

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

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

== Reaction of Butadiene with Ethylene ==

===Reaction Scheme===

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

===MO diagram and Jmols===

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

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

'''Cycloaddition Transition State MOs'''

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

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

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

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

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

'''Bond Lengths and TS Vibration'''

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

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

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

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

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

=== LOG Files ===

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

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

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

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

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

===Reaction Scheme and MO diagrams===

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

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

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 4. FOs for cyclohexadiene and 1,3-dioxole MOs for the TS (S=symmetric, AS=anti symmetric)'''
! colspan="2"|ENDO Transition State Orbitals
! colspan="2"|EXO Transition State Orbitals
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<title> ENDO TS HOMO-1 (AS), E = -0.1965</title>
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<uploadedFileContents>GUNNY ENDO B3LYP TS.LOG</uploadedFileContents>
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<title>ENDO TS HOMO (S), E = -0.1905</title>
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<uploadedFileContents>GUNNY ENDO B3LYP TS.LOG</uploadedFileContents>
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| <jmol>
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<title>EXO TS HOMO-1(AS), E = -0.1980</title>
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<uploadedFileContents>GUNNY EXO B3LYP TS.LOG</uploadedFileContents>
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<title>EXO TS HOMO(S), E = -0.1856</title>
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<uploadedFileContents>GUNNY EXO B3LYP TS.LOG</uploadedFileContents>
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<title>ENDO LUMO (S), E = -0.0046</title>
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<uploadedFileContents>GUNNY ENDO B3LYP TS.LOG</uploadedFileContents>
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<title>ENDO LUMO+1 (AS), E = 0.0154</title>
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<uploadedFileContents>GUNNY ENDO B3LYP TS.LOG</uploadedFileContents>
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<title>EXO TS LUMO (S), E = -0.0069</title>
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<uploadedFileContents>GUNNY EXO B3LYP TS.LOG</uploadedFileContents>
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<title>EXO TS LUMO+1 (AS), E = 0.0102</title>
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<uploadedFileContents>GUNNY EXO B3LYP TS.LOG</uploadedFileContents>
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===Inverse Or Normal Electron Demand===

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 5. HOMO of 1,3-dioxole and LUMO of cyclohexadiene (reactants in ENDO orientation)'''
!HOMO of 1,3-dioxole
!LUMO of cyclohexadiene
|-
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Normal electron demand Diels Alder (4 + 2 cycloaddition) reactions are described by the dienophile being electron deficient and diene being electron rich, thus the LUMO of the dienophile interacts with the HOMO of the diene. The opposite case is true for inverse electron demand alternative. '''<ref name="six"/>'''

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

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

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

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

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

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

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

=== LOG Files ===

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

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

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

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

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

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

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

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

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

===Reaction Scheme===

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

===IRC Calculations===

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

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

===Thermochemistry===

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

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

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

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

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

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

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

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

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

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

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

|}

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

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

=== LOG Files ===

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

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

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

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

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

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

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

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

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

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

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

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

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

===Reaction Scheme===

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

===Möbius–Hückel Treatment===

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

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

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

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

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

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

=== LOG Files ===

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

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

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

== Conclusion ==

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

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

== References ==

<references>

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

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

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

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

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

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

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

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

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

Rep:Mod:jd2615TS

2018-04-04T14:34:10Z

Tam10: /* Extension */

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

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

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

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

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

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

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

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

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

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

==Exercise 1==
===Computational Method===
The starting materials were optimized to a minimum using semi-empirical PM6. The product was also optimized using this technique. Once the product was optimized, the bonds between the alkene and the diene were removed, moved slightly apart but still within the Van der Waals radius, and frozen using redundant coordinates. This structure was optimized to a miniumum using semi-empirical PM6 to minimise a transition state-like structure. The minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using semi-empirical PM6.

===Reaction Scheme===

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

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

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

===MO diagram===

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

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

===Jmol of orbitals===

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>ETHENE HOMO</title>
<size>200</size>
<script>frame 10; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT jd2615 1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>ETHENE LUMO</title>
<size>200</size>
<script>frame 10; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT jd2615 1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
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<title>Butadiene HOMO</title>
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<script>frame 28; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_OPT_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Butadiene LUMO</title>
<size>200</size>
<script>frame 28; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_OPT_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>TS HOMO - 1</title>
<size>200</size>
<script>frame 28; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>TS HOMO</title>
<size>200</size>
<script>frame 28; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>TS LUMO</title>
<size>200</size>
<script>frame 28; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>TS LUMO + 1</title>
<size>200</size>
<script>frame 28; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS T1 opt jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

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

|}

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

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

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

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

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

[[Media: DIENE_OPT_jd2615.LOG| BUTADIENE]]

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

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

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

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

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

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

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

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

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

===Energy Calculations===

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

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

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

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS HOMO-1</title>
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<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS HOMO</title>
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<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS LUMO</title>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS LUMO+1</title>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

===Thermodynamics===

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

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

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

[[Media: DIENE_OPT_1_B3LYP_T2_jd2615.LOG| CYCLOHEXADIENE]]

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

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

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

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

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

===Reaction Scheme===

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[Media: XYLYLENE_jd2615.LOG| XYLYLENE]]

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

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

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

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

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

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

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

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

Extension Log files: Failed to converge

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

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

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

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

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

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

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

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

==IRC Calculation==

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

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

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

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

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

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

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

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

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

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

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

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

=References=

Rep:Mod:jd2615TS

2018-04-04T14:27:00Z

Tam10: /* Exercise 3 */

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

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

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

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

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

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

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

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

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

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

==Exercise 1==
===Computational Method===
The starting materials were optimized to a minimum using semi-empirical PM6. The product was also optimized using this technique. Once the product was optimized, the bonds between the alkene and the diene were removed, moved slightly apart but still within the Van der Waals radius, and frozen using redundant coordinates. This structure was optimized to a miniumum using semi-empirical PM6 to minimise a transition state-like structure. The minimised structure was then optimised to a transition state (Berny) where the force constants were calculated once using semi-empirical PM6.

===Reaction Scheme===

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

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

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

===MO diagram===

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

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

===Jmol of orbitals===

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

===Bond Distances===
{|style="margin: 0 auto;"
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</jmol>

|}

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

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

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

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

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

[[Media: DIENE_OPT_jd2615.LOG| BUTADIENE]]

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

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

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

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

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

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

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

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

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

===Energy Calculations===

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

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

===Jmol images===
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Dioxole HOMO</title>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> DIOXOLE_T2_OPT_1_B3LYP_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Dioxole LUMO</title>
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<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> DIOXOLE_T2_OPT_1_B3LYP_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
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<uploadedFileContents> DIENE_OPT_1_B3LYP_T2_jd2615.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
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<title>Cyclohexadiene LUMO</title>
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<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> DIENE_OPT_1_B3LYP_T2_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
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{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
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<title>Exo TS HOMO-1</title>
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<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
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| <jmol>
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<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
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<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
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| <jmol>
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<color>white</color>
<title>Exo TS LUMO+1</title>
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<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> EXO_TS_B3LYP_TS1_jd2615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

===Thermodynamics===

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

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

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

[[Media: DIENE_OPT_1_B3LYP_T2_jd2615.LOG| CYCLOHEXADIENE]]

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

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

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

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

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

===Reaction Scheme===

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[Media: XYLYLENE_jd2615.LOG| XYLYLENE]]

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

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

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

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

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

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

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

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

Extension Log files: Failed to converge

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

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

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

For a thermal reaction with 4 pi electrons, Huckel theory states that if the reaction is to proceed via a Huckel transition state, the sigma bond forms via disrotatory motion of the p orbitals at the end of the diene which are in an antarafacial arrangement:
{|style="margin: 0 auto;"
| [[File:Disrotatory_jd2615.jpg|400px|thumb|left|Suprafacial, disrotatory motions of p orbitals]]
|}

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

{|style="margin: 0 auto;"
|<jmol>
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<color>white</color>
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<script>frame 23; vibration 1;rotate x -20; </script>
<uploadedFileContents>E1_TS+PM6_2_jd2615.LOG</uploadedFileContents>
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</jmol>
|}

==IRC Calculation==

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

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

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

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

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

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

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

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

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

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

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

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

=References=

Rep:Yg5515ts

2018-04-04T14:11:39Z

Tam10: /* Exercise 3 o-Xylylene-SO2 Cycloaddition */

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

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

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

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

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

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

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

The transition state is defined to satisfy the following relationship:

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

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

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

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

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

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

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

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

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

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

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

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

C2-C3:1.34

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

C3-C4:1.38

C5-C6:1.38

C1-C6:2.11

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

C6-C5:1.54

C4-C5:1.54
|}

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

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

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

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

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

====Optimization of reactants and products====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 8. B3LYP/6-31G(d) Optimisation of reactant and products'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |1,3-Dioxole
| style="text-align: center;" |product(endo)
| style="text-align: center;" |product (exo)
|-
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====TS optimization and characterization====
{| class="wikitable"
| colspan="4" style="text-align: center; background: #f0ddf0" | '''Table 9. B3LYP/6-31G(d)Optimisation of TS, frequency analysis and IRC'''
|-
|
| style="text-align: center;" |TS (endo)
| style="text-align: center;" |TS (exo)
|-
|optimized structure
| <jmol>
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|-
|frequency analysis
|[[File:Yihan ex2Endo TS freq.PNG]]
|[[File:Yihan ex2Exo TS freq.PNG]]
|-
|IRC(total energy)
|[[File:YihanEndo IRC total E.PNG|400px]]
|[[File:YihanExo IRC total E.PNG|400px]]
|-
|IRC( RMS gradient norm)
|[[File:YihanEndo IRC g.PNG|400px]]
|[[File:YihanExo IRC g.PNG|400px]]
|-
|reaction progress
|[[File:Yihan ex2Endo movie.gif]]
|[[File:Yihan ex2Exo movie.gif]]
|}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

====Thermochemical analysis====

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

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

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

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

Files:
Ex1:

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

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

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

Ex2

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

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

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

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

Ex3

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

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

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

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

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

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

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

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

References
<references/>

Rep:Mod:HZ4315

2018-04-04T13:12:53Z

Tam10:

== Introduction ==

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

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

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

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

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

=== Potential Energy Surfaces ===

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

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

=== Computational Techniques ===

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

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

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

====B3LYP Optimisation====

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

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

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

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

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

3. IRC analysis of the reaction.

4. Optimisation of the cyclohexene product.

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

===Key Molecular Orbitals===

====Reactants====

{| class="wikitable" style="margin: auto;"
!
! Ethylene
! Butadiene
|-
| '''HOMO'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 ETHYLENE GS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 MIN BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| '''LUMO'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 ETHYLENE GS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HZ4315 MIN BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ align="bottom" style="caption-side: bottom" | '''Table 1:''' Reactant HOMOs and LUMOs.
|}
<br>

====Transition State====

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

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

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

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

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

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

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

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

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

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

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

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

- Carbon VdW radius = 1.7Å

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

===Key Molecular Orbitals===

====Reactants====

{| class="wikitable" style="margin: auto;"
!
! Cyclohexadiene
! 1,3-Dioxole
|-
| '''HOMO'''
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|-
| '''LUMO'''
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<uploadedFileContents>HZ4315 EX2 Diox.LOG</uploadedFileContents>
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</jmol>
|+ align="bottom" style="caption-side: bottom" | '''Table 4:''' Reactant HOMOs and LUMOs.
|}
<br>

====Transition State====

=====Endo=====

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

=====Exo=====

<br>
{| class="wikitable" style="margin: auto;"
!
! HOMO (-1)
! HOMO
! LUMO
! LUMO (+1)
|-
| '''TS (Exo)'''
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|+ align="bottom" style="caption-side: bottom" | Table 6: HOMO (-1), HOMO, LUMO and LUMO (+1) of the Exo TS.
|}
<br>

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

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

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

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

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

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

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

=====Endo=====

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

=====Exo=====

<br>
{| class="wikitable" style="margin: auto;"
!
! HOMO (-1)
! HOMO
! LUMO
! LUMO (+1)
|-
| '''TS (Exo)'''
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</jmol>
| <jmol>
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|<jmol>
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|+ align="bottom" style="caption-side: bottom" | Table 9: HOMO (-1), HOMO, LUMO and LUMO (+1) of the Exo TS (energies obtained using an SPE calculation).
|}
<br>

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

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

===Energy Analysis/Reaction Coordinate===

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

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

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

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

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

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

These energies give rise to the following reaction coordinate:

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

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

Product Energy Log Files:

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

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

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

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

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

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

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

4. IRC analysis.

5. Establishment of the reaction coordinates using reaction energies.

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

===IRC Analysis===

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

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

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

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

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

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

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

===Energy Analysis/Reaction Coordinate===

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

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

There energies gave rise to the following coordinate:

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

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

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

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

====IRC Analysis====

=====Endo=====

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

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

=====Exo=====

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

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

====Energy Analysis====

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

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

===Log Files===

Reactants:

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

Exocyclic Reaction (Endo):

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

Exocyclic Reaction (Exo):

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

Exocyclic Reaction (Cheletropic):

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

Endocyclic Reaction (Endo):

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

Endocyclic Reaction (Exo):

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

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

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

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

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

===Transition State Vibration===

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

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

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

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

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

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

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

== Conclusion ==

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

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

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

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

== References ==

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

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

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

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

Rep:Lo915 Transition States and Reactivity

2018-04-04T12:36:37Z

Tam10: /* Electrocyclic reaction */

=Introduction=

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

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

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

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

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

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

=Exercise 1=
This exercise involved a Diels-Alder Reaction between ethene and butadiene. The transition state was optimised using a PM6 calculation, with the reactants and product also optimised at this level. An MO diagram was constructed and compared to the MOs visualised for both the transition state and reactants. The bond distances of the carbon atoms were compared along the reaction coordinate from the reactants to the products, and the reaction path vibration was visualised.

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

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

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

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

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

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

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

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

===Reaction path Vibration===
<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<uploadedFileContents>Lo915_1_TS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 17;frank off</script>
<name>TS1</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>TS1</target>
</jmolbutton>
</jmol>
Figure 7. Reaction path vibration

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

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

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

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

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

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

Figure 11. shows the visualisation of the endo and exo transition state orbitals. From these the orientation of the 1,3-dioxole in the endo relative to the exo can be clearly seen, as well as the symmetry of each of the orbitals.
{| style="margin-left: auto; margin-right: auto; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 11. Transition state MOs for the endo and exo reaction
|-
!colspan="4"|Endo Transition State MOs
|-
| <jmol>
<jmolApplet>
<title>HOMO - 1</title>
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<script>frame 34; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_ENDO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_ENDO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_ENDO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO + 1</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_ENDO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!colspan="4"|Exo Transition state MOs
|-
| <jmol>
<jmolApplet>
<title>HOMO - 1</title>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_EXO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_EXO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_EXO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO + 1</title>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_EXO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Secondary Orbital Interactions===

The reason for the lower energy of the HOMO of the endo transition state relative to the exo can be seen in the secondary orbital interactions between the p orbitals of the cyclohexadiene and the p orbitals on the oxygens of the 1,3-dioxole. The endo transition state places these in the correct position for overlap between them, therefore stabilising the transition state and lowering its energy, however as the exo transition state has the oxygens on the opposite side, there is no opporunity for interaction between these orbitals, and therefore no stabilisation. Another reason for the lower energy of the endo transition state is due to steric hindrance that occurs in the exo product, as the 1,3-dioxole is positioned up towards the carbon bridge, while in the endo product, it points down away from the carbon bridge, and therefore avoids this destabilising steric interaction.
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 12. Secondary orbital interactions of the transition state HOMO orbital
|-
|<jmol>
<jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 41;mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_ENDO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO</title>
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<script>frame 20; mo 41;mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_2_TS_EXO_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- style="text-align: center;"
|}

===Energies===
The energies of the reactants, transistion states and products were obtained from the B3LYP optimised structures, and converted from Hartrees to kJmol<sup>-1</sup>.These vaules can be seen in table 3. From this, the activation energies and reaction energies were calculated and an energy profile diagram was created to clearly illustrate these values (Figure 12).
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; background: none;"
|+ Table 3. Energies of the reactants, transition states and product, with the activation and reaction energies calculated
! colspan="1" style="border: none; background: none;"|
! colspan="7"| Energy (kJmol<sup>-1</sup>)
|-
! Reaction type !! 1,3-dioxole !! Cyclohexadiene !! Reactant total !! Transition State !! Activation Energy !! Product !! Reaction Energy
|-
!Endo
| rowspan="2" | -701187.38
| rowspan="2" |-612593.15
| rowspan="2" |-1313780.53
| -1313622.06
| 158.47
| -1313849.27
| -68.75
|-
!Exo
| -1313614.22
| 168.27
| -1313845.68
| -65.15
|-
|}

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

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

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

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

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

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

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

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

===Alternative Diels-Alder Reactions===

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

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

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

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

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

<jmol>
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<script>vibrating=0; spinning=0; frame 127; frank off</script>
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<jmolbutton>
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<text>Vibration</text>
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Figure 17. Vibration of reaction path
[[File:lo915_4_conrotation2.jpg|thumb|Figure 18. Controtation in electrocyclic reaction|center|500px]]

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

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

{| style="margin-left: auto; margin-right: auto; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 20. Reactant, product and transition state MOs
|-
!colspan="4"|Reactant MOs
|-
| <jmol>
<jmolApplet>
<title>HOMO - 1</title>
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| <jmol>
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| <jmol>
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<title>LUMO</title>
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<uploadedFileContents>Lo915_4_IRC_INITIAL.LOG</uploadedFileContents>
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</jmol>
| <jmol>
<jmolApplet>
<title>LUMO + 1</title>
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<script>frame 20; mo 35; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_4_IRC_INITIAL.LOG</uploadedFileContents>
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|-
!colspan="4"|Product MOs
|-
| <jmol>
<jmolApplet>
<title>HOMO - 1</title>
<color>white</color>
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<uploadedFileContents>Lo915_4_IRC_FINAL.LOG</uploadedFileContents>
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</jmol>
| <jmol>
<jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 20; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_4_IRC_FINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>200</size>
<script>frame 20; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_4_IRC_FINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO + 1</title>
<color>white</color>
<size>200</size>
<script>frame 20; mo 35; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Lo915_4_IRC_FINAL.LOG</uploadedFileContents>
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|-
!colspan="4"|Transition State MOs
|-
| <jmol>
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<title>HOMO - 2</title>
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<uploadedFileContents>Lo915_4_TS.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<title>HOMO</title>
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<uploadedFileContents>Lo915_4_TS.LOG</uploadedFileContents>
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| <jmol>
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<title>LUMO</title>
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<uploadedFileContents>Lo915_4_TS.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<title>LUMO + 1</title>
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<script>frame 126; mo 35; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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=Conclusion=
For all of the reactions, the transition state was found and optimised successfully. It was found that the first Diels-Alder reaction was normal demand, while the second Diels-Alder was inverse electron demand, due to the electron rich nature of the dienophile. For both exercises 2 and 3, it was found that the endo Diels-Alder reaction was thermodynamically preferred to the exo reaction, due to the stabilising secondary orbital overlap. For exercise 3, the cheletropic product was the thermodynamically preferred product, while the alternate Diels-Alder reactions were thermodynamically unfavourable as there is no aromatic ring formation as for the original Diels-Alder reactions and the cheletropic reaction. In the electrocyclic reaction it was found to proceed in a conrotatory fashion, as expected for a thermal 4n eletron elecrocyclic reaction. This could be extended by investigated the photochemical reaction, which would preocceed in a disrotatory fashion, however the PM6 level could not be used for these calculations due to the need for excited states.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=References=

Rep:Lo915 Transition States and Reactivity

2018-04-04T12:35:10Z

Tam10: /* Exercise 3 */

=Introduction=

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

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

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

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

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

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

=Exercise 1=
This exercise involved a Diels-Alder Reaction between ethene and butadiene. The transition state was optimised using a PM6 calculation, with the reactants and product also optimised at this level. An MO diagram was constructed and compared to the MOs visualised for both the transition state and reactants. The bond distances of the carbon atoms were compared along the reaction coordinate from the reactants to the products, and the reaction path vibration was visualised.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

===Alternative Diels-Alder Reactions===

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

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

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

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

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

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Figure 17. Vibration of reaction path
[[File:lo915_4_conrotation2.jpg|thumb|Figure 18. Controtation in electrocyclic reaction|center|500px]]
Figure 18 shows the formation of the HOMO of the product, with the C<sub>2</sub> axis of symmetry labelled. This axis of symmetry is used to label the orbitals as either symmetric or asymmetric. Figure 19 shows the correlation diagram for the reaction, where it can be seen that the order of the occupied orbitals is reversed, with symmetric HOMO of the reactant forming the symmetric σ orbital formed in the product, while the HOMO orbital of the product (the π orbital) has the same symmetry as the HOMO-1 of the reactant. The same occurs with the unoccupied orbitals, with the asymmetric LUMO of the reactant forming the asymmetric LUMO+1 of the product (the σ<sup>*</sup> orbital), and the LUMO+1 orbitals of the reactant forming the LUMO of the product (the π<sup>*</sup> orbital)
[[File:lo915_4_MOs2.jpg|thumb|Figure 19. Correlation diagram|center|500px]]
The reaction goes through a mobius transition state, with a node in the phases of the orbitals. As it is a 4n electron reaction, the transition state is termed 'aromatic'.<ref>Dolbier, W. R''Acc. Chem. Res.'', '''1996''', ''29'', 471-477</ref> This can be seen in the visualisation of the transition state orbitals in figure 16.

{| style="margin-left: auto; margin-right: auto; background: none;"
|+ align="bottom" style="font-width:normal"|Figure 20. Reactant, product and transition state MOs
|-
!colspan="4"|Reactant MOs
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| <jmol>
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<uploadedFileContents>Lo915_4_IRC_INITIAL.LOG</uploadedFileContents>
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<uploadedFileContents>Lo915_4_IRC_INITIAL.LOG</uploadedFileContents>
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!colspan="4"|Product MOs
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<uploadedFileContents>Lo915_4_IRC_FINAL.LOG</uploadedFileContents>
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<uploadedFileContents>Lo915_4_IRC_FINAL.LOG</uploadedFileContents>
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!colspan="4"|Transition State MOs
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<uploadedFileContents>Lo915_4_TS.LOG</uploadedFileContents>
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=Conclusion=
For all of the reactions, the transition state was found and optimised successfully. It was found that the first Diels-Alder reaction was normal demand, while the second Diels-Alder was inverse electron demand, due to the electron rich nature of the dienophile. For both exercises 2 and 3, it was found that the endo Diels-Alder reaction was thermodynamically preferred to the exo reaction, due to the stabilising secondary orbital overlap. For exercise 3, the cheletropic product was the thermodynamically preferred product, while the alternate Diels-Alder reactions were thermodynamically unfavourable as there is no aromatic ring formation as for the original Diels-Alder reactions and the cheletropic reaction. In the electrocyclic reaction it was found to proceed in a conrotatory fashion, as expected for a thermal 4n eletron elecrocyclic reaction. This could be extended by investigated the photochemical reaction, which would preocceed in a disrotatory fashion, however the PM6 level could not be used for these calculations due to the need for excited states.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=References=

Rep:SJP115 Transition States And Reactivity By Sarah Patterson

2018-04-04T12:19:36Z

Tam10:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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<br />

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115 Reaction Scheme EXtension2.PNG|thumb|500x500px| Figure 20: IRC for the ring opening of a substituted butadiene]]
|}

The electrocyclic ring opening reaction illustrated in figure 20 reacts antrafacially according to the Woodward Hoffman rules. This system is also a 4nπ electron system that will proceed with conrotation. The TS shows the intermediate step in the formation of the butadiene double bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+
![[File:SJP115_Extension2_GIF.gif|thumb|500x500px| Figure 21: IRC for the ring opening of a substituted butadiene]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
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!HOMO of Reactant
!HOMO of TS
!HOMO of Product
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==<u>Conclusion</u>==

A number of pericyclic reactions were successfully modeled in Gaussian. PM6 was used as the primary method of carrying out calculations as a compromise between rapidity and accuracy. B3YLP was used when it was necessary to probe reactions with a higher level of accuracy. For example, in exercise 2 the transition state geometries of the exo and endo Diels Alder pathways were elucidated using B3YLP.

Gaussian not only provides a means of locating and characterising transition states, but it also enables the visualization of molecular orbitals. The energies of these molecular orbitals can be used to gain insight into the mechanistic pathway behind the reaction; for example, whether a Diels Alder proceeds via normal or inverse electron demand. The Diels Alder reaction between ethene and butadiene (exercise 1) was found to proceed via a normal electron demand, whilst the Diels Alder between the electron rich 1,3 dioxole and the cyclohexadiene was found to occur via inverse electron demand. Further mechanistic insights can be obtained by animation of the imaginary frequency vibration. This gave an insight into how bond formation occurred, whether bond formation was synchronous or asynchronous. Finally, analysis of the thermochemical data aided in identifying the kinetic and thermodynamic pathways and products.

==<u> Files </u>==

===<u>Reaction of Butadiene with Ethylene</u>===

[[Media:SJP115_ETHENE.LOG|Log file of ethene]]

[[Media:SJP115 BUTADIENE2.LOG| Log file of butadiene]]

[[Media:SJP115 EX1 ETHENE AND BUTADIENE SAME FRAME.LOG| Log file of butadiene and ethene in the same frame PM6]]

[[Media: SJP115 Ex1 TS IRC INITIAL SINGLE POINT ENERGY.LOG| Log file of single point energy of ethene and butadiene]]

[[Media:SJP115 TS PM6.LOG| Log file of TS PM6 Optimised]]

[[Media: SJP115 TS IRC.LOG|Log file of the IRC PM6]]

[[Media: SJP115 TS PM6 SYMBROKEN2.LOG| Log file of the PM6 product ]]

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

[[Media:SJP115 DIOXANE BY3.LOG|Log file of 1,3 Dioxole B3YLP]]

[[Media:SJP115 DIENE B3LYP 631GD.LOG|Log file of 1,3 Cyclohexadiene B3YLP]]

[[Media:SJP115 Ex2 Exo TS B3LYP 631GD.LOG|Log file of Exo TS B3YLP]]

[[Media:SJP115_Ex3_Endo_TS_B3LYP_631GD_NOPTEIGEN.LOG|Log file of Endo TS B3YLP]]

[[Media: SJP115 Ex2 Exo TS IRC.LOG|Log file of Exo IRC PM6]]

[[Media:SJP115 Ex2 Endo TS PM6 IRC.LOG|Log file of Endo IRC PM6]]

[[Media:SJP115 Ex2 Exo PRODUCT B3LYP6 31GSD.LOG| Log file of Exo Product B3YLP]]

[[Media:SJP115 Ex2 ENDO PRODUCT B3LYP 631GD.LOG| Log file of Endo Product B3YLP]]

===<u>Diels-Alder vs Cheletropic</u>===

[[Media:SJP115 SO2 2 PM6.LOG|Log file of SO<sub>2</sub>]]

[[Media:SJP115 O-XYLYENE PM6.LOG|Log file of o-Xylyene]]

[[Media:SJP115 Exercise3 TS PM6.LOG| Log file of Exo TS PM6]]

[[Media:SJP115 Exercise3 TS IRC PM6.LOG| Log file of Exo IRC PM6]]

[[Media:SJP115 Exercise3 EXO PRODUCT PM6.LOG| Log file of Exo Product]]

[[Media:SJP115 Exercise3 Endo TS PM6.LOG|Log file of Endo TS PM6]]

[[Media: SJP115 Exercise3 Endo TS IRC.LOG|Log file of Endo IRC PM6]]

[[Media:SJP115 Exercise3 Endo PRODUCT PM6.LOG|Log file of Endo Product]]

[[Media:SJP115 CHELE TS PM6.LOG|Log file of Cheletropic TS PM6]]

[[Media:SJP115 chele IRC 2.LOG|Log file of Cheletropic IRC PM6]]

[[Media:SJP115 CHELE PRODUCT 2 PM6.LOG| Log file of Cheletopic Product]]

[[Media: SJP115 EX3 AP Endo TS PM6.LOG|Log file of Alternative Path Endo TS PM6]]

[[Media:SJP115 EX3 AP Endo TS IRC.LOG| Log file of Alternative Path Endo IRC PM6]]

[[Media:SJP115 EX3 AP ENDO PRODUCT PM6.LOG| Log file of Alternative Path Endo Product PM6]]

[[Media:SJP115 Ex3 AP Exo TS PM6.LOG| Log file of Alternative Path Exo TS PM6]]

[[Media:SJP115 Ex3 AP Exo TS IRC.LOG| Log file of Alternative Path Exo IRC PM6]]

[[Media:SJP115 Ex3 AP Exo PRODUCT PM6.LOG| Log file of Alternative Path Exo Product PM6]]

===<u>Electrocyclic Ring Closing Reaction</u>===

[[Media:SJP115 EXTENSION PRODUCTS FROM IRC.LOG| Log file of Electrocyclic Ring Closing Reactants PM6]]

[[Media: SJP115 Extension1 TS IRC FINAL.LOG| Log file of Electrocyclic Ring Closing IRC PM6]]

[[Media: SJP115 Extension TS PM6 2.LOG| Log file of Electrocyclic Ring Closing TS PM6]]

[[Media:SJP115 EXTENSION REACTANTS FROM IRC.LOG| Log file of Electrocyclic Ring Closing Products PM6]]

[[Media:SJP115 Extension HF OPT.LOG| Log file of Electrocyclic Ring Closing Reactant HF]]

[[Media:SJP115 Extension CAS S1 opt.log| Log File of Electrocyclic Ring Closing CAS of first excited state]]

===<u> Electrocyclic Ring Opening Reaction </u>===

[[Media: SJP115 EXTENSION2 REACTANTS.LOG| Log file of Electrocyclic Ring Opening Reactants]]

[[Media: SJP115 Extension2 TS PM6.LOG| Log file of Electrocyclic Ring Opening TS PM6]]

[[Media: SJP115 Extension2 TS IRC.LOG| Log file of Electrocyclic Ring Opening IRC PM6]]

[[Media: SJP115 EXTENSION2 PRODUCT.LOG| Log file of Electrocyclic Ring Opening Product]]

==<u>References</u>==

Rep:BT1215 CP3MD Lab

2018-04-04T12:04:27Z

Tam10: /* 4π Electrocyclic Reactions: [1,1']-bicyclohexene - PM6 Level */

== Introduction ==
The ability to model reactions using computational simulations is something of great interest, particularly with regard to understanding experimental mechanisms or molecular properties<ref>R. Breslow et. al., Beyond the Molecular Frontier: Challenges for Chemistry and Chemical Engineering, National Research Council, 2003.</ref>. Modern computational software, such as Gaussian, is able to use a series of quantum mechanical calculations to optimise a reaction system and determine a lowest energy reaction pathway, as well as the predicted energies and structures of any reactants, transition states, and products involved. Within these calculations, there are two important theoretical considerations to take into account:

''1. Potential Energy Surface (PES)'' - The potential energy of a system given as a function of molecular geometry. By changing the molecular geometry (e.g. bond lengths during a reaction), the change in energy and transition state can be computed.

''2. Computational Method'' - Defines the approximations made within the quantum mechanics, balancing accuracy (fewer approximations lead to more precise results) with computational cost (fewer assumptions mean more resource-intensive calculations).

=== Potential Energy Surface (PES) ===
[[File:BT1215 PES Example.JPG|right|thumb|210x205px|'''''Figure 1 - An example PES surface, AB<sup>+</sup> and A<sup>+</sup> + B represent local minima, which are separated by a labelled saddle point<ref>L. Sleno and D. A. Volmer, J. Mass Spectrom., 2004, 39, 1091–1112.</ref>.''''']]
As mentioned before, the PES is a representation of the relationship between the potential energy of a system and its molecular geometry. Given that non-linear molecules have a geometrical freedom of 3N-6 modes (or 3N-5 for linear molecules), where N = the number of atoms in the molecule, the PES therefore has the same dependency, relying on the internal coordinates of the atoms in the system. In order to model a reaction PES, the number of degrees of freedom that are varied is often reduced in order to make the calculation computationally feasible. When plotted graphically, the PES represents a landscape of high and low energy configurations that correspond to turning or stationary points on the surface, with an example plot shown in '''Figure 1'''<sup>[2]</sup>. Low energy turning points correspond to an energetically stable molecular geometry, which are mathematically characterised by having a first derivative equal to 0 ('''Eq 1'''), and a positive second derivative ('''Eq 2'''), where <math>{V}</math> is potential energy and <math>{x}</math> represents an atomic or reaction coordinate:
<br>
<br>
<div style="text-align: center;"><math>\frac{\partial V}{\partial x}= 0 </math> '''Eq 1'''</div>
<br>
<div style="text-align: center;"><math>\frac{\partial^{2} V}{\partial x^{^{2}}}> 0</math> '''Eq 2'''</div>
<br>
[[File:BT1215 2D PES to TS Example.gif|right|thumb|313x553px|'''''Figure 2 - A PES diagram of ozone which has been mapped to an IRC along a reaction coordinate, showing the transition state, reactants and products<ref>1 E. G. Lewars, in Computational Chemistry, 2011, vol. 26, pp. 9–43.</ref>.''''']]
The potential energy well surrounding the minimum can be modelled as a Simple Harmonic Oscillator, where the lowest energy point is described by a Taylor expansion. Assuming a harmonic motion modelled by Hooke's law, force constant <math>{k}</math> can be equated to the second derivative in '''Eq 2'''. Since the vibrational wavenumber, <math>{v}</math>, is directly proportional to <math>\sqrt{k}</math>, it can therefore be seen that the molecular configurations corresponding to minimum turning points will '''''only''''' have positive vibrations<ref>P. Atkins and J. De Paula, Atkins’ physical chemistry, 2009.</ref>.

The transition state of a reaction corresponds to a saddle point which separates two local minima in the PES, and is essentially a maximum turning point along a particular reaction coordinate of the surface. This can be modelled as a barrier separating two wells, shown in '''Figure 2'''<sup>[2]</sup>. An activation energy is required to overcome this transition state and thus interconvert between the two wells, often denoted reactants and products. The saddle point on the PES surface can be mathematically described as being a local minimum in all directions except for one, where it is equivalent to a maximum turning point. This leads to one reaction coordinate where the second derivative of potential energy is '''negative'''. Following the same key discussion above, '''''one negative vibration frequency will be observed in the transition state''''', while all other frequencies observed will be positive.

It is important to note that, while this discussion of a singular force constant holds true for one-dimentional systems, polyatomic systems require more complicated treatment, since there are multiple force constants and vibrational motions within the system that can actually couple (i.e. one vibration could affect the likelihood of another happening). The general form of these force constants is shown below in '''Eq 3''', where ''i'' and ''j'' represent degrees of freedom (or coordinates) up to 3N-6:
<br>
<br>
<div style="text-align: center;"><math>\frac{\partial^{2} V}{\partial x_i x_j} = k_{ij} </math> '''Eq 3'''</div>

Software such as Gaussian simplifies these complicated raw motions by first converting the internal coordinates into mass-weighted coordinates to make the coupled force constants equally weighted, before creating a large Hessian matrix of all the coupled force constants. The software then diagonalises the Hessian matrix to give the decoupled, vibrational modes of the molecule<ref>A. Ghysels, V. Van Speybroeck, E. Pauwels, S. Catak, B. R. Brooks, D. Van Neck and M. Waroquier, J. Comput. Chem., 2010, 31, 994–1007./</ref>. A simplified example of the Hessian matrix that is diagonalised is shown below in '''Figure 3''', where <math>K_{ij}</math> represents the force constants with respect to the mass-weighted coordinates.
<br>
<br>
[[File:BT1215 Hessian Matrix.JPG|centre|thumb|799x169px|'''''Figure 3 - A simplified example of the Hessian matrix which is solved to give the vibrational modes''''']]

=== Computational Method ===

In order to compute the potential energy surface and obtain molecular energies, Gaussian uses quantum mechanical calculations based on the Linear Combination of Atomic Orbitals (LCAO) method. As implied by the existence of the PES, the Born-Oppenheimer approximation is used to separate the electron and nuclear timescales, meaning the nuclei are effectively static on an electron timescale and can be manipulated as such. If this approximation was not true then it would be impossible to calculate the PES, since the electronic energies would constantly be affected by nuclear motion. The LCAO method is essentially a sum of atomic orbitals, <math>\phi_i</math>, which combine with a weighting coefficient, <math>c_i</math>, to give the overall molecular orbital wavefunction, <math>\psi_m</math>, shown below in '''Eqn 4''':
<br>
<br>
<div style="text-align: center;"><math>\psi_m = \sum_{i}^N c_i \phi_i</math> '''Eq 4'''</div>
<br>
The number of atomic orbitals used to ''build'' the LCAO is called the '''Basis Set''', which will be discussed further below. The total energy of the molecule is then calculated as a sum of the orbital energies, using the Hamiltonian Operator to solve the Schrödinger equation, where '''Eqn 5''' shows the general form, and '''Eqn 6''' shows the same equation but with the sum of atomic orbitals:
<br>
<br>
<div style="text-align: center;"><math><\psi|\widehat{H}|\psi> = E</math> '''Eq 5'''</div>
<br>
<div style="text-align: center;"><math>\sum_{i}^N \sum_{j}^N<\phi_i|\widehat{H}|\phi_j>c_i c_j = E</math> '''Eq 6'''</div>
<br>
Gaussian represents these equations in matrix form and solves to give the molecular orbital energies, as well as the overall molecule energy. Both the method of calculation and the size of the basis set used to construct the molecular orbital are fundamental factors in determining the accuracy of the computed MOs and energy output, but also in the amount of computational power required. A variety of methods and basis sets can be used to perform optimisations and energy calculations, depending on the computational method chosen. The two methods chosen for all of the following calculations are PM6 and B3LYP (with a 6-31G (d) basis set).

'''PM6''' is a Semi-Empirical method based on the Hartree-Fock method, however it utilises experimental data and/or DFT results (where experimental data is not available) to help speed up the calculation time. Naturally, these assumptions require the system to be modelled by the experimental data used, which may not be an accurate representation. As with the Hartree-Fock method, it also treats electrons as largely independent, and does not account for electron correlation. As a result it represents a rough approximation of the system, although its speed does make it useful for very large systems which would require far too much computational power with a more accurate method. <ref>J. Řezáč, J. Fanfrlík, D. Salahub and P. Hobza, J. Chem. Theory Comput., 2009, 5, 1749–1760.</ref>

'''B3LYP''' is a hybrid method based on both the Hartree-Fock and Density Functional Theory (DFT) techniques. The Hartree-Fock method is employed in the calculation of the exchange-correlation energy, while DFT is used elsewhere due to its improved efficiency. This is because it only depends on a 3-coordinate system describing the electron, and thus scales 3-dimensionally with the number of basis functions, versus the four-dimensional scaling of the Hartree-Fock method. The smaller scaling results in faster computation, though it is still a lot slower than Semi-Empirical methods. A 6-31G (d) Pople basis set used for the B3LYP calculations, where the numbers represent the basis functions used in the calculation. In general terms, a larger basis set corresponds to a more accurate calculation<sup>[4]</sup>.

To localise the transition state in the reaction systems below, three main methods are possible in Gaussian. The first method is adequate when there is previous knowledge surrounding the reaction mechanism, meaning it is possible to guess the transition state structure and then optimise it. Unfortunately this is very difficult to correctly guess, often missing the transition state. The second method has a higher level of accuracy, and involves optimising the reactants, before setting and freezing the distance between the atoms involved in the reaction. Optimisation to a minima is then performed, followed by a transition state optimisation. This approach provides Gaussian with more information surrounding the reaction pathway, and thus helps guide the optimisation to the correct result. This method was used for Exercise 1.

For Exercises 2, 3, and 4, a third, more complex method was chosen. This involves optimising the product, before breaking the bonds that are formed in the reaction. The distance between the atoms that form these bonds is set and frozen at a specific distance that resembles the transition state. The same calculations as in the second method are then used to identify and optimise the transition state structure. This method is the longest, but is also the most reliable, which was the main reason for its use in more complicated reaction systems.

== Exercise 1: Diels-Alder Reaction of Butadiene + Ethylene - PM6 Level ==

=== Reaction Overview ===
Butadiene and ethylene can react to form cyclohexene, shown below in '''Scheme 1'''. The reaction occurs via a type of [4+2] cycloaddition, commonly known as a Diels-Alder reaction, through a concerted syn addition<ref>K. N. Houk, Y. T. Lin and F. K. Brown, J. Am. Chem. Soc., 1986, 108, 554–556.</ref>. In the case of butadiene and ethylene, since butadiene (the diene) is more electron rich than ethylene (the dienophile), the reaction represents a ''normal electron demand'' Diels-Alder cycloaddition.

[[File:BT1215 Diels-Alder RS Butadiene Ethylene.jpg|centre|thumb|757x757px|'''''Scheme 1 - Diels-Alder reaction between butadiene and ethylene''''']]

=== Molecular Orbital Discussion ===
The frontier molecular orbital (MO) diagram for the reaction between butadiene and ethylene is shown below in '''Figure 1''', and was generated using the calculated Gaussian energies of the transition state and reactants. The transition state and reactants were used in the MO diagram for clarity, since conformational changes and significant orbital mixing in the product make the connection more complicated. As a result, the energies computed for the overlapping MOs are significantly higher than those of the optimised product, especially since the transition state represents a strained conformation. It is also important to note that these energies can only be considered relative to each other due to the inaccuracy of the PM6 optimisation method.

[[File:BT1215 Diels-Alder TS Butadiene Ethylene Y3TS.jpg|centre|thumb|783x783px|'''''Figure 4 - MO diagram showing frontier orbital interactions in the Diels-Alder reaction between butadiene and ethylene.''''']]

Interactive JMOLs of the two starting materials, as well as the orbitals involved in the bonding interaction can be seen below in '''Table 1''', labelled with both their number, computed energy and occupancy. It is possible to toggle through the generated frontier MOs using the drop down box. Please note that they may not appear to work correctly until after all of the Jmols on the page have loaded.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 1 - Frontier orbitals in the Diels-Alder Reaction between butadiene + ethylene'''''
!Reactant Orbitals
!Transition State Orbitals
!Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 SPE REACT PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_BEDIELSALDER_ORB_COMB_REACT_TS_PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneDielsAlder</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneDielsAlder</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneDielsAlder</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 PROD CYCLOHEXENE OPT PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneP</target>
</item>
</jmolmenu>
</jmol>
|}

Orbitals can form stabilising overlap interactions when their associated overlap integral is '''''non-zero'''''. The integral is a quantitative representation of the spatial overlap of the orbitals, and thus an integral equal to 0 is equivalent to '''''no''''' spatial overlap. In order for the overlap integral to be non-zero, the overall integral of the interacting orbital wavefunctions must be a symmetric function. As a result, only orbitals which are '''''both''''' symmetric (S × S = S) or '''''both''''' antisymmetric (AS × AS = S) result in a non-zero overlap integral that allows for a stabilising orbital overlap. Interaction between a symmetric and antisymmetric orbital would lead to an overall antisymmetric function (S × AS = AS) and an integral equal to 0 (representing no interaction). <sup>[4]</sup> This can also be seen in the MO diagram above, where only orbitals of the same symmetry interact in the Diels-Alder reaction.

=== Bond Length Discussion ===
Diels-Alder reactions involve the creation of two new σ-bonds between the diene and dienophile, while three π-bonds are lost and another one is created to complete the cycloaddition. The curly-arrow mechanism for the cycloaddition between butadiene and ethylene is shown below in '''Figure 5''', where each carbon has been numbered so as to allow for the discussion of how each bond length changes throughout the course of the reaction.

[[File:BT1215_Diels-Alder_Curly_Arrows.jpg|centre|thumb|584x129px|'''''Figure 5 - Currly arrow mechanism for the Diels-Alder Reaction between Butadiene + Ethylene''''']]

The changes in bond lengths with the reaction coordinate are shown below in '''Graph 1''', and were extracted from the PM6 optimised IRC reaction pathway. The typical values for bond lengths between two sp<sup>3</sup> hybridised carbon atoms, two sp<sup>2</sup> carbon atoms (both single and double bonds), and sp<sup>3</sup> and sp<sup>2</sup> carbon atoms is shown in '''Table 2''', where all values were obtained from the CRC Handbook of Chemistry and Physics<ref>D. R. Lide, CRC Handbook of Chemistry and Physics, 2003, 53, 2616.</ref>. The calculated bond lengths for the PM6 optimised reactants, products, and transition state can be seen in '''Table 3'''. While there are several slightly distinct values for the van der waals radius of a carbon atom, the overall consensus corresponds to a value of 1.70 Å<ref>1 S. S. Batsanov, Inorg. Mater., 2001, 37, 871–885.</ref>.

[[File:BT1215 Exercise 1 C-C Bond Length Change IRC.jpg|thumb|650x650px|'''''Graph 1 - Change of bond lengths with the reaction coordinate in the Diels-Alder reaction between butadiene and ethylene'''''|left]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 2 - Typical C-C bond lengths'''''
!Bond Type
!Bond Length (Å)
|-
|C-C (sp<sup>3</sup>-sp<sup>3</sup>)
|1.530
|-
|C-C (sp<sup>2</sup>-sp<sup>2</sup>)
|1.460
|-
|C=C (sp<sup>2</sup>-sp<sup>2</sup>)
|1.316
|-
|C-C (sp<sup>3</sup>-sp<sup>2</sup>)
|1.503
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 3 - Optimised bond length values (PM6)'''''
!
! colspan="3" |Bond Length (Å)
|-
!Bond
!Reactants
!Transition State
!Products
|-
|C<sup>1</sup>-C<sup>2</sup>
|1.327
|1.382
|1.541
|-
|C<sup>2</sup>-C<sup>3</sup>
|3.413*
|2.115
|1.540
|-
|C<sup>3</sup>-C<sup>4</sup>
|1.335
|1.380
|1.501
|-
|C<sup>4</sup>-C<sup>5</sup>
|1.468
|1.411
|1.338
|-
|C<sup>5</sup>-C<sup>6</sup>
|1.335
|1.380
|1.501
|-
|C<sup>6</sup>-C<sup>1</sup>
|3.414*
|2.115
|1.540
|}

It is important to note for the reactant values marked with an asterisk that as C<sup>2</sup>-C<sup>3</sup> and C<sup>6</sup>-C<sup>1</sup> are bonds formed during the reaction, the bond length can essentially be assumed as infinite, since there is no interaction between the carbon atoms. The same bonds in the transition state have a length of 2.115 Å, which is significantly larger than the van der waal radius for carbon atoms, suggesting a very weak interaction that still does not have a significant bonding character. In the products these bonds represent C-C (sp<sup>3</sup>-sp<sup>3</sup>) bonds, however the optimised value of 1.540 Å shows significant deviation to the typical bond value of 1.530 Å. Comparison with experimentally determined bond lengths of cyclohexene showed reasonable agreement with literature values<ref>V. A. Naumov, V. G. Dashevskii and N. M. Zaripov, J. Struct. Chem., 1971, 11, 736–742.</ref>, highlighting the limitation that treating bonds individually from a valence bond theory perspective does not take into account complex orbital interactions that can affect bond length.

C<sup>3</sup>-C<sup>4</sup> and C<sup>5</sup>-C<sup>6</sup> represent the sp<sup>2</sup>-sp<sup>2</sup> double bonds of butadiene in the reactants, while C<sup>4</sup>-C<sup>5</sup> represents the sp<sup>2</sup>-sp<sup>2</sup> single bond connecting them. Their deviation from typical bond length values can be explained by delocalisation through the overlapping p-orbitals, which lengthens the double bonds (due to loss of electron density in the stabilised bonding orbitals) and shortens the single bond (as it gains partial double bond character). Throughout the reaction, the two double bonds lengthen to form sp<sup>3</sup>-sp<sup>2</sup> single bonds, while the single bond shortens to become a sp<sup>2</sup>-sp<sup>2</sup> double bond in cyclohexene.

Finally C<sup>1</sup>-C<sup>2</sup> represents the ethylene sp<sup>2</sup>-sp<sup>2</sup> double bond in the reactants, which again lengthens to form a sp<sup>3</sup>-sp<sup>3</sup> single bond in the cyclohexene product. Once again, the values obtained all agree strongly with literature values for the cyclohexene product<sup>[10]</sup>.

From the bond length data, the transition state appears to have a structure similar to the reactants. Following on from Hammond's postulate, it can be suggested that this reaction must have an ''early'' transition state, whereby there is little difference in structure and therefore energy between the reactants and transition state, but a large difference between the transition state and products. This suggestion was confirmed by the IRC calculation, which follows the lowest energy pathway to determine the 1D PES, similar to that seen in '''Figure 2'''. The resultant plot, as well as the animated .gif file are shown below in '''Table 4'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 4 - IRC plot and .gif file for the Diels-Alder reaction between Butadiene + Ethylene'''
!IRC Plot
!IRC .gif File
|-
|[[File:BT1215_Butadiene_Ethylene_IRC.png|490x340px]]
|[[File:BT1215_Buteth.gif]]
|}

=== Transition State Vibration Discussion ===
As mentioned before, the Diels-Alder reaction between butadiene and ethylene has been experimentally and theoretically proven through various experimental and theoretical studies, however the '''''concerted''' ''nature of the pathway can also be formed by looking at the vibration which corresponds to the transition state formation. As can be seen below, the vibration shows the key C<sup>1</sup>-C<sup>6</sup> and C<sup>2</sup>-C<sup>3</sup> bonds forming at the same time, hence identifying a synchronous reaction mechanism.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>BT1215_BEDIELSALDER_ORB_COMB_REACT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 17; frank off </script>
<name>VibTSBT1215</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibrate</text>
<target>VibTSBT1215</target>
</jmolbutton>
</jmol>

=== Output Calculation Files ===

SM: [[File:BT1215 CIS BUTADIENE OPT PM6.LOG]]
<br>
IRC: [[File:BT1215 COMB REACT IRC PM6.LOG]]
<br>
PRETS OPT: [[File:BT1215 COMB REACT PM6 PRETS OPT.LOG]]
<br>
TS: [[File:BT1215 BEDIELSALDER ORB COMB REACT TS PM6.LOG]]
<br>
SM: [[File:BT1215 ETHYLENE OPT PM6.LOG]]
<br>
PROD: [[File:BT1215 PROD CYCLOHEXENE OPT PM6.LOG]]
<br>
SINGLE POINT ENERGY REACT: [[File:BT1215 SPE REACT PM6.LOG]]

== Exercise 2: Cyclohexadiene + 1,3-Dioxole - PM6 & B3LYP Level ==

=== Reaction Overview ===
As with Exercise 1, cyclohexadiene and 1,3-dioxole can undergo a [4+2] Diels-Alder cycloaddition reaction, however in this example there are two fundamental points to be aware of. Firstly, by having two disubstituted alkene components, stereoselectivity is introduced whereby the orientation of the alkenes affect the reaction product. The two products formed are denominated endo and exo and are a function of their orientation in the cyclic product. The endo product corresponds to an axially fused ring system (where the extra ring faces downwards), while the exo product represents the equatorial equivalent. For this reaction, the two possible stereoisomers are shown below in '''Scheme 2'''.

[[File:BT1215 Cyclodioxone Reaction Scheme.jpg|centre|thumb|843x418px|'''''Scheme 2 - Reaction scheme showing the stereoselectivity of the Diels-Alder reaction between cyclohexadiene + 1,3-dioxole''''']]

The second key point is that the presence of two electron-donating oxygen atoms adjacent to the dienophile results in an '''''inverse electron demand''''' for the reaction, whereby the electron rich dienophile has a higher energy HOMO and essentially acts as the electron donor. This interacts with the lower energy LUMO of cyclohexadiene to result in an apparent 'reverse' electron flow, and thus generates the HOMO of the transition state. This can be seen qualitatively by comparing the relative reactant MO positions of the normal electron demand reaction above ('''Figure 4''') with those shown below in '''Figure 6 '''and '''Figure 7'''. The comparative energy gap between HOMO-LUMO overlap interactions in both the normal and inverse demand cases was also compared by looking at the computed orbitals in the optimised PM6 structures, and is shown below in '''Table 5'''. As can be seen, the energy gap between the Dienophile HOMO and Diene LUMO is smaller in the Diels-Alder reacton between cyclohexadiene and 1,3-dioxole, leading to the perceived inverse flow. This is confirmed by experimental data with 1,3-dioxole Diels-Alder reactions<ref>M. A. Mckervey, Alicyclic Chemistry, The Chemical Society, 1978.</ref>. The reaction is still thermally allowed following the Woodward-Hoffman rules, since the diene is a (4q+2)<sub>s</sub> component, and there is no (4r)<sub>a</sub> component, thus yielding an odd number which corresponds to a thermal reaction<ref>R. Hoffmann and R. B. Woodward, Acc. Chem. Res., 1968, 1, 17–22.</ref>.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 5 - Comparison of diene and dienophile HOMO-LUMO energy gaps for normal and inverse electron demands'''
!Diels-Alder Reaction
!Diene''' HOMO-Dienophile LUMO Energy gap / Hartrees'''
!Dienophile HOMO-Diene LUMO Energy gap''' / Hartrees'''
!Reaction Type
|-
|Butadiene + Ethylene (PM6)
|'''0.39770'''
|0.39854
|Normal Electron Demand
|-
|Cyclohexadiene + 1,3-Dioxole (PM6)
|0.35354
|'''0.33984'''
|Inverse Electron Demand
|}

It should be noted that the values shown in '''Table 5 '''represent the values obtained from single point energy PM6 calculations, since the B3LYP single point energy optimisations of butadiene + ethylene actually suggest an Inverse Electron Demand reaction. This is likely due to the fact that the butadiene + ethylene case is borderline, making it very difficult to distinguish which pathway the reaction undergoes. In addition, there are several different definitions for normal and inverse electron demand, meaning that while the discussion regarding the HOMO-LUMO gap is still important, it does not always accurately predict the electron demand of the reaction.

Unlike in the previous exercise, the reactants, products, and transition states were all optimised with the more accurate B3LYP method (and 6-31G basis set) after an initial PM6 optimisation, giving a more precise comparison of the orbital interactions in the transition state.

=== Molecular Orbital Discussion ===
The MO diagrams for both the endo and exo transition states are shown below in '''Figure 6''' and '''Figure 7'''. As with the MO diagram in Exercise 1, the occupied orbitals shown for the transition state are significantly destabilised compared to the expected orbitals in the product, since the transition state represents a significantly constrained and therefore high-energy conformation. While the order of the MO interactions is the same in both cases, the relative stability of the orbitals is significantly different for the endo and exo forms. For the frontier HOMO, the endo equivalent is significantly more stable, which can be explained by the involvement of secondary orbital interactions between the two oxygen p-orbitals and the two p-orbitals of the diene which are not directly involved in the diene-dienophile orbital overlap.

[[File:BT1215 cyclodioxone endo MO diagram.jpg|thumb|786x786px|'''''Figure 7 - Frontier MO diagram of the endo stereoisomer in the cyclohexadiene + (1,3)-dioxole Diels-Alder reaction.''''']]
[[File:BT1215 cyclodioxone exo MO diagram.jpg|left|thumb|771x771px|'''''Figure 6 - Frontier MO diagram of the exo stereoisomer in the cyclohexadiene + (1,3)-dioxole Diels-Alder reaction.''''']]

A more thorough discussion of the difference in stabilities is given below in the '''''Energy Discussion''''' section, but secondary orbital interactions can be seen below in the interactive Jmols of the endo orbitals (particularly orbitals 41 and 43). The endo pathway orbitals are shown in '''Table 6''', while those of the exo pathway are given in '''Table 7'''. As before, it is possible to toggle through all of the generated frontier MOs using the drop down box.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 6 - Frontier orbitals in the ENDO Diels-Alder Reaction between cyclohexadiene + 1,3-dioxole'''''
!ENDO Reactant Orbitals
!ENDO Transition State Orbitals
!ENDO Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_SPE_ENDO_OXONE_SM_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCDR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCDR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_OPT_TS_B3LYP_2ND.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCD</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCD</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCD</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCD</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_PROD_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCDP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCDP</target>
</item>
</jmolmenu>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 7 - Frontier orbitals in the EXO Diels-Alder Reaction between cyclohexadiene + 1,3-dioxole'''''
!EXO Reactant Orbitals
!EXO Transition State Orbitals
!EXO Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_SPE_EXO_OXONE_SM_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCDR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCDR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_OPT_TS_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCD</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCD</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCD</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCD</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_PROD_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 14; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCDP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 14; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCDP</target>
</item>
</jmolmenu>
</jmol>
|}

=== Energy Discussion ===
The thermochemical data for the activation and reaction energy of both the endo and exo pathway is given below in '''Table 8''', while the reaction profile is shown below in '''Figure 8'''. As can be seen, the endo reaction represents not only the kinetic product for the reaction (by having a lower activation energy) but also the thermodynamic product, as it has a lower energy than the exo form. The reactant, product, and transition state energies are given in Hartrees in '''Table 9''' for comparison. The reactant energies were summed from separate optimisations to ensure there was no interaction between the two that would affect the computed energy.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 8 - Thermochemical data for both stereochemical routes in the cyclohexadiene + 1,3-dioxole Diels-Alder reaction'''
!Reaction Pathway
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|'''Exo Pathway'''
|0.063853
|167.65
|<nowiki>-0.024302</nowiki>
|<nowiki>-63.81</nowiki>
|-
|'''Endo Pathway'''
|0.060871
|159.82
|<nowiki>-0.025671</nowiki>
|<nowiki>-67.40</nowiki>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 9 - Reactant, transition state, and product energies for the 1,3-dioxole + cyclohexadiene Diels-Alder reaction'''
!Reaction Pathway
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|'''Exo Pathway'''
|<nowiki>-500.393020</nowiki>
|<nowiki>-500.329167</nowiki>
|<nowiki>-500.417322</nowiki>
|-
|'''Endo Pathway'''
|<nowiki>-500.393020</nowiki>
|<nowiki>-500.332149</nowiki>
|<nowiki>-500.418691</nowiki>
|}
[[File:BT1215 cyclodioxone reaction pathway diagram.jpg|centre|thumb|499x499px|'''''Figure 8 - Reaction coordinate of the cyclohexadiene + 1,3-dioxole Diels-Alder reaction showing the activation and reaction energies for both the endo and exo stereoisomers''''']]
Generally, for alkenes containing substituents that are able to form secondary orbital interactions, the endo product is formed under kinetic control due to a lower energy transition state and therefore a lower activation energy. As mentioned before, these secondary orbital interactions consist of the involvement of the oxygen p-orbitals in the 1,3-dioxole ring which form constructive, symmetry allowed overlaps with the cyclohexadiene frontier orbitals. This increase in overlap leads to a greater stabilisation of the HOMO in the product and transition state, thus also lowering the overall energy of both. These interactions are 'secondary' as their contribution to the bonding is not essential for the reaction to occur, however their impact is significant in determining the stereochemistry of the product. The key secondary orbital interaction between oxygen and cyclohexadiene is shown below in '''Figure 9''', while an interactive Jmol of the endo transition state HOMO with a higher isovalue is shown below to highlight the interaction.
[[File:BT1215 Stabilising Orbital Interaction dioxone.jpg|centre|thumb|735x735px|'''''Figure 9 - Stabilising secondary orbital interactions observed in the endo conformer of the 1,3-dioxole + cyclohexadiene Diels-Alder reaction ''''']]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
!ENDO TS HOMO Showing Secondary Orbital Interactions
!EXO TS HOMO (No Secondary Interaction)
|-
|<jmol>
<jmolApplet>
<size>500</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_OPT_TS_B3LYP_2ND.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat "" rotate x -20; frank off</script>
<name>EndoDielsAlderCDO</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDO</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDO</target>
</jmolbutton>
</jmol>
|<jmol>
<jmolApplet>
<size>500</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_OPT_TS_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 20; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat "" rotate x -20; frank off</script>
<name>ExoDielsAlderCDO</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDO</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDO</target>
</jmolbutton>
</jmol>
|}

While secondary orbital interactions are important in determining kinetic control, the endo stereosiomer may not be the thermodynamic product if there is a significant steric clash. In this case, the endo form is actually also thermodynamically more stable than the exo form, due to fewer steric interactions between the bridge of the cyclohexene ring and the -CH<sub>2</sub> group in the 1,3-dioxole ring. A comparison of the steric interactions is shown below in '''Figure 10'''.
[[File:BT1215 Steric Clash Dioxone Diels-Alder.jpg|centre|thumb|649x649px|'''''Figure 10 - Steric clash observed in both stereoisomer products of the Diels-Alder reaction''''']]

=== Output Calculation Files ===

SM: [[File:BT1215 CYCLOHEXADIENE OPT PM6.LOG]]
<br>
SM: [[File:BT1215 CYCLOHEXADIENE OPT B3LYP 2.LOG]]
<br>
SM: [[File:BT1215 DIOXONE OPT PM6.LOG]]
<br>
SM: [[File:BT1215 DIOXONE OPT B3LYP.LOG]]
<br>
ENDO IRC: [[File:BT1215 ENDO OXONE IRC PM6.LOG]]
<br>
ENDO PRETS OPT: [[File:BT1215 ENDO OXONE PREOPT TS PM6.LOG]]
<br>
ENDO TS: [[File:BT1215 ENDO OXONE OPT TS B3LYP 2ND.LOG]]
<br>
ENDO PROD: [[File:BT1215 ENDO OXONE PROD OPT PM6.LOG]]
<br>
ENDO PROD: [[File:BT1215 ENDO OXONE PROD OPT B3LYP.LOG]]
<br>
ENDO SINGLE POINT ENERGY REACT: [[File:BT1215_SPE_ENDO_OXONE_SM.LOG]]
<br>
EXO IRC: [[File:BT1215 EXO OXONE IRC PM6.LOG]]
<br>
EXO PRETS OPT: [[File:BT1215 EXO OXONE PREOPT TS PM6.LOG]]
<br>
EXO TS: [[File:BT1215 EXO OXONE OPT TS B3LYP.LOG]]
<br>
EXO PROD: [[File:BT1215 EXO OXONE PROD OPT PM6.LOG]]
<br>
EXO PROD: [[File:BT1215 EXO OXONE PROD OPT B3LYP.LOG]]
<br>
EXO SINGLE POINT ENERGY REACT: [[File:BT1215 EXO OXONE SM OPT PM6.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic Reactions (Xylylene + SO<sub>2</sub>) - PM6 Level ==

=== Reaction Overview ===
The reaction of xylylene with SO<sub>2</sub> is of particular interest, since the involvement of an electron-rich atom such as sulphur, which can easily become hypervalent, allows for new pericyclic reactions. As before, a [4+2] Diels-Alder cycloaddition an occur between the two exocyclic double bonds and the S=O double bond to give two fused six-membered rings with an either endo or exo stereoselectivity. Alternatively, it is possible for the sulphur atom alone to react with the exocyclic diene to give a 5-membered ring fused to the aromatic phenyl ring, in what is called a cheletropic reaction. The reaction with xylylene also introduces an interesting regioselectivity discussion; as well as the cheletropic reaction, a second endocyclic cis-diene is available to react with the SO<sub>2</sub> to yield alternative products. This pathway is highly disfavoured compared to the exocyclic Diels-Alder, the reasons of which are explained in the '''''Energy Discussion Section'''''. All of the discussed reaction routes are shown below in '''Scheme 3'''

[[File:BT1215 Chele vs Diels Alder React Scheme.jpg|centre|thumb|800x418px|'''''Scheme 3 - Reaction scheme showing all of the Diels-Alder and cheletropic reactions between Xylylene + SO<sub>2</sub>''''']]

=== Energy Discussion ===
As for '''<u>Exercise 2</u>''', the activation and reaction energies for all of the possible routes are given below in '''Table 10''', while a visual representation of the reaction profile can be seen below in '''Figure 11'''. For comparison, the reactant, transition state, and product energies are given in Hartrees below in '''Table 11'''.

Comparing the activation energies, the endo pathway of the exocyclic Diels-Alder reaction appears to be the kinetic product of the reaction, since it has the lowest energy transition state compared to the reactants. The thermodynamic product for the reaction is clearly the '''cheletropic''' product, since it is significantly more stable than any of the Diels-Alder reaction products. This is in agreement with literature results<ref>D. Suárez, T. L. Sordo and J. A. Sordo, J. Org. Chem., 1995, 60, 2848–2852.</ref>, and is likely due to the fact that the cheletropic transition state suffers a higher level of ring strain due to the formation of a 5-membered fused ring, compared to the 6-membered ring formed in the Diels-Alder reactions, which makes the Diels-Alder route kinetically faster. Conversely, the retention of the highly stable S=O bond in the cheletropic product makes this the thermodynamic product. Indeed, as a result of this, the cheletropic product is significantly more accessible experimentally when compared to the reversible Diels-Alder routes. Both the exocyclic Diels-Alder reactions and the cheletropic reaction are all thermodynamically stable compared to the reactants, and can be explained by the formation of the highly stabilised aromatic phenyl ring which lowers the product energy.

In comparison, xylylene is destabilised as it does not possess any aromaticity. The same discussion can be applied to the unfavourable, high-energy endocyclic Diels-Alder reactions; their significantly higher activation barriers and reaction energies compared to the other routes can be explained by the fact there is no aromatic ring in the products, which are also destabilised compared to the reactants due to the creation of a strained bi-fused ring system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 10 - Thermochemical data for all possible reactions between xylylene and SO<sub>2</sub>'''
!Reaction Pathway
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|Cheletropic
|0.040671
|106.78
|<nowiki>-0.058385</nowiki>
|<nowiki>-153.29</nowiki>
|-
|'''Exo'''cyclic '''Exo '''Diels-Alder
|0.033694
|88.46
|<nowiki>-0.036928</nowiki>
|<nowiki>-96.95</nowiki>
|-
|'''Exo'''cyclic '''Endo '''Diels-Alder
|0.032177
|84.48
|<nowiki>-0.036685</nowiki>
|<nowiki>-96.32</nowiki>
|-
|'''Endo'''cyclic '''Exo '''Diels-Alder
|0.046672
|122.54
|0.008922
|23.42
|-
|'''Endo'''cyclic '''Endo '''Diels-Alder
|0.043687
|114.70
|0.007226
|18.97
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 11 - Reactant, transition state, and product energies for all possible reactions between xylylene + SO<sub>2</sub>'''
!Reaction Pathway
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|Cheletropic
|0.058383
|0.099054
|<nowiki>-0.000002</nowiki>
|-
|'''Exo'''cyclic '''Exo '''Diels-Alder
|0.058383
|0.092077
|0.021455
|-
|'''Exo'''cyclic '''Endo '''Diels-Alder
|0.058383
|0.090560
|0.021698
|-
|'''Endo'''cyclic '''Exo '''Diels-Alder
|0.058383
|0.105055
|0.067305
|-
|'''Endo'''cyclic '''Endo '''Diels-Alder
|0.058383
|0.102070
|0.065609
|}
[[File:BT1215 Exercise 3 Reaction Diagram.jpg|centre|thumb|869x869px|'''''Figure 11 - Reaction profile for the key cycloadditions between xylylene + SO<sub>2</sub>''''']]

The .gif files for the IRC calculations of the reaction routes are shown below. Please note that they may not play smoothly until the interactive Jmols above load. A variety of interesting results can be seen from the animations. All of the Diels-Alder reactions occur via an asynchronous bond formation, where the C-O bond forms before the C-S bond. This could be due to the fact that the smaller, more electron dense oxygen atom can get closer to the xylylene ring to form the C-O bond more quickly than the larger, more diffuse sulphur atom. However, this is merely observational and further calculations would be required to confirm this. In contrast, since only the sulphur atom is involved in the cheletropic reaction, both sigma bonds are formed in a synchronous manner. The IRC plots for all of the reactions are shown below, adjacent to the .gif files. It should be noted that for the Exocyclic Exo route the IRC ran from products to reactants, meaning the reactants are on the right side and the products are on the left side. When compared to the other plots the graph should be reversed.

(Be careful here: you can't use GaussView to decide when precisely a "bond" is formed, as it uses a cutoff distance to decide when to draw a bond [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:15, 4 April 2018 (BST))

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Cheletropic IRC Plot
!Cheletropic IRC .gif
|-
|[[File:BT1215_CheletropicIRC_(2).png|490x370px]]
|[[File:BT1215_Cheletropic.gif]]
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Exocyclic Exo IRC Plot
!Exocyclic Exo IRC .gif
!Exocyclic Endo IRC Plot
!Exocyclic Endo IRC .gif
|-
|[[File:BT1215 Exo Exo DA.png|320x330px]]
|[[File:BT1215 Exo Exo.gif]]
|[[File:BT1215 Exo Endo DA png.png|320x330px]]
|[[File:BT1215_Exo_Endo_DA.gif]]
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Endocyclic Exo IRC Plot
!Endocyclic Exo IRC .gif
!Endocyclic Endo IRC Plot
!Endocyclic Endo IRC .gif
|-
|[[File:BT1215 Endo Exo DA 2.png|320x330px]]
|[[File:BT1215_Endo_Exo.gif]]
|[[File:BT1215 Endo Endo DA 2.png|320x330px]]
|[[File:BT1215_Endo_Endo.gif]]
|}

=== Output Calculation Files ===

SM: [[File:BT1215 SO2 SM PM6.LOG]]
<br>
SM: [[File:BT1215 XYLYLENE SM PM6.LOG]]
<br>
CHELO IRC: [[File:BT1215 CHELO XYLYLENE IRC PM6.LOG]]
<br>
CHELO PRETS OPT: [[File:BT1215 CHELO XYLYLENE REDUNDANT OPT.LOG]]
<br>
CHELO TS: [[File:BT1215 CHELO XYLYLENE TS PM6.LOG]]
<br>
CHELO PROD: [[File:BT1215 CHELO XYLYLENE REOPT PM6.LOG]]
<br>
DA EXOCYCLIC ENDO IRC: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE IRC PM6.LOG]]
<br>
DA EXOCYCLIC ENDO PRETS: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE PRETS OPT PM6.LOG]]
<br>
DA EXOCYCLIC ENDO TS: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE TS PM6.LOG]]
<br>
DA EXOCYCLIC ENDO PROD: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE OPT.LOG]]
<br>
DA EXOCYCLIC EXO IRC: [[File:BT1215 DIELS-ALDER XYLYLENE IRC PM6.LOG]]
<br>
DA EXOCYCLIC EXO PRETS: [[File:BT1215 DIELS-ALDER XYLYLENE REDUNDANT OPT.LOG]]
<br>
DA EXOCYCLIC EXO TS: [[File:BT1215 DIELS-ALDER XYLYLENE TS PM6.LOG]]
<br>
DA EXOCYCLIC EXO PROD: [[File:BT1215 DIELS-ALDER XYLYLENE REOPT PM6.LOG]]
<br>
DA ENDOCYCLIC ENDO IRC: [[File:BT1215 HIGH ENERGY IRC.LOG]]
<br>
DA ENDOCYCLIC ENDO PRETS: [[File:BT1215 HIGH ENERGY PREOPT TS PM6 2.LOG]]
<br>
DA ENDOCYCLIC ENDO TS: [[File:BT1215 HIGH ENERGY TS PM6.LOG]]
<br>
DA ENDOCYCLIC ENDO TS: [[File:BT1215 HIGH ENERGY TS CHECK ORB.LOG]]
<br>
DA ENDOCYCLIC ENDO PROD: [[File:BT1215 HIGH ENERGY PRODUCT OPT PM6.LOG]]
<br>
DA ENDOCYCLIC EXO IRC: [[File:BT1215 DA EXO HIGH ENERGY IRC PM6.LOG]]
<br>
DA ENDOCYCLIC EXO PRETS: [[File:BT1215 DA EXO HIGH ENERGY RED OPT PM6.LOG]]
<br>
DA ENDOCYCLIC EXO TS: [[File:BT1215 DA EXO HIGH ENERGY TS PM6.LOG]]
<br>
DA ENDOCYCLIC EXO PROD: [[File:BT1215 DA EXO HIGH ENERGY PROD OPT PM6.LOG]]

== 4π Electrocyclic Reactions: [1,1']-bicyclohexene - PM6 Level ==

=== Reaction Overview ===
The Woodward-Hoffman rules are also essential in predicting the stereochemistry of other pericyclic reactions, including electrocyclic reactions which involve the loss of a π bond and the creation of a σ bond that causes the cyclisation of the molecule. The mechanism for this reaction, shown in '''Scheme 4''', is shown below. For this investigation, [1,1']-bicyclohexene was chosen, with a core diene structure analogous to that of butadiene. This electrocyclic reaction is denoted 4π as 4π electrons are involved in the cyclisation.
<br>
[[File:BT1215 Extension RS 1.jpg|centre|thumb|847x120px|'''''Scheme 4 - Reaction scheme showing the 4π electrocyclic reaction of [1,1']-bicyclohexene''''']]
<br>
The stereoselectivity concerns of this reaction are very important, as shown by the Woodward-Hoffman rules<sup>[13]</sup>, since two possible reactions can occur depending on the conditions that the diene is reacting under. [1,1']-bicyclohexene can cyclise under thermal conditions via a '''''conrotatory''' ''mechanism, shown below in '''Figure 12'''. This is allowed due to the presence of a <sub>π</sub>4<sub>a</sub> orbital component which, when 'pulled together', causes the Hydrogen atoms to rotate in the same direction. An alternative possibility is a '''''disrotatory''''' mechanism with a <sub>π</sub>4<sub>s</sub> orbital component; this is '''thermally disallowed''', but can occur under photochemical conditions to yield a trans-alkene product.
<br>
[[File:BT1215 WH Thermal Vs Photo.jpg|centre|thumb|475x400px|'''''Figure 12 - Symmetry Woodward-Hoffmann rules for both the thermal and photochemical reactions of dienes''''']]
<br>
The full explanation as to whether a reaction is thermally allowed or disallowed can be explained by looking at the frontier orbital overlaps in both a conrotatory and disrotatory mechanism. For simplicity, the orbitals of the analogous butadiene will be used, however the explanation can be directly applied to [1,1']-bicyclohexene. In a conrotatory mechanism, the two terminal symmetry orbitals of butadiene (on the top left of the diagram) shown in '''Figure 12''' can be superimposed using a C2 axis perpendicular to the plane of the screen. For a disrotatory mechanism however, the same orbitals are reflected in a σ symmetry plane that is perpendicular to the screen and runs through the centre of the butadiene. It is important to note that while the symmetry based orbitals often used to describe WH rules cannot be directly compared to the frontier molecular orbitals, the symmetry linking both sets of orbitals remains the same here.

The symmetry of the frontier orbitals of butadiene can then be determined based on these two operators, and a correlation diagram composed to identify which orbitals can overlap in the reaction to make the product. The correlation diagrams for the conrotatory and disrotatory mechanisms are shown below in '''Figure 13'''. As can be seen, the conrotatory mechanism involves the transfer of electrons from the ground state orbitals of the butadiene into the ground state orbitals of the cyclobutene, resulting in a small energy barrier for the reaction. In contrast, the disrotatory mechanism requires the excitation of electrons into an excited state antibonding orbital, giving it a much larger energy barrier and making the reaction thermally disallowed.

'''While this provides an elegant way of explaining the WH rules, it must be stated that it ''cannot'' provide significant insight into the structure of the product orbital, since the reaction proceeds via a 4n Mobius transition state and this allows all of the orbitals to rotate and switch symmetry. The actual frontier orbitals can be seen below in the MO/Energy Discussion'''.
<br>
[[File:BT1215 Extension FO Symmetry.jpg|centre|thumb|1458x415px|'''''Figure 13 - Frontier orbital symmetry of butadiene for conrotatory & disrotatory mechanisms''''']]
<br>

(Good intro, and you have labelled your symmetry axis [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:04, 4 April 2018 (BST))

=== MO/Energy Discussion ===

In this discussion, the thermally allowed pathway will be focused on due to time limitations that meant that the full calculation of the photochemical route could not be performed. All optimisations were performed at the PM6 level, with the key MOs for the reactant, transition state, and product, given below in '''Table 12'''. As can be seen, MO 32 of the product is different to the WH predicted frontier orbital. The expected bonding interaction appears as part of MO 31, along with a more complicated bonding interaction from the alkene of the cyclobutene that appears to be the same symmetry. This is likely a consequence of reacting through a twisted Mobius transition state. It is recommended that further calculations be performed with a more accurate method to confirm the orbital ordering. The rest of the orbitals are as expected in the '''Reaction Overview''' section.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 12 - Frontier orbitals in the 4π electrocyclic reaction of [1,1']-bicyclohexene'''''
!Reactant Orbitals
!Transition State Orbitals
!Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 DIENE SM PM6 OPT 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; mo 32; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 22; mo 32; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 33; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 34; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 35; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 DIENE TS OPT PM6 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 32; mo nodots nomesh fill translucent; mo cutoff 0.04; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneT</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneT</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneT</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 8; mo 32; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 33; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 34; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 35; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneT</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 PRODUCT ALKENE PM6 OPT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 48; mo 31; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 22; mo 31; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 31</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 32; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 33; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 34; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 35; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneP</target>
</item>
</jmolmenu>
</jmol>
|}

The thermochemical data for the reaction is shown below in '''Table 13''', while the energies of the reactant, transition state, and product are given in '''Table 14'''. The computed energies reveal that the starting diene is more stable, and therefore the predominant form. This is likely due to the high levels of ring strain in the cyclobutene ring destabilising the product. Kinetically this reaction is also highly unfavourable, with a much higher activation energy than the previous reaction systems discussed. It is possible that the complexity of the cyclohexene rings means a large amount of bond rearrangement is required in order to form the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 13 - Thermochemical data for the 4π electrocyclic reaction of [1,1']-bicyclohexene'''
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|0.104375
|274.04
|0.028329
|74.3777952
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 14 - Reactant, transition state, and product energies for the electrocyclic reaction of [1,1']-bicyclohexene'''
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|0.199543
|0.303918
|0.227872
|}

An IRC calculation was performed and both the plot and .gif file are shown below. As before, the reaction was computed from products to reactants in the IRC, so the graph should appear reversed. It is also important to note that in the IRC calculation the reactant energy appears to be higher energy than the product, likely due to it converging to a metastable minima where the diene is planar, and not the most stable form of the reactants.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!IRC Plot
!IRC .gif File
|-
|[[File:BT1215 Diene Extension.png|490x375px]]
|[[File:BT1215 Ext Diene.gif]]
|}

Finally, the imaginary vibration corresponding to the transition state can be seen below. As suggested by the vibration and the IRC, the bond formation in the electrocyclic reaction appears to be synchronous, with the hydrogen atoms rotating in a concerted manner.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>BT1215 DIENE TS OPT PM6 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 9; frank off </script>
<name>VibTS2BT1215</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibrate</text>
<target>VibTS2BT1215</target>
</jmolbutton>
</jmol>

=== Output Calculation Files ===

SM: [[File:BT1215 DIENE SM PM6 OPT 2.LOG]]
<br>
IRC: [[File:BT1215 DIENE IRC PM6.LOG]]
<br>
PRETS OPT: [[File:BT1215 DIENE TS PREOPT PM6 2.LOG]]
<br>
TS: [[File:BT1215 DIENE TS OPT PM6 2.LOG]]
<br>
PROD: [[File:BT1215 PRODUCT ALKENE PM6 OPT.LOG]]
<br>

== Conclusion ==
Computational analysis of 4 different pericyclic systems was performed with a large degree of success, both with the Semi-Empirical PM6 and DFT B3LYP methods. In all cases, it was possible to model and correctly predict experimentally determined reaction mechanisms and transition states. The use of Gaussian was also able to provide insight into the change in bond lengths throughout the reaction, the type of transition state, the electron demand of the reaction, and which routes represent the thermodynamic or kinetic product. The computation of molecular orbitals was crucial in justifying the observed stereoselectivities, providing an elegant visual representation of secondary orbital interactions, as well as other factors affecting product formation. Unfortunately, the complexity of the calculations, along with time constraints, meant that the majority of reaction systems could only be optimised using the PM6 method, and so can only yield qualitative results due to the limitations discussed in the introduction. Conclusions for the individual exercises were as follows:

*<u>Exercise 1 - PM6</u> - The Diels-Alder reaction of butadiene + ethylene was modelled and shown to occur via a synchronous 4+2 cycloaddition, with a normal electron demand for the reaction. The transition state was correctly identified and confirmed by the presence of a single imaginary vibration frequency, corresponding to product formation, and an IRC calculation was performed to determine an early transition state. This was also confirmed by modelling the change in bond lengths throughout the course of the reaction, showing a transition state structure close to that of the reactants. Despite the inaccuracies of the PM6 method, bond lengths were in reasonable agreement with the literature.

*<u>Exercise 2 - PM6 & B3LYP</u> - The stereoselectivity of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole was investigated in order to determine whether the endo or exo product represented kinetic and/or thermodynamic control. All structures were optimised first with the PM6 method, before being reoptimised with the B3LYP method in order to give a more accurate depiction of the reaction system and its energies. Relative HOMO-LUMO energy gaps were compared with butadiene + ethylene to determine an inverse electron demand reaction, caused by the electron rich atoms on the dienophile. An MO diagram was constructed, and the kinetic stability of the endo product was explained by the involvement of oxygen p-orbitals in secondary orbital interactions that help to stabilise the transition state. The endo product was also determined to be the thermodynamic product due to the absence of steric clash between the bridged ring and the 1,3-dioxole group.

*<u>Exercise 3 - PM6</u> - The relative stabilities of five different pericyclic routes for the reaction between Xylylene + SO<sub>2</sub> were probed. Optimisations of reactants, products, and transition states were all carried out with the PM6 method. The cheletropic reaction yielded the thermodynamic product via a synchronous bond formation, likely due to the preservation of both S=O bonds. The exocyclic endo Diels-Alder reaction, occurring through asynchronous bond formation, represented kinetic control, due to the fact that the transition state contains a 6-membered fused ring compared to the relatively strained 5-membered cheletropic transition state. An alternative, endocyclic Diels-Alder reaction was investigated and shown to be highly disfavoured due to the fact that no aromatic ring was formed in the product, and the resultant fused ring product had large steric interactions making it thermodynamically unstable compared to the reactants.

*<u>Exercise 4 - PM6</u> - The thermally allowed, conrotatory 4π electrocyclic reaction of [1,1']-bicylcohexene was investigated, with all optimisations taking place at the PM6 level. The reaction was determined to proceed via a 4n Mobius transition state, which could explain discrepancies between the predicted orbital overlap using orbital symmetry and the observed product orbitals. An IRC calculation was performed and showed a concerted bond formation, while the imaginary transition state frequency observed for the transition state also suggested a concerted, conrotatory mechanism. Due to time constraints, the photochemical disrotatory reaction could not be calculated.

Further work could be explored not only in the computation of the photochemical reaction route in Exercise 4, but also by further modelling more obscure pericyclic reaction routes, similar to computational research performed by W. Grimme et al into cheletropic ene reactions<ref>W. Grimme, M. W. Harter, C. A. Sklorz, J. Chem. Soc., Perkin Trans. 2, 1999, 9.</ref>. Alternatively, higher level calculations could be performed to further understand more complex systems, such as ''ab initio'' calculations by F. Monnatt et al into the cheletropic and hetero Diels-Alder additions of SO<sub>2</sub> to (E)-Methoxybutadiene.<ref>F. Monnat, P. Vogel, V. M. Rayón and J. A. Sordo, J. Org. Chem., 2002, 67, 1882–1889.</ref>

== References ==

Rep:BT1215 CP3MD Lab

2018-04-04T11:15:15Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic Reactions (Xylylene + SO2) - PM6 Level */

== Introduction ==
The ability to model reactions using computational simulations is something of great interest, particularly with regard to understanding experimental mechanisms or molecular properties<ref>R. Breslow et. al., Beyond the Molecular Frontier: Challenges for Chemistry and Chemical Engineering, National Research Council, 2003.</ref>. Modern computational software, such as Gaussian, is able to use a series of quantum mechanical calculations to optimise a reaction system and determine a lowest energy reaction pathway, as well as the predicted energies and structures of any reactants, transition states, and products involved. Within these calculations, there are two important theoretical considerations to take into account:

''1. Potential Energy Surface (PES)'' - The potential energy of a system given as a function of molecular geometry. By changing the molecular geometry (e.g. bond lengths during a reaction), the change in energy and transition state can be computed.

''2. Computational Method'' - Defines the approximations made within the quantum mechanics, balancing accuracy (fewer approximations lead to more precise results) with computational cost (fewer assumptions mean more resource-intensive calculations).

=== Potential Energy Surface (PES) ===
[[File:BT1215 PES Example.JPG|right|thumb|210x205px|'''''Figure 1 - An example PES surface, AB<sup>+</sup> and A<sup>+</sup> + B represent local minima, which are separated by a labelled saddle point<ref>L. Sleno and D. A. Volmer, J. Mass Spectrom., 2004, 39, 1091–1112.</ref>.''''']]
As mentioned before, the PES is a representation of the relationship between the potential energy of a system and its molecular geometry. Given that non-linear molecules have a geometrical freedom of 3N-6 modes (or 3N-5 for linear molecules), where N = the number of atoms in the molecule, the PES therefore has the same dependency, relying on the internal coordinates of the atoms in the system. In order to model a reaction PES, the number of degrees of freedom that are varied is often reduced in order to make the calculation computationally feasible. When plotted graphically, the PES represents a landscape of high and low energy configurations that correspond to turning or stationary points on the surface, with an example plot shown in '''Figure 1'''<sup>[2]</sup>. Low energy turning points correspond to an energetically stable molecular geometry, which are mathematically characterised by having a first derivative equal to 0 ('''Eq 1'''), and a positive second derivative ('''Eq 2'''), where <math>{V}</math> is potential energy and <math>{x}</math> represents an atomic or reaction coordinate:
<br>
<br>
<div style="text-align: center;"><math>\frac{\partial V}{\partial x}= 0 </math> '''Eq 1'''</div>
<br>
<div style="text-align: center;"><math>\frac{\partial^{2} V}{\partial x^{^{2}}}> 0</math> '''Eq 2'''</div>
<br>
[[File:BT1215 2D PES to TS Example.gif|right|thumb|313x553px|'''''Figure 2 - A PES diagram of ozone which has been mapped to an IRC along a reaction coordinate, showing the transition state, reactants and products<ref>1 E. G. Lewars, in Computational Chemistry, 2011, vol. 26, pp. 9–43.</ref>.''''']]
The potential energy well surrounding the minimum can be modelled as a Simple Harmonic Oscillator, where the lowest energy point is described by a Taylor expansion. Assuming a harmonic motion modelled by Hooke's law, force constant <math>{k}</math> can be equated to the second derivative in '''Eq 2'''. Since the vibrational wavenumber, <math>{v}</math>, is directly proportional to <math>\sqrt{k}</math>, it can therefore be seen that the molecular configurations corresponding to minimum turning points will '''''only''''' have positive vibrations<ref>P. Atkins and J. De Paula, Atkins’ physical chemistry, 2009.</ref>.

The transition state of a reaction corresponds to a saddle point which separates two local minima in the PES, and is essentially a maximum turning point along a particular reaction coordinate of the surface. This can be modelled as a barrier separating two wells, shown in '''Figure 2'''<sup>[2]</sup>. An activation energy is required to overcome this transition state and thus interconvert between the two wells, often denoted reactants and products. The saddle point on the PES surface can be mathematically described as being a local minimum in all directions except for one, where it is equivalent to a maximum turning point. This leads to one reaction coordinate where the second derivative of potential energy is '''negative'''. Following the same key discussion above, '''''one negative vibration frequency will be observed in the transition state''''', while all other frequencies observed will be positive.

It is important to note that, while this discussion of a singular force constant holds true for one-dimentional systems, polyatomic systems require more complicated treatment, since there are multiple force constants and vibrational motions within the system that can actually couple (i.e. one vibration could affect the likelihood of another happening). The general form of these force constants is shown below in '''Eq 3''', where ''i'' and ''j'' represent degrees of freedom (or coordinates) up to 3N-6:
<br>
<br>
<div style="text-align: center;"><math>\frac{\partial^{2} V}{\partial x_i x_j} = k_{ij} </math> '''Eq 3'''</div>

Software such as Gaussian simplifies these complicated raw motions by first converting the internal coordinates into mass-weighted coordinates to make the coupled force constants equally weighted, before creating a large Hessian matrix of all the coupled force constants. The software then diagonalises the Hessian matrix to give the decoupled, vibrational modes of the molecule<ref>A. Ghysels, V. Van Speybroeck, E. Pauwels, S. Catak, B. R. Brooks, D. Van Neck and M. Waroquier, J. Comput. Chem., 2010, 31, 994–1007./</ref>. A simplified example of the Hessian matrix that is diagonalised is shown below in '''Figure 3''', where <math>K_{ij}</math> represents the force constants with respect to the mass-weighted coordinates.
<br>
<br>
[[File:BT1215 Hessian Matrix.JPG|centre|thumb|799x169px|'''''Figure 3 - A simplified example of the Hessian matrix which is solved to give the vibrational modes''''']]

=== Computational Method ===

In order to compute the potential energy surface and obtain molecular energies, Gaussian uses quantum mechanical calculations based on the Linear Combination of Atomic Orbitals (LCAO) method. As implied by the existence of the PES, the Born-Oppenheimer approximation is used to separate the electron and nuclear timescales, meaning the nuclei are effectively static on an electron timescale and can be manipulated as such. If this approximation was not true then it would be impossible to calculate the PES, since the electronic energies would constantly be affected by nuclear motion. The LCAO method is essentially a sum of atomic orbitals, <math>\phi_i</math>, which combine with a weighting coefficient, <math>c_i</math>, to give the overall molecular orbital wavefunction, <math>\psi_m</math>, shown below in '''Eqn 4''':
<br>
<br>
<div style="text-align: center;"><math>\psi_m = \sum_{i}^N c_i \phi_i</math> '''Eq 4'''</div>
<br>
The number of atomic orbitals used to ''build'' the LCAO is called the '''Basis Set''', which will be discussed further below. The total energy of the molecule is then calculated as a sum of the orbital energies, using the Hamiltonian Operator to solve the Schrödinger equation, where '''Eqn 5''' shows the general form, and '''Eqn 6''' shows the same equation but with the sum of atomic orbitals:
<br>
<br>
<div style="text-align: center;"><math><\psi|\widehat{H}|\psi> = E</math> '''Eq 5'''</div>
<br>
<div style="text-align: center;"><math>\sum_{i}^N \sum_{j}^N<\phi_i|\widehat{H}|\phi_j>c_i c_j = E</math> '''Eq 6'''</div>
<br>
Gaussian represents these equations in matrix form and solves to give the molecular orbital energies, as well as the overall molecule energy. Both the method of calculation and the size of the basis set used to construct the molecular orbital are fundamental factors in determining the accuracy of the computed MOs and energy output, but also in the amount of computational power required. A variety of methods and basis sets can be used to perform optimisations and energy calculations, depending on the computational method chosen. The two methods chosen for all of the following calculations are PM6 and B3LYP (with a 6-31G (d) basis set).

'''PM6''' is a Semi-Empirical method based on the Hartree-Fock method, however it utilises experimental data and/or DFT results (where experimental data is not available) to help speed up the calculation time. Naturally, these assumptions require the system to be modelled by the experimental data used, which may not be an accurate representation. As with the Hartree-Fock method, it also treats electrons as largely independent, and does not account for electron correlation. As a result it represents a rough approximation of the system, although its speed does make it useful for very large systems which would require far too much computational power with a more accurate method. <ref>J. Řezáč, J. Fanfrlík, D. Salahub and P. Hobza, J. Chem. Theory Comput., 2009, 5, 1749–1760.</ref>

'''B3LYP''' is a hybrid method based on both the Hartree-Fock and Density Functional Theory (DFT) techniques. The Hartree-Fock method is employed in the calculation of the exchange-correlation energy, while DFT is used elsewhere due to its improved efficiency. This is because it only depends on a 3-coordinate system describing the electron, and thus scales 3-dimensionally with the number of basis functions, versus the four-dimensional scaling of the Hartree-Fock method. The smaller scaling results in faster computation, though it is still a lot slower than Semi-Empirical methods. A 6-31G (d) Pople basis set used for the B3LYP calculations, where the numbers represent the basis functions used in the calculation. In general terms, a larger basis set corresponds to a more accurate calculation<sup>[4]</sup>.

To localise the transition state in the reaction systems below, three main methods are possible in Gaussian. The first method is adequate when there is previous knowledge surrounding the reaction mechanism, meaning it is possible to guess the transition state structure and then optimise it. Unfortunately this is very difficult to correctly guess, often missing the transition state. The second method has a higher level of accuracy, and involves optimising the reactants, before setting and freezing the distance between the atoms involved in the reaction. Optimisation to a minima is then performed, followed by a transition state optimisation. This approach provides Gaussian with more information surrounding the reaction pathway, and thus helps guide the optimisation to the correct result. This method was used for Exercise 1.

For Exercises 2, 3, and 4, a third, more complex method was chosen. This involves optimising the product, before breaking the bonds that are formed in the reaction. The distance between the atoms that form these bonds is set and frozen at a specific distance that resembles the transition state. The same calculations as in the second method are then used to identify and optimise the transition state structure. This method is the longest, but is also the most reliable, which was the main reason for its use in more complicated reaction systems.

== Exercise 1: Diels-Alder Reaction of Butadiene + Ethylene - PM6 Level ==

=== Reaction Overview ===
Butadiene and ethylene can react to form cyclohexene, shown below in '''Scheme 1'''. The reaction occurs via a type of [4+2] cycloaddition, commonly known as a Diels-Alder reaction, through a concerted syn addition<ref>K. N. Houk, Y. T. Lin and F. K. Brown, J. Am. Chem. Soc., 1986, 108, 554–556.</ref>. In the case of butadiene and ethylene, since butadiene (the diene) is more electron rich than ethylene (the dienophile), the reaction represents a ''normal electron demand'' Diels-Alder cycloaddition.

[[File:BT1215 Diels-Alder RS Butadiene Ethylene.jpg|centre|thumb|757x757px|'''''Scheme 1 - Diels-Alder reaction between butadiene and ethylene''''']]

=== Molecular Orbital Discussion ===
The frontier molecular orbital (MO) diagram for the reaction between butadiene and ethylene is shown below in '''Figure 1''', and was generated using the calculated Gaussian energies of the transition state and reactants. The transition state and reactants were used in the MO diagram for clarity, since conformational changes and significant orbital mixing in the product make the connection more complicated. As a result, the energies computed for the overlapping MOs are significantly higher than those of the optimised product, especially since the transition state represents a strained conformation. It is also important to note that these energies can only be considered relative to each other due to the inaccuracy of the PM6 optimisation method.

[[File:BT1215 Diels-Alder TS Butadiene Ethylene Y3TS.jpg|centre|thumb|783x783px|'''''Figure 4 - MO diagram showing frontier orbital interactions in the Diels-Alder reaction between butadiene and ethylene.''''']]

Interactive JMOLs of the two starting materials, as well as the orbitals involved in the bonding interaction can be seen below in '''Table 1''', labelled with both their number, computed energy and occupancy. It is possible to toggle through the generated frontier MOs using the drop down box. Please note that they may not appear to work correctly until after all of the Jmols on the page have loaded.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 1 - Frontier orbitals in the Diels-Alder Reaction between butadiene + ethylene'''''
!Reactant Orbitals
!Transition State Orbitals
!Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 SPE REACT PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneR</target>
</item>
<item>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_BEDIELSALDER_ORB_COMB_REACT_TS_PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneDielsAlder</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneDielsAlder</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneDielsAlder</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
<item>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneDielsAlder</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 PROD CYCLOHEXENE OPT PM6.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ButadieneEthyleneP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ButadieneEthyleneP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ButadieneEthyleneP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 16</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 17</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 18; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 18</text>
<target>ButadieneEthyleneP</target>
</item>
<item>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 19</text>
<target>ButadieneEthyleneP</target>
</item>
</jmolmenu>
</jmol>
|}

Orbitals can form stabilising overlap interactions when their associated overlap integral is '''''non-zero'''''. The integral is a quantitative representation of the spatial overlap of the orbitals, and thus an integral equal to 0 is equivalent to '''''no''''' spatial overlap. In order for the overlap integral to be non-zero, the overall integral of the interacting orbital wavefunctions must be a symmetric function. As a result, only orbitals which are '''''both''''' symmetric (S × S = S) or '''''both''''' antisymmetric (AS × AS = S) result in a non-zero overlap integral that allows for a stabilising orbital overlap. Interaction between a symmetric and antisymmetric orbital would lead to an overall antisymmetric function (S × AS = AS) and an integral equal to 0 (representing no interaction). <sup>[4]</sup> This can also be seen in the MO diagram above, where only orbitals of the same symmetry interact in the Diels-Alder reaction.

=== Bond Length Discussion ===
Diels-Alder reactions involve the creation of two new σ-bonds between the diene and dienophile, while three π-bonds are lost and another one is created to complete the cycloaddition. The curly-arrow mechanism for the cycloaddition between butadiene and ethylene is shown below in '''Figure 5''', where each carbon has been numbered so as to allow for the discussion of how each bond length changes throughout the course of the reaction.

[[File:BT1215_Diels-Alder_Curly_Arrows.jpg|centre|thumb|584x129px|'''''Figure 5 - Currly arrow mechanism for the Diels-Alder Reaction between Butadiene + Ethylene''''']]

The changes in bond lengths with the reaction coordinate are shown below in '''Graph 1''', and were extracted from the PM6 optimised IRC reaction pathway. The typical values for bond lengths between two sp<sup>3</sup> hybridised carbon atoms, two sp<sup>2</sup> carbon atoms (both single and double bonds), and sp<sup>3</sup> and sp<sup>2</sup> carbon atoms is shown in '''Table 2''', where all values were obtained from the CRC Handbook of Chemistry and Physics<ref>D. R. Lide, CRC Handbook of Chemistry and Physics, 2003, 53, 2616.</ref>. The calculated bond lengths for the PM6 optimised reactants, products, and transition state can be seen in '''Table 3'''. While there are several slightly distinct values for the van der waals radius of a carbon atom, the overall consensus corresponds to a value of 1.70 Å<ref>1 S. S. Batsanov, Inorg. Mater., 2001, 37, 871–885.</ref>.

[[File:BT1215 Exercise 1 C-C Bond Length Change IRC.jpg|thumb|650x650px|'''''Graph 1 - Change of bond lengths with the reaction coordinate in the Diels-Alder reaction between butadiene and ethylene'''''|left]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 2 - Typical C-C bond lengths'''''
!Bond Type
!Bond Length (Å)
|-
|C-C (sp<sup>3</sup>-sp<sup>3</sup>)
|1.530
|-
|C-C (sp<sup>2</sup>-sp<sup>2</sup>)
|1.460
|-
|C=C (sp<sup>2</sup>-sp<sup>2</sup>)
|1.316
|-
|C-C (sp<sup>3</sup>-sp<sup>2</sup>)
|1.503
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 3 - Optimised bond length values (PM6)'''''
!
! colspan="3" |Bond Length (Å)
|-
!Bond
!Reactants
!Transition State
!Products
|-
|C<sup>1</sup>-C<sup>2</sup>
|1.327
|1.382
|1.541
|-
|C<sup>2</sup>-C<sup>3</sup>
|3.413*
|2.115
|1.540
|-
|C<sup>3</sup>-C<sup>4</sup>
|1.335
|1.380
|1.501
|-
|C<sup>4</sup>-C<sup>5</sup>
|1.468
|1.411
|1.338
|-
|C<sup>5</sup>-C<sup>6</sup>
|1.335
|1.380
|1.501
|-
|C<sup>6</sup>-C<sup>1</sup>
|3.414*
|2.115
|1.540
|}

It is important to note for the reactant values marked with an asterisk that as C<sup>2</sup>-C<sup>3</sup> and C<sup>6</sup>-C<sup>1</sup> are bonds formed during the reaction, the bond length can essentially be assumed as infinite, since there is no interaction between the carbon atoms. The same bonds in the transition state have a length of 2.115 Å, which is significantly larger than the van der waal radius for carbon atoms, suggesting a very weak interaction that still does not have a significant bonding character. In the products these bonds represent C-C (sp<sup>3</sup>-sp<sup>3</sup>) bonds, however the optimised value of 1.540 Å shows significant deviation to the typical bond value of 1.530 Å. Comparison with experimentally determined bond lengths of cyclohexene showed reasonable agreement with literature values<ref>V. A. Naumov, V. G. Dashevskii and N. M. Zaripov, J. Struct. Chem., 1971, 11, 736–742.</ref>, highlighting the limitation that treating bonds individually from a valence bond theory perspective does not take into account complex orbital interactions that can affect bond length.

C<sup>3</sup>-C<sup>4</sup> and C<sup>5</sup>-C<sup>6</sup> represent the sp<sup>2</sup>-sp<sup>2</sup> double bonds of butadiene in the reactants, while C<sup>4</sup>-C<sup>5</sup> represents the sp<sup>2</sup>-sp<sup>2</sup> single bond connecting them. Their deviation from typical bond length values can be explained by delocalisation through the overlapping p-orbitals, which lengthens the double bonds (due to loss of electron density in the stabilised bonding orbitals) and shortens the single bond (as it gains partial double bond character). Throughout the reaction, the two double bonds lengthen to form sp<sup>3</sup>-sp<sup>2</sup> single bonds, while the single bond shortens to become a sp<sup>2</sup>-sp<sup>2</sup> double bond in cyclohexene.

Finally C<sup>1</sup>-C<sup>2</sup> represents the ethylene sp<sup>2</sup>-sp<sup>2</sup> double bond in the reactants, which again lengthens to form a sp<sup>3</sup>-sp<sup>3</sup> single bond in the cyclohexene product. Once again, the values obtained all agree strongly with literature values for the cyclohexene product<sup>[10]</sup>.

From the bond length data, the transition state appears to have a structure similar to the reactants. Following on from Hammond's postulate, it can be suggested that this reaction must have an ''early'' transition state, whereby there is little difference in structure and therefore energy between the reactants and transition state, but a large difference between the transition state and products. This suggestion was confirmed by the IRC calculation, which follows the lowest energy pathway to determine the 1D PES, similar to that seen in '''Figure 2'''. The resultant plot, as well as the animated .gif file are shown below in '''Table 4'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 4 - IRC plot and .gif file for the Diels-Alder reaction between Butadiene + Ethylene'''
!IRC Plot
!IRC .gif File
|-
|[[File:BT1215_Butadiene_Ethylene_IRC.png|490x340px]]
|[[File:BT1215_Buteth.gif]]
|}

=== Transition State Vibration Discussion ===
As mentioned before, the Diels-Alder reaction between butadiene and ethylene has been experimentally and theoretically proven through various experimental and theoretical studies, however the '''''concerted''' ''nature of the pathway can also be formed by looking at the vibration which corresponds to the transition state formation. As can be seen below, the vibration shows the key C<sup>1</sup>-C<sup>6</sup> and C<sup>2</sup>-C<sup>3</sup> bonds forming at the same time, hence identifying a synchronous reaction mechanism.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>BT1215_BEDIELSALDER_ORB_COMB_REACT_TS_PM6.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 17; frank off </script>
<name>VibTSBT1215</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibrate</text>
<target>VibTSBT1215</target>
</jmolbutton>
</jmol>

=== Output Calculation Files ===

SM: [[File:BT1215 CIS BUTADIENE OPT PM6.LOG]]
<br>
IRC: [[File:BT1215 COMB REACT IRC PM6.LOG]]
<br>
PRETS OPT: [[File:BT1215 COMB REACT PM6 PRETS OPT.LOG]]
<br>
TS: [[File:BT1215 BEDIELSALDER ORB COMB REACT TS PM6.LOG]]
<br>
SM: [[File:BT1215 ETHYLENE OPT PM6.LOG]]
<br>
PROD: [[File:BT1215 PROD CYCLOHEXENE OPT PM6.LOG]]
<br>
SINGLE POINT ENERGY REACT: [[File:BT1215 SPE REACT PM6.LOG]]

== Exercise 2: Cyclohexadiene + 1,3-Dioxole - PM6 & B3LYP Level ==

=== Reaction Overview ===
As with Exercise 1, cyclohexadiene and 1,3-dioxole can undergo a [4+2] Diels-Alder cycloaddition reaction, however in this example there are two fundamental points to be aware of. Firstly, by having two disubstituted alkene components, stereoselectivity is introduced whereby the orientation of the alkenes affect the reaction product. The two products formed are denominated endo and exo and are a function of their orientation in the cyclic product. The endo product corresponds to an axially fused ring system (where the extra ring faces downwards), while the exo product represents the equatorial equivalent. For this reaction, the two possible stereoisomers are shown below in '''Scheme 2'''.

[[File:BT1215 Cyclodioxone Reaction Scheme.jpg|centre|thumb|843x418px|'''''Scheme 2 - Reaction scheme showing the stereoselectivity of the Diels-Alder reaction between cyclohexadiene + 1,3-dioxole''''']]

The second key point is that the presence of two electron-donating oxygen atoms adjacent to the dienophile results in an '''''inverse electron demand''''' for the reaction, whereby the electron rich dienophile has a higher energy HOMO and essentially acts as the electron donor. This interacts with the lower energy LUMO of cyclohexadiene to result in an apparent 'reverse' electron flow, and thus generates the HOMO of the transition state. This can be seen qualitatively by comparing the relative reactant MO positions of the normal electron demand reaction above ('''Figure 4''') with those shown below in '''Figure 6 '''and '''Figure 7'''. The comparative energy gap between HOMO-LUMO overlap interactions in both the normal and inverse demand cases was also compared by looking at the computed orbitals in the optimised PM6 structures, and is shown below in '''Table 5'''. As can be seen, the energy gap between the Dienophile HOMO and Diene LUMO is smaller in the Diels-Alder reacton between cyclohexadiene and 1,3-dioxole, leading to the perceived inverse flow. This is confirmed by experimental data with 1,3-dioxole Diels-Alder reactions<ref>M. A. Mckervey, Alicyclic Chemistry, The Chemical Society, 1978.</ref>. The reaction is still thermally allowed following the Woodward-Hoffman rules, since the diene is a (4q+2)<sub>s</sub> component, and there is no (4r)<sub>a</sub> component, thus yielding an odd number which corresponds to a thermal reaction<ref>R. Hoffmann and R. B. Woodward, Acc. Chem. Res., 1968, 1, 17–22.</ref>.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 5 - Comparison of diene and dienophile HOMO-LUMO energy gaps for normal and inverse electron demands'''
!Diels-Alder Reaction
!Diene''' HOMO-Dienophile LUMO Energy gap / Hartrees'''
!Dienophile HOMO-Diene LUMO Energy gap''' / Hartrees'''
!Reaction Type
|-
|Butadiene + Ethylene (PM6)
|'''0.39770'''
|0.39854
|Normal Electron Demand
|-
|Cyclohexadiene + 1,3-Dioxole (PM6)
|0.35354
|'''0.33984'''
|Inverse Electron Demand
|}

It should be noted that the values shown in '''Table 5 '''represent the values obtained from single point energy PM6 calculations, since the B3LYP single point energy optimisations of butadiene + ethylene actually suggest an Inverse Electron Demand reaction. This is likely due to the fact that the butadiene + ethylene case is borderline, making it very difficult to distinguish which pathway the reaction undergoes. In addition, there are several different definitions for normal and inverse electron demand, meaning that while the discussion regarding the HOMO-LUMO gap is still important, it does not always accurately predict the electron demand of the reaction.

Unlike in the previous exercise, the reactants, products, and transition states were all optimised with the more accurate B3LYP method (and 6-31G basis set) after an initial PM6 optimisation, giving a more precise comparison of the orbital interactions in the transition state.

=== Molecular Orbital Discussion ===
The MO diagrams for both the endo and exo transition states are shown below in '''Figure 6''' and '''Figure 7'''. As with the MO diagram in Exercise 1, the occupied orbitals shown for the transition state are significantly destabilised compared to the expected orbitals in the product, since the transition state represents a significantly constrained and therefore high-energy conformation. While the order of the MO interactions is the same in both cases, the relative stability of the orbitals is significantly different for the endo and exo forms. For the frontier HOMO, the endo equivalent is significantly more stable, which can be explained by the involvement of secondary orbital interactions between the two oxygen p-orbitals and the two p-orbitals of the diene which are not directly involved in the diene-dienophile orbital overlap.

[[File:BT1215 cyclodioxone endo MO diagram.jpg|thumb|786x786px|'''''Figure 7 - Frontier MO diagram of the endo stereoisomer in the cyclohexadiene + (1,3)-dioxole Diels-Alder reaction.''''']]
[[File:BT1215 cyclodioxone exo MO diagram.jpg|left|thumb|771x771px|'''''Figure 6 - Frontier MO diagram of the exo stereoisomer in the cyclohexadiene + (1,3)-dioxole Diels-Alder reaction.''''']]

A more thorough discussion of the difference in stabilities is given below in the '''''Energy Discussion''''' section, but secondary orbital interactions can be seen below in the interactive Jmols of the endo orbitals (particularly orbitals 41 and 43). The endo pathway orbitals are shown in '''Table 6''', while those of the exo pathway are given in '''Table 7'''. As before, it is possible to toggle through all of the generated frontier MOs using the drop down box.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 6 - Frontier orbitals in the ENDO Diels-Alder Reaction between cyclohexadiene + 1,3-dioxole'''''
!ENDO Reactant Orbitals
!ENDO Transition State Orbitals
!ENDO Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_SPE_ENDO_OXONE_SM_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCDR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCDR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_OPT_TS_B3LYP_2ND.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCD</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCD</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCD</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCD</target>
</item>
<item>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCD</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_PROD_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>EndoDielsAlderCDP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>EndoDielsAlderCDP</target>
</item>
<item>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>EndoDielsAlderCDP</target>
</item>
</jmolmenu>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 7 - Frontier orbitals in the EXO Diels-Alder Reaction between cyclohexadiene + 1,3-dioxole'''''
!EXO Reactant Orbitals
!EXO Transition State Orbitals
!EXO Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_SPE_EXO_OXONE_SM_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCDR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCDR</target>
</item>
<item>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCDR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_OPT_TS_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCD</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCD</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCD</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCD</target>
</item>
<item>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCD</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_PROD_OPT_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 14; mo 40; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExoDielsAlderCDP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 14; mo 40; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 40</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 41</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 42</text>
<target>ExoDielsAlderCDP</target>
</item>
<item>
<script>frame 14; mo 43; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 43</text>
<target>ExoDielsAlderCDP</target>
</item>
</jmolmenu>
</jmol>
|}

=== Energy Discussion ===
The thermochemical data for the activation and reaction energy of both the endo and exo pathway is given below in '''Table 8''', while the reaction profile is shown below in '''Figure 8'''. As can be seen, the endo reaction represents not only the kinetic product for the reaction (by having a lower activation energy) but also the thermodynamic product, as it has a lower energy than the exo form. The reactant, product, and transition state energies are given in Hartrees in '''Table 9''' for comparison. The reactant energies were summed from separate optimisations to ensure there was no interaction between the two that would affect the computed energy.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 8 - Thermochemical data for both stereochemical routes in the cyclohexadiene + 1,3-dioxole Diels-Alder reaction'''
!Reaction Pathway
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|'''Exo Pathway'''
|0.063853
|167.65
|<nowiki>-0.024302</nowiki>
|<nowiki>-63.81</nowiki>
|-
|'''Endo Pathway'''
|0.060871
|159.82
|<nowiki>-0.025671</nowiki>
|<nowiki>-67.40</nowiki>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 9 - Reactant, transition state, and product energies for the 1,3-dioxole + cyclohexadiene Diels-Alder reaction'''
!Reaction Pathway
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|'''Exo Pathway'''
|<nowiki>-500.393020</nowiki>
|<nowiki>-500.329167</nowiki>
|<nowiki>-500.417322</nowiki>
|-
|'''Endo Pathway'''
|<nowiki>-500.393020</nowiki>
|<nowiki>-500.332149</nowiki>
|<nowiki>-500.418691</nowiki>
|}
[[File:BT1215 cyclodioxone reaction pathway diagram.jpg|centre|thumb|499x499px|'''''Figure 8 - Reaction coordinate of the cyclohexadiene + 1,3-dioxole Diels-Alder reaction showing the activation and reaction energies for both the endo and exo stereoisomers''''']]
Generally, for alkenes containing substituents that are able to form secondary orbital interactions, the endo product is formed under kinetic control due to a lower energy transition state and therefore a lower activation energy. As mentioned before, these secondary orbital interactions consist of the involvement of the oxygen p-orbitals in the 1,3-dioxole ring which form constructive, symmetry allowed overlaps with the cyclohexadiene frontier orbitals. This increase in overlap leads to a greater stabilisation of the HOMO in the product and transition state, thus also lowering the overall energy of both. These interactions are 'secondary' as their contribution to the bonding is not essential for the reaction to occur, however their impact is significant in determining the stereochemistry of the product. The key secondary orbital interaction between oxygen and cyclohexadiene is shown below in '''Figure 9''', while an interactive Jmol of the endo transition state HOMO with a higher isovalue is shown below to highlight the interaction.
[[File:BT1215 Stabilising Orbital Interaction dioxone.jpg|centre|thumb|735x735px|'''''Figure 9 - Stabilising secondary orbital interactions observed in the endo conformer of the 1,3-dioxole + cyclohexadiene Diels-Alder reaction ''''']]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
!ENDO TS HOMO Showing Secondary Orbital Interactions
!EXO TS HOMO (No Secondary Interaction)
|-
|<jmol>
<jmolApplet>
<size>500</size>
<color>white</color>
<uploadedFileContents>BT1215_ENDO_OXONE_OPT_TS_B3LYP_2ND.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat "" rotate x -20; frank off</script>
<name>EndoDielsAlderCDO</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>EndoDielsAlderCDO</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoDielsAlderCDO</target>
</jmolbutton>
</jmol>
|<jmol>
<jmolApplet>
<size>500</size>
<color>white</color>
<uploadedFileContents>BT1215_EXO_OXONE_OPT_TS_B3LYP.LOG </uploadedFileContents>
<script>vibrating=0; spinning=0; frame 20; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat "" rotate x -20; frank off</script>
<name>ExoDielsAlderCDO</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExoDielsAlderCDO</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoDielsAlderCDO</target>
</jmolbutton>
</jmol>
|}

While secondary orbital interactions are important in determining kinetic control, the endo stereosiomer may not be the thermodynamic product if there is a significant steric clash. In this case, the endo form is actually also thermodynamically more stable than the exo form, due to fewer steric interactions between the bridge of the cyclohexene ring and the -CH<sub>2</sub> group in the 1,3-dioxole ring. A comparison of the steric interactions is shown below in '''Figure 10'''.
[[File:BT1215 Steric Clash Dioxone Diels-Alder.jpg|centre|thumb|649x649px|'''''Figure 10 - Steric clash observed in both stereoisomer products of the Diels-Alder reaction''''']]

=== Output Calculation Files ===

SM: [[File:BT1215 CYCLOHEXADIENE OPT PM6.LOG]]
<br>
SM: [[File:BT1215 CYCLOHEXADIENE OPT B3LYP 2.LOG]]
<br>
SM: [[File:BT1215 DIOXONE OPT PM6.LOG]]
<br>
SM: [[File:BT1215 DIOXONE OPT B3LYP.LOG]]
<br>
ENDO IRC: [[File:BT1215 ENDO OXONE IRC PM6.LOG]]
<br>
ENDO PRETS OPT: [[File:BT1215 ENDO OXONE PREOPT TS PM6.LOG]]
<br>
ENDO TS: [[File:BT1215 ENDO OXONE OPT TS B3LYP 2ND.LOG]]
<br>
ENDO PROD: [[File:BT1215 ENDO OXONE PROD OPT PM6.LOG]]
<br>
ENDO PROD: [[File:BT1215 ENDO OXONE PROD OPT B3LYP.LOG]]
<br>
ENDO SINGLE POINT ENERGY REACT: [[File:BT1215_SPE_ENDO_OXONE_SM.LOG]]
<br>
EXO IRC: [[File:BT1215 EXO OXONE IRC PM6.LOG]]
<br>
EXO PRETS OPT: [[File:BT1215 EXO OXONE PREOPT TS PM6.LOG]]
<br>
EXO TS: [[File:BT1215 EXO OXONE OPT TS B3LYP.LOG]]
<br>
EXO PROD: [[File:BT1215 EXO OXONE PROD OPT PM6.LOG]]
<br>
EXO PROD: [[File:BT1215 EXO OXONE PROD OPT B3LYP.LOG]]
<br>
EXO SINGLE POINT ENERGY REACT: [[File:BT1215 EXO OXONE SM OPT PM6.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic Reactions (Xylylene + SO<sub>2</sub>) - PM6 Level ==

=== Reaction Overview ===
The reaction of xylylene with SO<sub>2</sub> is of particular interest, since the involvement of an electron-rich atom such as sulphur, which can easily become hypervalent, allows for new pericyclic reactions. As before, a [4+2] Diels-Alder cycloaddition an occur between the two exocyclic double bonds and the S=O double bond to give two fused six-membered rings with an either endo or exo stereoselectivity. Alternatively, it is possible for the sulphur atom alone to react with the exocyclic diene to give a 5-membered ring fused to the aromatic phenyl ring, in what is called a cheletropic reaction. The reaction with xylylene also introduces an interesting regioselectivity discussion; as well as the cheletropic reaction, a second endocyclic cis-diene is available to react with the SO<sub>2</sub> to yield alternative products. This pathway is highly disfavoured compared to the exocyclic Diels-Alder, the reasons of which are explained in the '''''Energy Discussion Section'''''. All of the discussed reaction routes are shown below in '''Scheme 3'''

[[File:BT1215 Chele vs Diels Alder React Scheme.jpg|centre|thumb|800x418px|'''''Scheme 3 - Reaction scheme showing all of the Diels-Alder and cheletropic reactions between Xylylene + SO<sub>2</sub>''''']]

=== Energy Discussion ===
As for '''<u>Exercise 2</u>''', the activation and reaction energies for all of the possible routes are given below in '''Table 10''', while a visual representation of the reaction profile can be seen below in '''Figure 11'''. For comparison, the reactant, transition state, and product energies are given in Hartrees below in '''Table 11'''.

Comparing the activation energies, the endo pathway of the exocyclic Diels-Alder reaction appears to be the kinetic product of the reaction, since it has the lowest energy transition state compared to the reactants. The thermodynamic product for the reaction is clearly the '''cheletropic''' product, since it is significantly more stable than any of the Diels-Alder reaction products. This is in agreement with literature results<ref>D. Suárez, T. L. Sordo and J. A. Sordo, J. Org. Chem., 1995, 60, 2848–2852.</ref>, and is likely due to the fact that the cheletropic transition state suffers a higher level of ring strain due to the formation of a 5-membered fused ring, compared to the 6-membered ring formed in the Diels-Alder reactions, which makes the Diels-Alder route kinetically faster. Conversely, the retention of the highly stable S=O bond in the cheletropic product makes this the thermodynamic product. Indeed, as a result of this, the cheletropic product is significantly more accessible experimentally when compared to the reversible Diels-Alder routes. Both the exocyclic Diels-Alder reactions and the cheletropic reaction are all thermodynamically stable compared to the reactants, and can be explained by the formation of the highly stabilised aromatic phenyl ring which lowers the product energy.

In comparison, xylylene is destabilised as it does not possess any aromaticity. The same discussion can be applied to the unfavourable, high-energy endocyclic Diels-Alder reactions; their significantly higher activation barriers and reaction energies compared to the other routes can be explained by the fact there is no aromatic ring in the products, which are also destabilised compared to the reactants due to the creation of a strained bi-fused ring system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 10 - Thermochemical data for all possible reactions between xylylene and SO<sub>2</sub>'''
!Reaction Pathway
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|Cheletropic
|0.040671
|106.78
|<nowiki>-0.058385</nowiki>
|<nowiki>-153.29</nowiki>
|-
|'''Exo'''cyclic '''Exo '''Diels-Alder
|0.033694
|88.46
|<nowiki>-0.036928</nowiki>
|<nowiki>-96.95</nowiki>
|-
|'''Exo'''cyclic '''Endo '''Diels-Alder
|0.032177
|84.48
|<nowiki>-0.036685</nowiki>
|<nowiki>-96.32</nowiki>
|-
|'''Endo'''cyclic '''Exo '''Diels-Alder
|0.046672
|122.54
|0.008922
|23.42
|-
|'''Endo'''cyclic '''Endo '''Diels-Alder
|0.043687
|114.70
|0.007226
|18.97
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 11 - Reactant, transition state, and product energies for all possible reactions between xylylene + SO<sub>2</sub>'''
!Reaction Pathway
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|Cheletropic
|0.058383
|0.099054
|<nowiki>-0.000002</nowiki>
|-
|'''Exo'''cyclic '''Exo '''Diels-Alder
|0.058383
|0.092077
|0.021455
|-
|'''Exo'''cyclic '''Endo '''Diels-Alder
|0.058383
|0.090560
|0.021698
|-
|'''Endo'''cyclic '''Exo '''Diels-Alder
|0.058383
|0.105055
|0.067305
|-
|'''Endo'''cyclic '''Endo '''Diels-Alder
|0.058383
|0.102070
|0.065609
|}
[[File:BT1215 Exercise 3 Reaction Diagram.jpg|centre|thumb|869x869px|'''''Figure 11 - Reaction profile for the key cycloadditions between xylylene + SO<sub>2</sub>''''']]

The .gif files for the IRC calculations of the reaction routes are shown below. Please note that they may not play smoothly until the interactive Jmols above load. A variety of interesting results can be seen from the animations. All of the Diels-Alder reactions occur via an asynchronous bond formation, where the C-O bond forms before the C-S bond. This could be due to the fact that the smaller, more electron dense oxygen atom can get closer to the xylylene ring to form the C-O bond more quickly than the larger, more diffuse sulphur atom. However, this is merely observational and further calculations would be required to confirm this. In contrast, since only the sulphur atom is involved in the cheletropic reaction, both sigma bonds are formed in a synchronous manner. The IRC plots for all of the reactions are shown below, adjacent to the .gif files. It should be noted that for the Exocyclic Exo route the IRC ran from products to reactants, meaning the reactants are on the right side and the products are on the left side. When compared to the other plots the graph should be reversed.

(Be careful here: you can't use GaussView to decide when precisely a "bond" is formed, as it uses a cutoff distance to decide when to draw a bond [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:15, 4 April 2018 (BST))

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Cheletropic IRC Plot
!Cheletropic IRC .gif
|-
|[[File:BT1215_CheletropicIRC_(2).png|490x370px]]
|[[File:BT1215_Cheletropic.gif]]
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Exocyclic Exo IRC Plot
!Exocyclic Exo IRC .gif
!Exocyclic Endo IRC Plot
!Exocyclic Endo IRC .gif
|-
|[[File:BT1215 Exo Exo DA.png|320x330px]]
|[[File:BT1215 Exo Exo.gif]]
|[[File:BT1215 Exo Endo DA png.png|320x330px]]
|[[File:BT1215_Exo_Endo_DA.gif]]
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Endocyclic Exo IRC Plot
!Endocyclic Exo IRC .gif
!Endocyclic Endo IRC Plot
!Endocyclic Endo IRC .gif
|-
|[[File:BT1215 Endo Exo DA 2.png|320x330px]]
|[[File:BT1215_Endo_Exo.gif]]
|[[File:BT1215 Endo Endo DA 2.png|320x330px]]
|[[File:BT1215_Endo_Endo.gif]]
|}

=== Output Calculation Files ===

SM: [[File:BT1215 SO2 SM PM6.LOG]]
<br>
SM: [[File:BT1215 XYLYLENE SM PM6.LOG]]
<br>
CHELO IRC: [[File:BT1215 CHELO XYLYLENE IRC PM6.LOG]]
<br>
CHELO PRETS OPT: [[File:BT1215 CHELO XYLYLENE REDUNDANT OPT.LOG]]
<br>
CHELO TS: [[File:BT1215 CHELO XYLYLENE TS PM6.LOG]]
<br>
CHELO PROD: [[File:BT1215 CHELO XYLYLENE REOPT PM6.LOG]]
<br>
DA EXOCYCLIC ENDO IRC: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE IRC PM6.LOG]]
<br>
DA EXOCYCLIC ENDO PRETS: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE PRETS OPT PM6.LOG]]
<br>
DA EXOCYCLIC ENDO TS: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE TS PM6.LOG]]
<br>
DA EXOCYCLIC ENDO PROD: [[File:BT1215 ENDO DIELS-ALDER XYLYLENE OPT.LOG]]
<br>
DA EXOCYCLIC EXO IRC: [[File:BT1215 DIELS-ALDER XYLYLENE IRC PM6.LOG]]
<br>
DA EXOCYCLIC EXO PRETS: [[File:BT1215 DIELS-ALDER XYLYLENE REDUNDANT OPT.LOG]]
<br>
DA EXOCYCLIC EXO TS: [[File:BT1215 DIELS-ALDER XYLYLENE TS PM6.LOG]]
<br>
DA EXOCYCLIC EXO PROD: [[File:BT1215 DIELS-ALDER XYLYLENE REOPT PM6.LOG]]
<br>
DA ENDOCYCLIC ENDO IRC: [[File:BT1215 HIGH ENERGY IRC.LOG]]
<br>
DA ENDOCYCLIC ENDO PRETS: [[File:BT1215 HIGH ENERGY PREOPT TS PM6 2.LOG]]
<br>
DA ENDOCYCLIC ENDO TS: [[File:BT1215 HIGH ENERGY TS PM6.LOG]]
<br>
DA ENDOCYCLIC ENDO TS: [[File:BT1215 HIGH ENERGY TS CHECK ORB.LOG]]
<br>
DA ENDOCYCLIC ENDO PROD: [[File:BT1215 HIGH ENERGY PRODUCT OPT PM6.LOG]]
<br>
DA ENDOCYCLIC EXO IRC: [[File:BT1215 DA EXO HIGH ENERGY IRC PM6.LOG]]
<br>
DA ENDOCYCLIC EXO PRETS: [[File:BT1215 DA EXO HIGH ENERGY RED OPT PM6.LOG]]
<br>
DA ENDOCYCLIC EXO TS: [[File:BT1215 DA EXO HIGH ENERGY TS PM6.LOG]]
<br>
DA ENDOCYCLIC EXO PROD: [[File:BT1215 DA EXO HIGH ENERGY PROD OPT PM6.LOG]]

== 4π Electrocyclic Reactions: [1,1']-bicyclohexene - PM6 Level ==

=== Reaction Overview ===
The Woodward-Hoffman rules are also essential in predicting the stereochemistry of other pericyclic reactions, including electrocyclic reactions which involve the loss of a π bond and the creation of a σ bond that causes the cyclisation of the molecule. The mechanism for this reaction, shown in '''Scheme 4''', is shown below. For this investigation, [1,1']-bicyclohexene was chosen, with a core diene structure analogous to that of butadiene. This electrocyclic reaction is denoted 4π as 4π electrons are involved in the cyclisation.
<br>
[[File:BT1215 Extension RS 1.jpg|centre|thumb|847x120px|'''''Scheme 4 - Reaction scheme showing the 4π electrocyclic reaction of [1,1']-bicyclohexene''''']]
<br>
The stereoselectivity concerns of this reaction are very important, as shown by the Woodward-Hoffman rules<sup>[13]</sup>, since two possible reactions can occur depending on the conditions that the diene is reacting under. [1,1']-bicyclohexene can cyclise under thermal conditions via a '''''conrotatory''' ''mechanism, shown below in '''Figure 12'''. This is allowed due to the presence of a <sub>π</sub>4<sub>a</sub> orbital component which, when 'pulled together', causes the Hydrogen atoms to rotate in the same direction. An alternative possibility is a '''''disrotatory''''' mechanism with a <sub>π</sub>4<sub>s</sub> orbital component; this is '''thermally disallowed''', but can occur under photochemical conditions to yield a trans-alkene product.
<br>
[[File:BT1215 WH Thermal Vs Photo.jpg|centre|thumb|475x400px|'''''Figure 12 - Symmetry Woodward-Hoffmann rules for both the thermal and photochemical reactions of dienes''''']]
<br>
The full explanation as to whether a reaction is thermally allowed or disallowed can be explained by looking at the frontier orbital overlaps in both a conrotatory and disrotatory mechanism. For simplicity, the orbitals of the analogous butadiene will be used, however the explanation can be directly applied to [1,1']-bicyclohexene. In a conrotatory mechanism, the two terminal symmetry orbitals of butadiene (on the top left of the diagram) shown in '''Figure 12''' can be superimposed using a C2 axis perpendicular to the plane of the screen. For a disrotatory mechanism however, the same orbitals are reflected in a σ symmetry plane that is perpendicular to the screen and runs through the centre of the butadiene. It is important to note that while the symmetry based orbitals often used to describe WH rules cannot be directly compared to the frontier molecular orbitals, the symmetry linking both sets of orbitals remains the same here.

The symmetry of the frontier orbitals of butadiene can then be determined based on these two operators, and a correlation diagram composed to identify which orbitals can overlap in the reaction to make the product. The correlation diagrams for the conrotatory and disrotatory mechanisms are shown below in '''Figure 13'''. As can be seen, the conrotatory mechanism involves the transfer of electrons from the ground state orbitals of the butadiene into the ground state orbitals of the cyclobutene, resulting in a small energy barrier for the reaction. In contrast, the disrotatory mechanism requires the excitation of electrons into an excited state antibonding orbital, giving it a much larger energy barrier and making the reaction thermally disallowed.

'''While this provides an elegant way of explaining the WH rules, it must be stated that it ''cannot'' provide significant insight into the structure of the product orbital, since the reaction proceeds via a 4n Mobius transition state and this allows all of the orbitals to rotate and switch symmetry. The actual frontier orbitals can be seen below in the MO/Energy Discussion'''.
<br>
[[File:BT1215 Extension FO Symmetry.jpg|centre|thumb|1458x415px|'''''Figure 13 - Frontier orbital symmetry of butadiene for conrotatory & disrotatory mechanisms''''']]
<br>

=== MO/Energy Discussion ===

In this discussion, the thermally allowed pathway will be focused on due to time limitations that meant that the full calculation of the photochemical route could not be performed. All optimisations were performed at the PM6 level, with the key MOs for the reactant, transition state, and product, given below in '''Table 12'''. As can be seen, MO 32 of the product is different to the WH predicted frontier orbital. The expected bonding interaction appears as part of MO 31, along with a more complicated bonding interaction from the alkene of the cyclobutene that appears to be the same symmetry. This is likely a consequence of reacting through a twisted Mobius transition state. It is recommended that further calculations be performed with a more accurate method to confirm the orbital ordering. The rest of the orbitals are as expected in the '''Reaction Overview''' section.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; font-size: 120%"
|+'''''Table 12 - Frontier orbitals in the 4π electrocyclic reaction of [1,1']-bicyclohexene'''''
!Reactant Orbitals
!Transition State Orbitals
!Product Orbitals
|-
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 DIENE SM PM6 OPT 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 22; mo 32; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneR</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneR</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneR</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 22; mo 32; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 33; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 34; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneR</target>
</item>
<item>
<script>frame 22; mo 35; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneR</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 DIENE TS OPT PM6 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 8; mo 32; mo nodots nomesh fill translucent; mo cutoff 0.04; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneT</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneT</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneT</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 8; mo 32; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 33; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 34; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneT</target>
</item>
<item>
<script>frame 8; mo 35; mo nodots nomesh fill translucent;mo cutoff 0.04; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneT</target>
</item>
</jmolmenu>
</jmol>
|<jmol>
<jmolApplet>
<size>400</size>
<color>white</color>
<uploadedFileContents>BT1215 PRODUCT ALKENE PM6 OPT.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 48; mo 31; mo nodots nomesh fill translucent; mo titleformat; rotate x -20; frank off</script>
<name>ExtDieneP</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle Vibrate</text>
<target>ExtDieneP</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExtDieneP</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 22; mo 31; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 31</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 32; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 32</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 33; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 33</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 34; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 34</text>
<target>ExtDieneP</target>
</item>
<item>
<script>frame 48; mo 35; mo nodots nomesh fill translucent; mo titleformat; set antialiasdisplay on</script>
<text>MO 35</text>
<target>ExtDieneP</target>
</item>
</jmolmenu>
</jmol>
|}

The thermochemical data for the reaction is shown below in '''Table 13''', while the energies of the reactant, transition state, and product are given in '''Table 14'''. The computed energies reveal that the starting diene is more stable, and therefore the predominant form. This is likely due to the high levels of ring strain in the cyclobutene ring destabilising the product. Kinetically this reaction is also highly unfavourable, with a much higher activation energy than the previous reaction systems discussed. It is possible that the complexity of the cyclohexene rings means a large amount of bond rearrangement is required in order to form the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 13 - Thermochemical data for the 4π electrocyclic reaction of [1,1']-bicyclohexene'''
!Activation Energy / Hartrees
!Activation Energy / kJmol<sup>-1</sup> (2 d.p.)
!Reaction Energy / Hartrees
!Reaction Energy / kJmol<sup>-1</sup> (2 d.p.)
|-
|0.104375
|274.04
|0.028329
|74.3777952
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+'''Table 14 - Reactant, transition state, and product energies for the electrocyclic reaction of [1,1']-bicyclohexene'''
!Reactant Energy / Hartrees
!Transition State Energy / Hartrees
!Product Energy / Hartrees
|-
|0.199543
|0.303918
|0.227872
|}

An IRC calculation was performed and both the plot and .gif file are shown below. As before, the reaction was computed from products to reactants in the IRC, so the graph should appear reversed. It is also important to note that in the IRC calculation the reactant energy appears to be higher energy than the product, likely due to it converging to a metastable minima where the diene is planar, and not the most stable form of the reactants.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!IRC Plot
!IRC .gif File
|-
|[[File:BT1215 Diene Extension.png|490x375px]]
|[[File:BT1215 Ext Diene.gif]]
|}

Finally, the imaginary vibration corresponding to the transition state can be seen below. As suggested by the vibration and the IRC, the bond formation in the electrocyclic reaction appears to be synchronous, with the hydrogen atoms rotating in a concerted manner.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>BT1215 DIENE TS OPT PM6 2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 9; frank off </script>
<name>VibTS2BT1215</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibrate</text>
<target>VibTS2BT1215</target>
</jmolbutton>
</jmol>

=== Output Calculation Files ===

SM: [[File:BT1215 DIENE SM PM6 OPT 2.LOG]]
<br>
IRC: [[File:BT1215 DIENE IRC PM6.LOG]]
<br>
PRETS OPT: [[File:BT1215 DIENE TS PREOPT PM6 2.LOG]]
<br>
TS: [[File:BT1215 DIENE TS OPT PM6 2.LOG]]
<br>
PROD: [[File:BT1215 PRODUCT ALKENE PM6 OPT.LOG]]
<br>

== Conclusion ==
Computational analysis of 4 different pericyclic systems was performed with a large degree of success, both with the Semi-Empirical PM6 and DFT B3LYP methods. In all cases, it was possible to model and correctly predict experimentally determined reaction mechanisms and transition states. The use of Gaussian was also able to provide insight into the change in bond lengths throughout the reaction, the type of transition state, the electron demand of the reaction, and which routes represent the thermodynamic or kinetic product. The computation of molecular orbitals was crucial in justifying the observed stereoselectivities, providing an elegant visual representation of secondary orbital interactions, as well as other factors affecting product formation. Unfortunately, the complexity of the calculations, along with time constraints, meant that the majority of reaction systems could only be optimised using the PM6 method, and so can only yield qualitative results due to the limitations discussed in the introduction. Conclusions for the individual exercises were as follows:

*<u>Exercise 1 - PM6</u> - The Diels-Alder reaction of butadiene + ethylene was modelled and shown to occur via a synchronous 4+2 cycloaddition, with a normal electron demand for the reaction. The transition state was correctly identified and confirmed by the presence of a single imaginary vibration frequency, corresponding to product formation, and an IRC calculation was performed to determine an early transition state. This was also confirmed by modelling the change in bond lengths throughout the course of the reaction, showing a transition state structure close to that of the reactants. Despite the inaccuracies of the PM6 method, bond lengths were in reasonable agreement with the literature.

*<u>Exercise 2 - PM6 & B3LYP</u> - The stereoselectivity of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole was investigated in order to determine whether the endo or exo product represented kinetic and/or thermodynamic control. All structures were optimised first with the PM6 method, before being reoptimised with the B3LYP method in order to give a more accurate depiction of the reaction system and its energies. Relative HOMO-LUMO energy gaps were compared with butadiene + ethylene to determine an inverse electron demand reaction, caused by the electron rich atoms on the dienophile. An MO diagram was constructed, and the kinetic stability of the endo product was explained by the involvement of oxygen p-orbitals in secondary orbital interactions that help to stabilise the transition state. The endo product was also determined to be the thermodynamic product due to the absence of steric clash between the bridged ring and the 1,3-dioxole group.

*<u>Exercise 3 - PM6</u> - The relative stabilities of five different pericyclic routes for the reaction between Xylylene + SO<sub>2</sub> were probed. Optimisations of reactants, products, and transition states were all carried out with the PM6 method. The cheletropic reaction yielded the thermodynamic product via a synchronous bond formation, likely due to the preservation of both S=O bonds. The exocyclic endo Diels-Alder reaction, occurring through asynchronous bond formation, represented kinetic control, due to the fact that the transition state contains a 6-membered fused ring compared to the relatively strained 5-membered cheletropic transition state. An alternative, endocyclic Diels-Alder reaction was investigated and shown to be highly disfavoured due to the fact that no aromatic ring was formed in the product, and the resultant fused ring product had large steric interactions making it thermodynamically unstable compared to the reactants.

*<u>Exercise 4 - PM6</u> - The thermally allowed, conrotatory 4π electrocyclic reaction of [1,1']-bicylcohexene was investigated, with all optimisations taking place at the PM6 level. The reaction was determined to proceed via a 4n Mobius transition state, which could explain discrepancies between the predicted orbital overlap using orbital symmetry and the observed product orbitals. An IRC calculation was performed and showed a concerted bond formation, while the imaginary transition state frequency observed for the transition state also suggested a concerted, conrotatory mechanism. Due to time constraints, the photochemical disrotatory reaction could not be calculated.

Further work could be explored not only in the computation of the photochemical reaction route in Exercise 4, but also by further modelling more obscure pericyclic reaction routes, similar to computational research performed by W. Grimme et al into cheletropic ene reactions<ref>W. Grimme, M. W. Harter, C. A. Sklorz, J. Chem. Soc., Perkin Trans. 2, 1999, 9.</ref>. Alternatively, higher level calculations could be performed to further understand more complex systems, such as ''ab initio'' calculations by F. Monnatt et al into the cheletropic and hetero Diels-Alder additions of SO<sub>2</sub> to (E)-Methoxybutadiene.<ref>F. Monnat, P. Vogel, V. M. Rayón and J. A. Sordo, J. Org. Chem., 2002, 67, 1882–1889.</ref>

== References ==

Rep:Mod:nrwy3ts

2018-04-04T11:03:13Z

Tam10:

= Transition States and Reactivity =

== Introduction ==

The aim of this lab was to investigate a number of Diels-Alder cyclic reactions using the program Gaussian, in order to determine the structure of the transition state formed during these reactions. The transition state in a reaction is the point of highest energy along a reaction coordinate, with a first derivative of zero, and a second negative derivative in the direction of the products, which occurs between the two energies of the reactants and the products, whose firsts derivative are also equal to zero. The enthalpy change of a reaction is determined by calculation of the difference in energy between these two points, and the activation energy corresponds to the difference in energy between the reactant minima and the transition state maxima.

In reality there are many degrees of freedom than seen in the 2D Reaction Coordinate plot, determined by the equation 3N-6, where N is the number of atoms in a molecule. The degrees of freedom can be used to plot a multidimensional Potential Energy Surface, and the reaction coordinate then plotted as a function of the degrees of freedom produced. Depending on the basis set selected, a greater number of basis vectors, such as with 631-G, can be utilised during calculation in order to produce a result with fewer approximations, at the expense of a longer calculation time. The Energy Profile normally corresponds to the minimum energy reaction pathway plotted from a Potential Energy Surface of a reaction, as there is the potential for there to be more than one saddle point on a Potential Energy Surface. In order to determine if the correct energy pathway is calculated using Gaussian, only one negative imaginary frequency should be seen, otherwise there is the possibility that the programme may have plotted another higher energy pathway instead.
[[File:nrwy3ts_Reaction_Coordinate_Diagram.png|x600px|600px]]

''Figure 1 - Reaction Coordinate Diagram''

Location of a transition state using Gaussian can be achieved via 3 different methods, depending on the initial knowledge of the transition state and the accuracy of the calculation required.

=== Method 1 ===
Involves the initial optimisation of the reactants and then placement of the reactants in a geometry similar to that of the transition state (such as 2.2Å being the average between the combined van der Waals radii and a C-C bond length), hence this method is unreliable unless some knowledge of the transition state is known. Although this is the quickest of the methods suggested, it is also the most unreliable, potentially producing multiple transition states, imaginary negative values or fail altogether. This method is best left for smaller systems if completely necessary.

=== Method 2 ===
Requires initial optimisation of the reactants, but during calculation of the transition state, bonds included in the reaction are frozen in place. This allows the system to be as close to the transition state as possible before optimisation, by allowing the unfrozen parts of the system to minimise around the frozen ‘bonds’. This method is more reliable than the previous method and almost as fast, yet still requires some understanding of the transition state before application.

=== Method 3 ===
Requires little knowledge of the transition state, and allows determination of the transition state from either the reactants or the products after optimisation. Using the desired product, the bonds which are formed during the transition state are frozen and placed a sensible distance apart (such as 2.4Å for a S-C bond). The broken bonds are frozen and optimised, then the transition state calculated. Although this is the most reliable of the methods, this method may fail if the transition state closely resembles the structure of the reactants when optimising and changing the structure from the products, as well as requiring multiple additional steps.

All these methods use a combination of both the semi-empirical method PM6 and the DFT method B3LYP, the former of which is quicker and used to optimise the structures initially, before the latter can further optimise the structure produced, giving a more reliable structure via the use of a greater amount of basis vectors.

== Exercise 1 ==
The electrocyclic reaction between Ethene and Butadiene to form Cyclohexene was investigated to determine the orbitals involved in the formation of the transition state of the reaction, the energies of the relevant orbitals and the change in the bond lengths between the carbons upon formation of the transition state and products. The carbons are labelled as shown in Figure 2 and the change in bond lengths between the carbons reported in the table below.

=== Reaction Scheme ===

[[File:nrwy3ts_Cyclohexane_Reaction.png|x400px|400px]]

''Figure 2 - Reaction Scheme for the reaction of ethene and butadiene''

=== Molecular Orbital Diagram ===

[[File:nrwy3ts_MO_Diagram.png|x800px|2000px]]

''Figure 3 - Molecular Orbital Diagram for the reaction of ethene and butadiene''

In order for the orbitals to overlap and combine, the orbitals must have the same symmetry to produce a molecular orbital of that same symmetry. Therefore, only symmetric-symmetric and antisymmetric-antisymmetric interactions can occur to produce a non-zero orbital overlap integral and are ‘allowed’, conversely a symmetric-antisymmetric orbital overlap would produce a zero value orbital overlap integral and as such is a ‘forbidden’ reaction. The final produced molecular orbitals are of the same symmetry as the original molecular orbitals, and the energy of the products normally lower than that of the reactants, as discussed earlier. However, as this diagram depicts the formation of the transition state, the molecular orbitals are higher in energy than the final orbitals formed, as shown by the reaction coordinate diagram.

=== HOMOs and LUMOs for Reactants and Transition States ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Ethene HOMO
! style="background: #6ca0dc; color: white;" |Ethene LUMO
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Butadiene HOMO
! style="background: #6ca0dc; color: white;" |Butadiene LUMO
|-
| <jmol><jmolApplet>
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<uploadedFileContents>BUTADIENE1.LOG</uploadedFileContents></jmolApplet></jmol>
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Transition State HOMO -1
! style="background: #6ca0dc; color: white;" |2 - Transition State HOMO
|-
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |3 - Transition State LUMO
! style="background: #6ca0dc; color: white;" |4 - Transition State LUMO +1
|-
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{| class="wikitable"
! style="background: #6ca0dc; color: white;" | Bond
! style="background: #6ca0dc; color: white;" | Reactants Bond Length/Å
! style="background: #6ca0dc; color: white;" | Transition State Bond Length/Å
! style="background: #6ca0dc; color: white;" | Product Bond Length/Å
|-
| C1-C2
| 1.35520
| 1.38177
| 1.53773
|-
| C2-C3
| -
| 2.11468
| 1.53582
|-
| C3-C4
| 1.33345
| 1.37979
| 1.49266
|-
| C4-C5
| 1.47077
| 1.41109
| 1.33305
|-
| C5-C6
| 1.33345
| 1.37979
| 1.49266
|-
| C6-C1
| -
| 2.11468
| 1.53582
|}
''Table 1 - Carbon Bond Lengths in the Formation of Cyclohexene''

From the table above, it can be seen that upon formation of the transition state, bonds C1-C2, C3-C4 and C5-C6 all lengthen as the sp hydridisation increases. Conversely, C4-C5 decreases from 1.47Å to 1.41Å due to the formation of a double bond from the single bond seen in the reactants and the increased s character of the MO. This bond further decreases upon completion of the double bond formation. The initial C6-C1 and C2-C3 'bonds' shorten in length, producing a value of 1.53582Å, incredibly close to the 1.54Å for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond<sup>1</sup>, showing the structure was successfully optimised by Gaussian. Due to the increased s character of the bonds when closer to the sp<sup>2</sup> carbons and C=C bond, there is a slight decrease in bond length from C1-C2 to C2-C3/C6-C1. As expected this increase in s character continues when looking at the bonds around the sp<sup>2</sup> C5 and C4, with the C3-C4/C5-C6 having intermediate values between the 1.54Å for a C-C bond and 1.34Å for an alkene C=C bond. This is consistent with the reported sp<sup>3</sup>-sp<sup>2</sup> value of 1.50Å<sup>1</sup>. The initial transition state produces a bond length of 2.11468Å for C2-C3/C6-C1, which decreases to 1.53582Å upon formation of cyclohexene. The initial bond length of 2.11468Å is comparable to the sum of two carbon van der Waals radii (3.400Å)<sup>2</sup>, and shows a bonding character interaction due to the shorter length observed.

=== Transition State Vibration and IRC ===

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'' Figure 4 - Reaction Path at the Transition State Vibration ''

Figure 4 shows the vibration corresponding to the imaginary frequency produced by the transition state, which represents the reaction path at the transition state. In the IRC, the bonds from the diene and alkene form at the same time, and such is a synchronous, concerted reaction.

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Transition State IRC
|-
| [[File:nrwy3ts_Ex1_Transition_State_IRC.gif]]
|}

==Exercise 2==

The molecular orbital diagrams for the Diels-Alder reaction between 1,3-dioxone and cyclohexadiene were produced to determine the molecular orbitals involved and the overlap of the orbitals in the transition state. Here the production of both the endothermic and exothermic products was investigated, where the approach of the dienophile 1,3-dioxone differs. During formation of the endothermic product, the ring oxygens approach beneath the alkene bonds in cyclohexadiene due to a favourable stabilising interaction. However for the exothermic product, the ring oxygens are positioned away from the alkene bonds. As seen in the previous exercise, only overlap between orbitals of the same symmetry is allowed for a reaction to occur.

=== Reaction Scheme ===

[[File:Reaction_Scheme_Exercise_2.png|x400px|400px]]

''Figure 4 - Reaction Scheme for the Reaction of Cyclohexadiene and 1,3-dioxole''

=== Molecular Orbital Diagram ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Exothermic MO Diagram
! style="background: #6ca0dc; color: white;" |Endothermic MO Diagram
|-
| [[File:nrwy3ts_Exo_MO_Diagram.png|x800px|2000px]]
| [[File:nrwy3ts_Endo_MO_Diagram.png|x800px|2000px]]
|}
''Figure 5 - Molecular Orbital Diagram for the Reaction of Cyclohexadiene and 1,3-dioxole''

A standard Diels-Alder reaction involves the combindation of a diene and a dienophile, where the HOMO of the diene interacts with the LUMO of the diene. However in the reaction investigated here, the electron donating oxygens in the 1,3-dioxone ring increase the energy of the HOMO of the alkene, and thus instead the HOMO of the alkene interacts with the LUMO of the diene in an inverse demand Diels-Alder reaction. Here it can be seen that molecular orbitals 1, 3 and 4 for the endothermic product are higher in energy than the exothermic counterparts, whilst molecular orbital 2 is lower in energy in the endothermic transition state than the exothermic. This effect seen in the endothermic product is due to secondary orbital interactions and is discussed later on, shown in the molecular orbital Jmol images below.

=== HOMOs and LUMOs for Reactants and Transition States ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1,3-Dioxole HOMO
! style="background: #6ca0dc; color: white;" |1,3-Dioxole LUMO
! style="background: #6ca0dc; color: white;" |Cyclohexadiene HOMO
! style="background: #6ca0dc; color: white;" |Cyclohexadiene LUMO
|-
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Exo Transition State LUMO +1
! style="background: #6ca0dc; color: white;" |2 - Exo Transition State LUMO
! style="background: #6ca0dc; color: white;" |3 - Exo Transition State HOMO
! style="background: #6ca0dc; color: white;" |4 - Exo Transition State HOMO -1
|-
| <jmol><jmolApplet>
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{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |1 - Endo Transition State LUMO +1
! style="background: #6ca0dc; color: white;" |2 - Endo Transition State LUMO
! style="background: #6ca0dc; color: white;" |3 - Endo Transition State HOMO
! style="background: #6ca0dc; color: white;" |4 - Endo Transition State HOMO -1
|-
| <jmol><jmolApplet>
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=== Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Endo
| -1313771.847
| -1313622.1573
| -1313852.8626
| 149.6897
| -81.01537
|-
| Exo
| -1313771.847
| -1313614.3096
| -1313845.7396
| 157.53763
| -73.8926
|}
'' Table 2 - Activation and Reaction Energies for the Reactions between Cyclohexadiene and 1,3-dioxole ''

From the calculated data in the table above, the exothermic product is shown to have a greater activation energy than the endothermic product. This can be explained by the lack of a non-bonding stabilising interaction between the ring oxygen orbitals overlapping with the alkene bond orbitals during the transition state, meaning the energy of the exothermic transition state is higher than that of the endothermic pathway. This secondary orbital overlap can been seen below (Figure 6). Both reactions are exothermic and thermodynamically favourable enough to overcome the decrease in entropy upon formation of the product. However, the endothermic product is the lower in energy and therefore most stable of the products, which may be due to reduced steric interactions with 1,3-dioxole species avoiding steric clashes with the carbon chain bridging the 2 C=C bonds. This leads to a further favouring of the endothermic product, with both the stabilising oxygen non-bonding interactions and the lack of steric repulsion by bridging carbons, as seen in the data produced.
(It should be noted that upon optimisation of the cyclohexadiene, a negative frequency was observed, corresponding to the stretching of the sp<sup>3</sup> C-H bonds. This resulted in a slightly higher energy in the products than expected.)

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Exo Transition State HOMO
! style="background: #6ca0dc; color: white;" |Endo Transition State HOMO
|-
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'' Figure 6 - Secondary Orbital Effect ''

== Exercise 3 ==

O-Xylylene and sulfur dioxide undergo multiple cycloaddition reactions, which consist of a Diels-Alder and Cheletropic reaction, forming 10 and 9 membered rings respectively with the external cis-butadiene and 6 membered with the internal. During the [4+2] Diels-Alder reactions, the orientation of the SO<sub>2</sub> to the external cis-butadiene during formation of the transition state allows production of an exothermic and endothermic product. The preference of forming either the exothermic or endothermic product via a Diels-Alder reaction, or the cheletropic product, was investigated here by optimisation of each transition state at the PM6 level, and the energies calculated from the data. These pathways were then compared to the [4+2] cycloaddition pathways possible with the internal cis-butadiene.

(You should still count members of a ring by the smallest continuous joined system ie 5 and 6 for both external and internal reaction products [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:03, 4 April 2018 (BST))

=== Reaction Scheme ===

[[File:nrwy3ts_Ex_3_Reaction_Scheme.png|x500px|500px]]

'' Figure 7 - Reaction Scheme for the Reaction of o-Xylylene and Sulfur Dioxide''

=== External Transition State IRCs ===

{| class="wikitable"
|-
! style="background: #6ca0dc; color: white;" |Diels-Alder Exo Transition State IRC
! style="background: #6ca0dc; color: white;" |Diels-Alder Endo Transition State IRC
! style="background: #6ca0dc; color: white;" |Chemetropic Transition State IRC
|-
| [[File:nrwy3ts_DA_EXO_TS_IRC.gif|500px|]]
| [[File:nrwy3ts_DA_ENDO_TS_IRC.gif|500px|]]
| [[File:nrwy3ts_CHELOTROPIC_TS_IRC.gif|500px|]]
|}

(Your exo TS is actually endo as well [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:03, 4 April 2018 (BST))

=== External Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Diels-Alder Endo
| 156.39
| 235.4534
| 56.4044
| 79.0634
| -99.9856
|-
| Diels-Alder Exo
| 156.39
| 235.4612
| 55.7804
| 79.0712
| -100.6096
|-
| Cheletropic
| 156.39
| 257.5612
| 0.013
| 101.1712
| -156.377
|}
'' Table 3 - Activation and Reaction Energies for the External Reactions between o-Xylylene and Sulfur Dioxide ''

From Table 3, it can be seen that the Diels-Alder reactions form a more favourable transition state than the Cheletropic pathway, although the Cheletropic product is lower in energy, at an almost 0 value, corresponding to the thermodynamic product. The increased stability in the product is due to the formation of 2 C-S bonds, and lack of breaking of a S-O bond. Although the C-O bond energy formed during the Diels-Alder reaction is greater than the C-S bonds only formed during the Cheletropic reaction, 358kJ/mol compared to 272kJ/mol<sup>3</sup>, this does not compensate the energy used breaking the S-O bond. The activation energy for the Cheletropic reaction is high due to the formation of a strained 5 membered ring, as opposed to the 6 membered ring formed during the Diels-Alder reaction. All products lead to a decrease in energy due to the produced aromatic molecule, with the Diels-Alder Endo product being the kinetic product due to the smallest activation energy, albeit only by a marginally small amount than the exothermic. The ability for o-Xylylene to form planar aromatic products is the reason for its high reactivity and low stability, at least at the external cis-butadiene site.

=== Reaction Coordinate Diagram ===

[[File:nrwy3ts_Ex_3_Reaction_Coordinate_Diagram.png|x600px|1000px]]

'' Figure 8 - Reaction Coordinate Diagram for the Reaction of o-Xylylene and Sulfur Dioxide''

=== Internal Transition State IRCs ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Exo IRC
! style="background: #6ca0dc; color: white;" |Endo IRC
|-
| [[File:nrwy3ts_Internal_DA_Exo_IRC.gif]]
| [[File:nrwy3ts_Internal_DA_Endo_IRC.gif]]
|}

=== Internal Reaction Energies ===

{| class="wikitable"
! style="background: #6ca0dc; color: white;" |Type of Reaction
! style="background: #6ca0dc; color: white;" |Energy of Reactants/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Transition State/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Energy of Product/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Activation Energy/kJ mol<sup>-1</sup>
! style="background: #6ca0dc; color: white;" |Reaction Energy/kJ mol<sup>-1</sup>
|-
| Diels-Alder Endo
| 156.39
| 265.382
| 170.5834
| 108.992
| 14.1934
|-
| Diels-Alder Exo
| 156.39
| 273.1404
| 174.9956
| 116.7504
| 18.6056
|}
'' Table 4 - Activation and Reaction Energies for the Internal Reactions between o-Xylylene and Sulfur Dioxide ''

When reacting with the internal cis-butadiene, there is no overall aromatic stabilisation, and the alkene bonds are left as unsubstituted and terminal. Hence in comparison to the external reaction, the internal is far less favoured, as not only is the activation energy higher, but the disturbing of the conjugated pi system leads to a destabilisation of the products in comparison to the reactants. From Table 3, it can be seen that the activation energy upon formation of the transition state with the internal cis-butadiene bond is greater than with the external, with both the endothermic and exothermic transition states. The overall reaction energy is actually positive for this cycloaddition, due to an increase in energy in the products from the reactants. Upon reacting at the internal cis-butadiene, not only is there a lack of aromatic stabilisation in comparison to the external reaction, but the planar conjugated structure is also disturbed.

== Conclusion ==

The reactants, transition states and products were all successfully optimised using Gaussian, with imaginary frequencies only obtained when expected on a transition state. Study into multiple electrocyclic reactions allowed determination of the molecular orbitals involved in the production of the transition state, of the change in bond lengths during a reaction, of the kinetic and thermodynamic products and how effects from non-bonding orbital interactions and aromatic stabilisation may affect the products produced. Use of both 631-G and PM6 allowed practice of situations with different basis sets and methods to produce the desired optimised transition state and products required for energy calculations and discussion, which agreed with the expected trends.

== References ==

1. Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. ISBN 978-3-86025-249-9.

2. S. S. Batsanov, Inorg. Mater., 2001, 37, 871-885.

3. Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds", 1958, 2nd ed., Butterworths, London

Rep:Mod:em2815ts

2018-04-04T10:48:48Z

Tam10:

=Introduction=

===Potential Energy Surfaces===

A potential energy surface (PES) describes the energy of a system in terms of certain parameters, for example nuclear position. For a linear molecule, the potential energy is dependent on 3N-6 degrees of freedom ie normal modes of vibration, where N = the number of atoms.<ref name="one"/> From the PES, a reaction coordinate can be derived; this is a progress variable which describes the reaction. It shows the progression of reactants to products and predicts the exact probability that a certain configuration will reach the product state.

The salient points on a PES are the stationary points, where the gradient, given by the first derivative, is 0. These points correspond to the reactants, products or transition states of the reaction. The curvature of these points, indicated by the second derivative, indicates the type of stationary point and allows the differentiation between the minima and the transition state.

It can be noted that the gradient and curvature of these points correspond to the force and force constant, respectively.

====Reactants and Products====
If the second derivative is > 0 with respect to all 3N-6 degrees of freedom, the stationary point is a minimum. This represents a minimum on the reaction coordinate. There are different types of minima, for example global and relative: the former is the lowest energy minimum which corresponds to the products and the latter can correspond to the reactants.
====Transition State====
If the second derivative is < 0 along the reaction coordinate but > 0 for all other degrees of freedom (in other words, a maximum along the reaction coordinate but a minimum in all other directions), the stationary point corresponds to a transition state. This gives rise to a single negative Hessian eigenvalue and represents a maximum energy point along the reaction coordinate (it is the maximum on the minimum energy path which connects the reactant and product minima).

===Computational Methods===

During this investigation, GaussView was used to locate the transition states of the relevant reactions. Two main computational methods were used, PM6 and B3LYP. PM6 is a fitted semi-empirical method which uses experimental data, ie previously calculated integrals, to solve the Hamiltonian matrix. This method is advantageous since it does not need to calculate all of the integrals in each optimisation; this makes it less expensive and also much faster. The PM6 method is, however, less accurate because it uses many approximations.<ref name="two"/> <ref name="three"/>

B3LYP is a method which uses Density Functional Theory (which uses the electron density) to calculate the terms of the Hamiltonian and the Hartree Fock calculation (which uses electronic position) to find the exchange correlation terms.<ref name="two"/> This method is extremely accurate but it is slower than the PM6 method since it does not use precalculated values. In this investigation, the B3LYP method uses the 6-31G(d) basis set, which is a set of functions which represent atomic orbitals which can be linearly combined to form molecular orbitals.<ref name="four"/> The 6-31G(d) set is high enough such that enough atomic orbitals are used to give an accurate view of the molecular orbitals without costing the computational effort too much. Higher basis sets result in higher computational effort which is expensive and time-consuming; the 6-31G(d) basis set offers a good compromise between accuracy and computational effort.

===Locating the Transition State===

The following methods were used to locate the transition states.

====Method 1====
Method 1 involves the use of the previously PM6 optimised reactants to estimate the transition state structure by altering the distances between the reacting terminii. The estimated structure is then optimised to a transition state at the PM6 or/and B3LYP/6-31G(d) level(s). This method is good because it is the fastest, but it is very unreliable and requires knowledge of the transition state (it will only work if the initial guess of the transition state structure is extremely close to the actual structure).

====Method 2====
Method 2 is similar to method 1 in that it involves the use of previously optimised reactants. The optimised reactants are placed close together and the distances between the reacting atoms are set. These pairs of reacting atoms are then 'frozen' and the frozen structure is optimised to a minimum. The resulting molecule is then optimised to a transition state at the PM6 level and can be further optimised at the B3LYP/6-31G(d) level. This method is much more reliable than method 1.

====Method 3====
Method 3 is slightly different to methods 1 and 2 in that it begins with the product. The product is constructed and optimised to a minimum at the PM6 level. The new bonds which have formed during the reaction are then broken and the distances between the reacting atoms are set. These bonds are then frozen and the structure is optimised to a minimum at the PM6 level. The resulting molecule from this calculation is then optimised to a transition state at the PM6 level and can be optimised further at the B3LYP/6-31G(d) level. Method 3 is the most reliable method since it does not require knowledge of the transition state and it is very easy and more likely to succeed. The only downsides of this method are that it requires more steps and that it may not work with all reactions.

====Checks====
The success of each optimisation was determined by analysing the vibrations/frequency calculations. All molecules which were successfully optimised to a minimum yielded all positive frequencies whereas molecules which were successfully optimised to a transition state resulted in the first normal mode having a negative frequency, indicative of an imaginary number. The transition state has a negative force constant, therefore when substituted into the equation for the simple harmonic oscillator, the output frequency is an imaginary number.

=Part 1: Reaction of 1,3-butadiene with Ethene=

Scheme 1 shows the Diels Alder reaction of ethene and 1,3-butadiene.

[[File:Em2815 e1 scheme.png|thumb|center|Scheme 1 : the reaction of ethene and 1,3-butadiene]]

The reactants were optimised at the PM6 level and the transition state was located using method 3, also at the PM6 level. The success of this reaction was confirmed by the presence of an imaginary frequency at 948.48i cm<sup>-1</sup>. The MOs generated computationally have been correlated with the MOs in Fig 1a (see Table 1).

===Molecular Orbitals===

The molecular orbital diagram for this reaction can be seen in Fig 1a and the molecular orbitals found computationally can be seen below.

[[File:Em2815_exercise1_modiagram.png|480px|thumb|center|Figure 1a: MO diagram for the reaction of ethene and 1,3-butadiene]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 1: shows the important MOs generated computationally for 1,3-butadiene, ethene and the transition state
!Ethene
!1,3-butadiene
!Transition State
|-
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LUMO (corresponds to MO 3)

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LUMO (corresponds to MO 2)

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LUMO +1 (corresponds to MO 8)

|-
|<jmol><jmolApplet>
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LUMO (corresponds to MO 7)
|-
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HOMO (corresponds to MO 4)

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HOMO (corresponds to MO 1)

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HOMO (corresponds to MO 6)

|-
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HOMO-1 (corresponds to MO 5)

|}

The MO diagram shows that the LUMO of 1,3-butadiene combines with the HOMO of ethene in-phase and out-of-phase to generate the HOMO and LUMO of the transition state, respectively. The HOMO of 1,3-butadiene also combines with the LUMO of ethene in-phase (a stabilising interaction) to generate HOMO-1 and out of phase (a destabilising interaction) to generate LUMO+1.

Evidently, orbitals of the same symmetry combine to form a molecular orbital with a retention of symmetry. Hence, two symmetric orbitals overlap to form an orbital which is symmetric and two antisymmetric orbitals overlap to form an antisymmetric orbital. If the orbitals have the same symmetry, they will overlap spatially and so the overlap integral will be non-zero (thus, the overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions and 0 for antisymmetric-symmetric interactions). This shows that for a reaction to be allowed, there is a requirement for the symmetry to be the same.<ref name="five"/>

In normal electron demand Diels Alder reactions, the HOMO of the diene and the LUMO of the dienophile are closer in energy than the LUMO of the diene and the HOMO of the dienophile.<ref name="six"/> After obtaining the energies of the molecular orbitals by looking at the MO analysis, it was found that this statement is true for this case, hence the reaction between 1,3-butadiene and ethene involves normal electron demand.

===Carbon-Carbon Bond Lengths===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: the carbon-carbon bond lengths in the reactants, transition state and cyclohexadiene product
!'''Bond'''
|'''''Bond Length in Reactants''' '''(Å)'''''
|'''''Bond Length in Transition State (Å)'''''
|'''Bond Length in Product ''(Å)'''''
|-
!1-2
|1.3334
|1.3798
|1.5008
|-
!2-3
|1.4708
|1.4111
|1.3370
|-
!3-4
|1.3334
|1.3798
|1.5009
|-
!4-5
|N/A
|2.1147
|1.5371
|-
!5-6
|1.3273
|1.3818
|1.5346
|-
!6-1
|N/A
|2.1148
|1.5371
|-
|}

The carbon-carbon bond lengths in ethene, 1,3-butadiene, the transition state and the cyclohexene product are shown in Table 2. It can be seen that bonds 1-2 and 3-4 get longer as the reaction proceeds from the reactants to the products; this makes sense since the hybridisation of the carbon atoms is changing from sp<sup>2</sup> to sp<sup>3</sup> as the double bonds change to single bonds. As expected, bond 2-3 gets shorter as the cyclohexene double bond forms (the carbon atoms go from sp<sup>3</sup> to sp<sup>2</sup>). Bonds 4-5 and 6-1 become shorter from the transition state to the product as the reacting terminii approach each other as the bonds form. It can be noted that the distances between the two pairs of reacting atoms in the transition state (4-5 and 6-1) are shorter than 2x the Van der Waals radius of the C atom (1.70 Å), thus confirming the interaction between the reacting terminii and the partial formation of these bonds in the transition state.

The bond lengths obtained computationally are mostly consistent with the typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths of 1.34 and 1.54 Å, respectively.<ref name="seven"/> One deviation, however, is bond 2-3 in the reactant butadiene. This length is slightly shorter than the typical sp<sup>3</sup> C-C bond length due to the delocalised pi system. Another notable deviation involves bonds 1-2 and 3-4 in the product, which are shorter than the expected sp<sup>3</sup> length due to the fact that one carbon atom of each of these bonds is sp<sup>2</sup> hybridised.

===Vibration Analysis===

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Fig 1b: the vibration at the transition state of the reaction between 1,3-butadiene and ethene

The vibration which corresponds to the reaction path at the transition state (see Fig 1b) is the vibration with the negative (imaginary) frequency. The animation shows that the reacting terminii of both reactants move towards each other simultaneously as the two new bonds form synchronously (ie, at the same time). This is also confirmed by the IRC, since both bonds form in Step 10 .

===Log Files===

[[Media:Em2815 e1 butadiene minPM6.LOG|LOG file of 1,3-butadiene minimum PM6]]

[[Media:Em2815 e1 ethene minPM6.LOG|LOG file of ethene minimum PM6]]

[[Media:Em2815 e1 cycloadd TS PM6.LOG|LOG file of transition state PM6]]

[[Media:em2815_e1_IRC.LOG|LOG file of IRC PM6]]

[[Media:Em2815_e1_product_min_PM6.LOG|LOG file of product minimum PM6]]

=Part 2: Reaction of Cyclohexadiene and 1,3-dioxole=

Scheme 2 shows the Diels Alder reaction of cyclohexadiene and 1,3-dioxole. This reaction can go via two pathways: exo or endo.

[[File:em2815_e2_scheme_720p.png|380px|thumb|center|Scheme 2: the reaction of cyclohexadiene with 1,3-dioxole to give the exo and endo products]]

The reactants and products were optimised at the B3LYP/6-31G(d) level and the transition state was located using method 3, also at the B3LYP/6-31G(d) level. The success of the endo and exo reactions were confirmed by the presence of the imaginary frequencies at 520.90i and 528.79i cm<sup>-1</sup>, respectively. The MOs generated computationally have been correlated with the MOs in Fig 2 (see Table 3).

===Molecular Orbitals===

The molecular orbital diagram for the exo reaction can be seen in Fig 2 and the molecular orbitals found computationally can be seen below.

[[File:em2815_e2_MO_480p.png|400px|thumb|center|Figure 2: the MO diagram for the exo pathway of the reaction of cyclohexadiene with 1,3-dioxole]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 3: shows the important MOs generated computationally for 1,3-dioxole, cyclohexadiene and the exo and endo transition states
!Cyclohexadiene
!1,3-dioxole
!Endo Transition State
!Exo Transition State
|-
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LUMO (corresponds to MO 2)

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LUMO (corresponds to MO 4)

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LUMO +1 (analogous to MO 8)

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LUMO +1 (corresponds to MO 8)

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LUMO (analogous to MO 7)

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LUMO (corresponds to MO 7)

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HOMO (corresponds to MO 1)

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HOMO (corresponds to MO 3)

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HOMO (analogous to MO 6)

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HOMO (corresponds to MO 6)

|-
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HOMO-1 (analogous to MO 5)

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HOMO-1 (corresponds to MO 5)

|}

The MO diagram shows that the LUMO of cyclohexadiene combines with the HOMO of 1,3-dioxole in-phase and out-of-phase to generate the HOMO and LUMO of the transition state, respectively. The HOMO of cyclohexadiene also combines with the LUMO of 1,3-dioxole in-phase (a stabilising interaction) to generate HOMO-1 and out of phase (a destabilising interaction) to generate LUMO+1.

This MO diagram can be compared to that of the Diels Alder reaction in Part 1. The presence of the electron-donating oxygen atoms in 1,3-dioxole destabilises the HOMO and LUMO of the alkene therefore they are higher in energy compared to the simple ethene molecule. This means that the HOMO of the electron deficient 1,3-dioxole is closer in energy to the LUMO of the electron rich cyclohexadiene, hence these are the orbitals that overlap and interact. Since the HOMO of the alkene (dienophile) and the LUMO of the diene are closer in energy than the LUMO of the alkene and the HOMO of the diene, the reaction goes via inverse electron demand.<ref name="five"/><ref name="six"/>

It is worth noting that the endo pathway would produce transition state molecular orbitals which are lower energy than those depicted for the exo pathway.

===Thermochemistry===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 4: shows the activation and reaction energies of the endo and exo pathways of the reaction of 1,3-dioxole with cyclohexadiene
!
!Endo
!Exo
|-
!Activation Energy (kJ/mol)
|<nowiki>+157.53</nowiki>
|<nowiki>+165.41</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>-70.89</nowiki>
|<nowiki>-65.64</nowiki>
|}

The 'Thermochemistry Data' from the optimisations were used to calculate the activation and reaction energies of the exo and endo pathways, see Table 4. Since the endo pathway has a smaller activation energy, it is kinetically favoured and leads to the kinetic/endo product, which is faster formed. This is the case because there is less steric clash in the endo transition state. Another possible reason is a stabilising secondary orbital overlap between the pi system of the diene and the pi orbitals of both oxygen atoms in 1,3-dioxole which decreases the energy of the transition state, lowering the activation energy.

The reaction energy for the endo pathway is also more negative than that for the exo pathway, suggesting that the endo product is the more thermodynamically stable (lower energy) product. This is the case because of the same reasons discussed earlier: the secondary orbital interaction is also present in the endo product and there is less steric clash. Hence, the endo product is kinetically and thermodynamically favoured.

The exo pathway has a larger activation energy and a smaller reaction energy than the endo pathway. This shows that the exo product is less thermodynamically stable (higher energy) than the endo product. The aforementioned secondary orbital interaction is not possible in the exo product since the 1,3-dioxole molecule is in the wrong orientation for the pi systems of the oxygen atoms and the diene to overlap. The exo product therefore does not benefit from the additional stabilisation, and this coupled with the fact that there is more steric clash means that the exo product is higher in energy.

===Log Files===

[[Media:Em2815 e2 dioxole min B3LYP.LOG|LOG file of dioxole minimum B3LYP]]

[[Media:Em2815 e2 endo cyclohexadiene min B3LYP.LOG|LOG file of cyclohexadiene minimum B3LYP]]

[[Media:A2 em2815 e2 endo ts B3LYP.LOG|LOG file of endo transition state B3LYP]]

[[Media:E2 EXO TS B3LYP.LOG|LOG file of exo transition state B3LYP]]

[[Media:Em2815 e2 endo product min B3LYP.LOG|LOG file of endo product minimum B3LYP]]

[[Media:Em2815 e2 exo product min B3LYP.LOG|LOG file of exo product minimum B3LYP]]

[[Media:Em2815 e2 endo irc.LOG|LOG file of endo IRC]]

[[Media:Em2815 e2 exo IRC.LOG|LOG file of exo IRC]]

=Part 3: Reaction of o-Xylylene and SO<sub>2</sub>=

Scheme 3 shows the Diels Alder and Cheletropic reactions of o-xylylene and SO<sub>2</sub>.

[[File:em2815_e3_scheme_.png|480px|thumb|center|Scheme 3: the Diels Alder and Cheletropic reactions of o-xylylene with SO<sub>2</sub>]]

The reactants and products were optimised at the PM6 level and the transition state was located using method 3, also at the PM6 level. The success of the endo, exo and cheletropic reactions were confirmed by the presence of the imaginary frequencies at 333.79i, 351.67i and 486.55i cm<sup>-1</sup>, respectively.

===IRC Calculations===

The Intrinsic Reaction Coordinate calculations for the endo, exo and cheletropic reactions can be seen in Figs 3a, 3b and 3c. Evidently, for the Diels Alder reactions, the reacting terminii of both reactants move towards each other at different rates. The C-O and C-S bonds are formed at different rates due to asymmetry, hence the bond formation is asynchronous. For the endo pathway, the C-S bond forms in step 56 whereas the C-O bond forms in step 52 and for the exo pathway, the C-S and C-O bonds form in steps 64 and 60, respectively. This however is not the case for the cheletropic reaction. Since this reaction is symmetric, the reacting terminii move towards each other at the same rate and the C-S bonds are formed synchronously (both C-S bonds form in step 78 of the IRC).

(Don't use the word "rate" here, as their formation is staggered in time. It's very difficult to say when exactly a "bond" is formed. The bonds that GaussView uses are aesthetic (except in molecular mechanical calculations) and are decided when atoms cross a cutoff distance [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:48, 4 April 2018 (BST))

[[File:em2815_e3_endo_IRC.gif|450px|thumb|center|Figure 3a : IRC for the Endo Diels-Alder Reaction of o-xylylene and SO<sub>2</sub>]]
[[File:em2815_e3_exo_IRC.gif|450px|thumb|center|Figure 3b : IRC for the Exo Diels-Alder Reaction of o-xylylene and SO<sub>2</sub>]]
[[File:em2815_e3_cheletropic_IRC.gif|450px|thumb|center|Figure 3c : IRC for the Cheletropic Reaction of o-xylylene and SO<sub>2</sub>]]

====o-Xylylene Stability====
The IRCs for the reactions show that the two double bonds in the 6 membered ring of xylylene break and a delocalised ring structure forms. This shows that xylylene is extremely reactive since there is a very large driving force for aromatisation.

===Thermochemistry===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 5: shows the activation and reaction energies of the endo, exo and cheletropic pathways of the reaction of o-xylylene with SO<sub>2</sub>
!
!Endo
!Exo
!Cheletropic
|-
!Activation Energy (kJ/mol)
|<nowiki>+82.72</nowiki>
|<nowiki>+86.72</nowiki>
|<nowiki>+105.08</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>-98.04</nowiki>
|<nowiki>-98.71</nowiki>
|<nowiki>-155.01</nowiki>
|}

The 'Thermochemistry Data' were used to calculate the activation and reaction energies of each of the three pathways, see Table 5. The endo pathway has the smallest activation energy, therefore it is kinetically favoured (thus the endo product is the kinetic product). The endo transition state could be lower in energy because there is reduced steric clash. It may also be stabilised by a secondary orbital overlap between the pi systems of the xylylene and the oxygen atoms from SO<sub>2</sub>. Since these factors stabilise the transition state, they result in a lower activation barrier.

The exo transition state has more steric clash and does not benefit from the secondary orbital overlap therefore it is higher in energy. Furthermore, the cheletropic transition state consists of a highly strained 5 membered ring. This is much higher in energy than the 6 membered ring in the exo and endo transition states (6 membered rings are essentially strain-free), therefore the cheletropic transition state is much less stable, resulting in the largest activation barrier.

The cheletropic reaction has the most negative reaction energy, indicating that the cheletropic product is the most energetically stable and therefore the thermodynamic product. This is the case because the S=O bonds are extremely strong and high energy therefore they stabilise the product.

The values for activation energy and reaction energy were used to generate the reaction profile shown in Fig 4.

[[File:Em2815_reactionprofileyay.png|550px|thumb|center|Figure 4: the reaction profile for the Diels Alder and Cheletropic pathways of the reaction of o-xylylene with SO<sub>2</sub>]]

===Alternative Diels-Alder Pathway===

So far, the reaction at the terminal diene has been discussed. There is also an alternative reaction pathway involving the second cis-butadiene fragment which is in the 6 membered ring of o-xylylene. See Scheme 4.

[[File:em2815_e3_altscheme_720p.png|480px|thumb|center|Scheme 4: the alternative reaction pathway involving the cis-butadiene fragment in the o-xylylene ring]]

The IRC calculations and thermodynamic data for the exo and endo pathways involving this cis-butadiene fragment can be seen below in Figs 5a & 5b and Table 6. The activation energies for both pathways are extremely high, indicating that reactions at this site are very kinetically unfavourable. The reaction energies are also positive, indicating that both the exo and endo products are relatively high in energy compared to the products of terminal diene pathway discussed earlier. Since both products are less stable, there is a lower driving force for the xylylene compound to react at this site. The positive reaction energy also indicates that the reactions are endothermic and hence thermodynamically unfavourable.

[[File:em2815_e3_ringendo_IRC.gif|450px|thumb|center|Figure 5a : IRC for the endo Diels-Alder reaction of o-xylylene and SO<sub>2</sub> at the alternative site]]
[[File:em2815_e3_ringexo_IRC.gif|450px|thumb|center|Figure 5b : IRC for the exo Diels-Alder reaction of o-xylylene and SO<sub>2</sub> at the alternative site]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 6: shows the activation and reaction energies of the endo and exo pathways of the reaction of o-xylylene with SO<sub>2</sub> at the alternative site
!
!Endo
!Exo
|-
!Activation Energy (kJ/mol)
|<nowiki>+112.94</nowiki>
|<nowiki>+120.78</nowiki>
|-
!Reaction Energy (kJ/mol)
|<nowiki>+17.22</nowiki>
|<nowiki>+21.67</nowiki>
|}

The kinetic and thermodynamic unfavourability of these pathways can be explained by the fact that these reactions do not achieve aromatisation of the xylylene ring in the product. The conjugation is also lost in this pathway, therefore the reactants are much less stable and are disfavoured. Aromatisation and conjugation can however be achieved and maintained in the reaction occurring at the terminal diene, therefore this is the kinetically and thermodynamically favourable site of the reaction.

===Log Files===

[[Media:Em2815_SO2_REACTANT_MINIMUM_PM6.LOG|LOG file of SO<sub>2</sub> Reactant Minimum PM6 ]]

[[Media:Em2815_e3_XYLYLENE_REACTANT_MINIMUM_PM6.LOG|LOG file of o-Xylylene Reactant Minimum PM6 ]]

[[Media:Em2815_e3_ENDO_TS_PM6.LOG‎|LOG file of endo transition state PM6 ]]

[[Media:Em2815_e3_ENDO_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of endo product minimum PM6 ]]

[[Media:Em2815_e3_Exo_TS_PM6.LOG‎|LOG file of exo transition state PM6 ]]

[[Media:Em2815_e3_Exo_Product_Minimum_PM6.LOG‎|LOG file of exo product minimum PM6 ]]

[[Media:Em2815_e3_CHELETROPIC_TS_PM6.LOG‎|LOG file of cheletropic transition state PM6 ]]

[[Media:E3_CHELETROPIC_MINIMUM_PROD_PM6.LOG|LOG file of cheletropic product minimum PM6 ]]

[[Media:Em2815 e3 ENDO IRC PM6.LOG|LOG file of endo pathway IRC]]

[[Media:Em2815 e3 EXO IRC PM6.LOG|LOG file of exo pathway IRC]]

[[Media:Em2815 e3 CHELETROPIC IRC PM6.LOG|LOG file of cheletropic pathway IRC ]]

Alternative Pathway

[[Media:Em2815_e3_ENDO_RING_TS_PM6.LOG‎|LOG file of endo transition state (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_ENDO_RING_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of endo product minimum(reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_EXO_RING_TS_PM6.LOG‎|LOG file of exo transition state (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815_e3_EXO_RING_PRODUCT_MINIMUM_PM6.LOG‎|LOG file of exo product minimum (reacting in the xylylene ring) PM6 ]]

[[Media:Em2815 e3 ENDO RING IRC PM6.LOG|LOG file of endo pathway (reacting in the xylylene ring) IRC]]

[[Media:Em2815 e3 EXO RING IRC PM6.LOG|LOG file of exo pathway (reacting in the xylylene ring) IRC]]

=Conclusion=

This investigation used the PM6 and B3LYP/6-31G(d) computational methods to locate the transition states of various cycloaddition reactions. Method 3 proved to be the most efficient and reliable method which lead to successful calculations. It was found that the type of reactants affected the type of reaction occurring; from part 1 to part 2, the addition of the heteroatoms in the alkene resulted in an inverse electron demand reaction, affecting the ordering of the orbitals involved in the reaction.

For part 2, the competition of different reacting pathways was investigated. The exo and endo pathways of the Diels Alder reaction of cyclohexadiene with 1,3-dioxole were observed and it was found that the endo pathway has a lower activation barrier than the exo pathway therefore the endo product is kinetically favoured. This product was also found to be more stable than the exo product, hence it is thermodynamically favoured too. It has been suggested that the kinetic and thermodynamic favouring of the endo product is due to the reduced steric clash and the secondary orbital overlap between the pi orbitals of the oxygen atoms and the pi system of the diene, which is only possible in the endo configuration.

In part 3, the competition of three different reacting pathways was investigated. SO<sub>2</sub> can react with o-xylylene in a Diels Alder fashion, with one S atom and one O atom as part of a 6 membered ring, or in a cheletropic fashion, with just the S atom as part of a 5 membered ring. It was found that the endo product is kinetically favoured for this reaction since it has the smallest activation energy, however the thermodynamically favoured product is the cheletropic molecule. Although the cheletropic transiton state is disfavoured in terms of kinetics (due to the strained 5 membered ring), it is the most thermodynamically stable due to its strong and unreactive S=O bonds.

=References=

<references>
<ref name="one">
P. Atkin, J. Paula, ''Physical chemistry'', 8th edn, 2006.
</ref>

<ref name="two">
X. Qu, D. Latino and J. Aires-De-sousa, ''J. Cheminform''., 2013, '''5''', 1.
</ref>

<ref name="three">
E. Lewars, ''Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics'', 1st edn, 2011.
</ref>

<ref name="four">
F. Jensen, ''Wiley Interdiscip. Rev. Comput. Mol. Sci.'', 2013, '''3''', 273–295.
</ref>

<ref name="five">
R. Hoffmann and R. B. Woodward, ''Acc. Chem. Res.'', 1968, '''1''', 17–22.
</ref>

<ref name="six">
D. Boger, ''Progress in Heterocyclic Chemistry'', 1st edn, 1989.
</ref>

<ref name="seven">
H. J. Bernstein, ''Trans. Faraday Soc.'', 1961, '''57''', 1649–1656.
</ref>

Rep:Mod:smw415TS

2018-03-16T15:48:05Z

Tam10: /* Diels Alder vs Cheletropic reactions */

== '''Transition States via Computational Methods''' ==

== Introduction ==

This study was carried out to analyse Molecular orbitals, reaction kinetics and thermodynamics of different pericyclic reactions

A potential energy surface is plot or a mathematical function that represents the potential energy of a chemical system as a function of multiple reaction coordinates. The number of dimensions of such surface is given by 3N-6 where N is the number of atoms considered in the molecular system. The first derivative relates to the force acting on atoms whereas the second derivative which determines the curvature relates to the force constant, k. The value of k obtained can be used to calculate the vibrational frequency of each 3N-6 mode.

A minimum point, with a positive second derivative, along the reaction coordinate represents a stable species which could be either a reactant, product or an intermediate of the reaction. A transition state (TS) is related to a maximum point (negative second derivative) along a reaction coordinate. A TS is a first order saddle point on a potential energy surface and always has one dimension of the negative curvature. This could be obtained by diagonalising the force constant and by evaluating the Eigen values.

In this exercise, two different optimisation methods were used; the semi-empirical route with PM6 and the density functional theory (DFT), B3LYP. These methods are based on the Hartree-Fock model which calculates electron-electron interactions by the assumption that any electron in the chemical system experiences an average field from other electrons. The PM6 method is faster as it uses pre-calculated empirical data to determine the electron density. The B3LYP uses the basis set 6-31(G) which includes the atomic orbitals that make up the molecular orbitals using the theory of Linear Combination of Atomic Orbitals (LCAO). These methods can solve the time-independant Schrödinger equation along the reaction coordinate in order to calculate the energy of the system at each point as well as the first and second derivatives of the energy. These produces optimised geometries which is either a stable species in the reacion (a minimum point with a positive second derivative) or a transition state.

The Gaussian software was used to find the TS of the reaction given below and three different methods were used. The guess TS of could be optimised directly however previous knowledge of the TS was required and this method is the most unreliable even though it is the fastest. Another method employed involved generating the guess TS and then freezing the reacting atoms which also required previous knowledge of the TS however it was more reliable and at the same time it was considered a relatively faster method. The final method started from either the reactants and product, then altering bond lengths and again freezing atoms. This was considered the most reliable method and it did not require any knowledge of the TS but the disadvantages were that it required additional steps and if the minimum point does not resemble the TS geometry, the method would not work.

== [4+2] Cycloaddition of ethene and butadiene ==

For this Diels Alder reaction (Figure 1), the reactants were separately optimised to a minimum, the structures placed in correct geometry and the distance between reacting atoms were frozen at 2.2 Â. This structure was optimised to a minimum and then to the TS. The product was separately optimised at PM6 level.

[[File:Reaction_Scheme.cdx|thumb|center|Figure 1: Reaction Scheme|600px]]

=== MO Diagram of the Transition State ===

[[File:MOD.jpg|thumb|center|Figure 2: Molecular Orbital Diagram of Transition State|1200px]]

The MO diagram illustrates how the MOs of the reactants, ethylene and butadiene, combine at the transition state. The IRC calculation for the optimised TS and the log file initial frame corresponding to the reactants, was run to make the relative energies of reactants and the optimised TS comparable.
As shown in the MO diagram, the MOs of TS is quite high in energy compared to the reactant species since the TS represents the highest energy point in the reaction coordinate. Therefore the theoretical activated species should be destabilised compared to the reactants.

=== HOMO and LUMO of reactants and optmised TS ===

The following table shows the HOMO and LUMO of ethylene and butadiene (optimised to a minimum with PM6) as well as the four MOs of the transition state resulting from the linear combination of frontier MOs of the reactants. The HOMO-1 (MO16) and LUMO+1 (MO19) result from the constructive (in-phase) and destructive (out-of-phase) interference respectively, between the HOMO of butadiene and the LUMO of ethylene. The HOMO (MO17) and LUMO (MO18) results from the constructive and destructive interference respectively, between HOMO of ethylene and LUMO of butadiene.
The resulting MOs of the optimised TS agrees with the MO diagram drawn above and as well as the principle of conservation of orbital symmetry. The presence of MOs resulting from symmetric-symmetric or asymmetric-asymmetric interactions and the absence of symmetric-asymmetric interactions could be explained using the overlap integral. The overlap between orbitals of different symmetry results in an equal amounts of in-phase and out-of-phase interactions, producing an overall overlap integral of zero. The overlap of orbitals of same symmetry results in either a net in-phase (Positive) or out-of-phase (negative) overlap, therefore the overlap integral is not zero. The HOMO (butadiene) and LUMO (ethylene) are asymmetric, therefore they linearly combine to produce MO16 and MO19 whereas both LUMO (Butadiene) and HOMO (ethylene) are symmetric and combine to produce MO17 and MO18 of the optimised TS.

{| class="wikitable" border="1"
|+ MOs of Optimised reactants, TS and Product
! Name !! MO Image
|-
| HOMO (Ethylene) || [[File:EthyleneHOMO.jpg|150px]]
|-
| LUMO (Ethylene) || [[File:EthyleneLUMO.jpg|150px]]
|-
| HOMO (Butadiene) || [[File:ButadieneHOMO.jpg|150px]]
|-
| LUMO (Butadiene) || [[File:ButadieneLUMO.jpg|150px]]
|-
| HOMO (TS) || [[File:HOMO.jpg|150px]]
|-
| HOMO-1 (TS) || [[File:HOMO-1.jpg|150px]]
|-
| LUMO (TS) || [[File:LUMO.jpg|150px]]
|-
| LUMO+1 (TS) || [[File:LUMO+1.jpg|150px]]
|}

=== C-C Bond Lengths of optimised reactants, TS and product ===

The following table shows the bond lengths calculated for the above mentioned species.

{| class="wikitable" border="1"
|+ C-C Bond lengths/ Å
! Optimised Structure !! C=C (Ethylene) !! C=C (Terminal Butadiene) !! C=C (Butadiene centre) !! C-C (Newly Formed)
|-
| Reactants || 1.33 || 1.34 || 1.47 || -
|-
| TS || 1.39 || 1.38 || 1.41 || -
|-
| Product || 1.53 || 1.50 || 1.34 || 1.54
|}

In Diels Alder reactions, the hybridisation of the reacting species changes. The typical C-C bond lengths of different levels of carbon hybridisation are given below,

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

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

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

C atom (Van der Waal radius) = 1.70 Å

The C-C bond lengths of the optimised produce and reactants agrees with the values given above. The carbons of ethylene (dienophile) undergoes a change in hybridisation from sp<sup>3</sup> to sp<sup>2</sup> which can be confirmed by the length of the same bond being 1.38 Å at the optimised TS which is between 1.54 (sp<sup>3</sup>-(sp<sup>3</sup>) and 1.34 (sp<sup>2</sup>-(sp<sup>2</sup>). The same explanation could be used to describe the changes in the bond length of terminal C-C bonds of butadiene. The distance between interacting atoms in the TS is lower than 1.70 Å (C-Van der Waal radius) which confirms the interaction between the reacting atoms at the TS. The central C-C bond of butadiene changes from sp<sup>3</sup> to sp<sup>2</sup> in cyclohexene. This is confirmed by the intermediate bond length of 1.41 Å in the TS. All the bond lengths in the TS consists of values which are in between the values of the corresponding bond lengths of reactants and product.

=== Vibration at the reaction path of Transition State ===

[[File:TS Animation165465.gif|thumb|centre|Figure 4: Transition State Vibration|450px]]

The above vibration relates to a negative frequency value of -949.30 cm<sup>-1</sup>. The frequency is negative because the force constant is negative at the TS as the energy is maximum, which produces a negative value for the second derivative which is related to the force constant. The above animation both bonds form at the same time which means this reaction is synchronous and thereby it is concerted.

=== LOG files ===

[[Media:BUTADIENEOPT.log| Optimised Butadiene]]

[[Media:OPTIMISED ETHYLENE.txt| Optimised ethylene]]

[[Media:Optimised TS.log| Optimised TS]]

[[Media:PRODUCT OPT1.LOG| Optimised Cyclohexene]]

== [4+2] Cycloaddition of 1,3-Dioxole and Cyclohexadiene ==

[[File:ReactionbloodyScheme.jpg|thumb|centre|Figure 5: Reaction Scheme|600px]]

The endo and exo reaction pathways of this Diels Alder reaction was investigated. The product structures were built and optimised to a minimum. The two C-C bonds which formed during reaction were broken and frozen at 2.2 Å to produce guess endo and exo TS structures. These were then minimised and then optimised at B3LYP to produce the final optimised TS structures. Then IRC calculations were performed at PM6 level.

=== Molecular Orbital Diagrams for Endo and Exo TS ===

[[File:Endo TS MO Diagram.jpg|thumb|left|Figure 6: Molecular Orbital Diagram of Endo Transition State|600px]]
[[File:Exo TS MO Diagram.jpg|thumb|right|Figure 7: Molecular Orbital Diagram of Exo Transition State|600px]]

The MO diagrams are broadly similar to the MO diagram in the previous exercise where the TS MOs are higher in energy compared to reactants.In a normal electron demand process the diene HOMO is higher in energy than the dienophile HOMO, and the diene HOMO-dienophile LUMO energy gap is smaller compared to the converse dienophile HOMO-diene LUMO energy gap. However, in this reaction the HOMO of the 1,3-dioxole (dienophile) is higher in energy than the cyclohexa-1,3-diene (diene) HOMO, and this means that the reaction is an inverse electron demand Diels-Alder. This is because the dienophile is relatively electron rich as the lone pairs of electrons on oxygen can donate electron density to the C=C π-bond, thereby raising the energy of MOs above the diene. This reaction obeys the principle of conservation of orbital symmetry as well.

It is observed that the energy levels of endo and exo TS are different. The HOMO (MO41) is lower in energy in the endo TS compared to the exo TS. This is due to the secondary orbital interactions between oxygen p-orbitals and the MOs of the diene component(see below). This in turn lowers the energy of TS and the activation energy barrier of the reaction.

{| class="wikitable" border="1"
|+ Reactants
! MO !! 1,3-Dioxole !! Cyclohexadiene
|-
| HOMO || [[File:Dioxole HOMO.jpg|150px]] || [[File:Cyclohexadiene HOMO123456.jpg|150px]]
|-
| LUMO || [[File:Dioxole LUMO.jpg|150px]] || [[File:Cyclohexadiene LUMO123456789.jpg|150px]]
|}

{| class="wikitable" border="1"
|+ Transition State MOs
! TS !! HOMO-1 !! HOMO !! LUMO !! LUMO+1
|-
| Endo || [[File:Endo TS HOMO-1 bkjdshfkjsdh.jpg|150px]] || [[File:Endo TS HOMO bkjdshfkjsdh.jpg|150px]] || [[File:Endo TS LUMO bkjdshfkjsdh.jpg|150px]] || [[File:Endo TS LUMO+1 bkjdshfkjsdh.jpg|150px]]
|-
| Exo || [[File:Exo TS HOMO-1 gfjhsgfksk.jpg|150px]] || [[File:Exo TS HOMO gfjhsgfksk.jpg|150px]] || [[File:Exo TS LUMO djhfkjsahdgfkdjs.jpg|150px]] || [[File:Exo TS LUMO+1 djhfkjsahdgfkdjs.jpg|150px]]
|}

=== Thermochemistry ===

{| class="wikitable" border="1"
|+ Electronic + Thermal Free energies
! Molecule !! Sum of electronic and thermal Free energies/ (Hartee/particle)
|-
| 1,3-Dioxole || -267.074708
|-
| Cyclohexadiene || -233.336102
|-
| Endo-TS || -500.350529
|-
| Exo-TS || -500.347583
|-
| Endo-Product || -500.436132
|-
| Exo-Product || -500.434786
|}

{| class="wikitable" border="1"
|+ Reaction Barrier and Energies
! Reaction Pathway !! Reaction Barrier/(kJ/mol) !! Reaction Energy/(kJ/mol)
|-
| Exo || 166.002501 || -62.9489928
|-
| Endo || 158.267778 || -66.48291606
|}

The thermochemistry section from the log output file contained values of the sum of electronic and thermal free energies which were used to calculate the reaction barriers and reaction energies. The values of the reaction barrier for the endo-pathway is lower than for the exo-pathway. This is due to the lower energy endo-TS which consists of stabilising secondary orbital interactions which do not exist in the exo-TS. The endo-product is comparatively lower in energy, thermodynamic product, which is shown by the more negative reaction energy. This could be explained by the presence of extra steric hindrance in the exo-product (see figure X below) and this raises the energy of the exo-product and lowers the reaction energy. Therefore it can be concluded that the endo reaction pathway provides both the kinetic and thermodynamic product. The steric repulsion between substituents in exo-pathway could increase the energy of the exo-TS as well which subsequently raises the reaction barrier energy.

[[File:Endo Product145414541.jpg|thumb|left|Figure 8: Endo Product which forms stabilising secondary orbital interactions|450px]]
[[File:Exo Product778778.jpg|thumb|left|Figure 9: Exo Product with steric repulsion|450px]]

=== LOG Files ===

[[Media:ENDO PRODUCT OPTfhgdhdhd.LOG| Optimised Endo-Product]]

[[Media:EXO PRODUCT OPThdhdfhdhds.LOG| Optimised Exo-Product]]

[[Media:DIOXOLE OPT1fdgdsgdf.LOG| Optimised 1,3-Dioxole]]

[[Media:CYCLOHEXADIENE OPTfgsaaaasgf.LOG| Optimised Cyclohexadiene]]

[[Media:ENDO TS OPT B3LYP.LOG| Optimised Endo-TS]]

[[Media:EXO TS OPT B3LYP.LOG| Optimised Exo-TS]]

== Diels Alder vs Cheletropic reactions ==

[[File:Reaction Scheme123456789.jpg|thumb|centre|Figure 10: Reaction Scheme|450px]]

In this exercise, the possible TS produced from different reaction pathways were optimised at PM6 level. The products from each reaction were minimised and the bonds at reacting atoms were broken and frozen. Then the structures were optimised to produce an accurate TS. The LOG output files from the final optimised TS were used for the IRC calculations and to determine the free energy values for the reactants, product and TS to subsequently calculate the reaction barriers and energies for each possible pathway.

=== Thermochemistry ===

[[File:Energy Profile of different pathways.jpg|thumb|center|Figure 11: Energy Profile|900px]]

Again, the above reaction profile illustrates that the endo-product is the kinetic product due to the lowest reaction barrier. The stabilising secondary orbital interactions in the endo-TS, as seen in the previous exercise, results in a lower activation energy for the reaction. The endo-pathway has a higher reaction energy than the exo-pathway which concludes that the endo-product is more thermodynamically favoured. The cheletropic reaction pathway consists of both the largest reaction barrier and the reaction energy which means that this is the least kinetically favoured and the most thermodynamically favoured pathway. The cheletropic-product does not form from the breaking of a relatively strong S=O bonds compared to exo/endo products. The presence of two strong S=O bonds in the final product raises the reaction energy of the cheletropic-pathway. This reaction also involves the initial formation of a five-membered ring which raises the ring strain in the system compared to the chair like six-membered ring in Diels Alder chemistry. This results in an increase in reaction barrier energy and the energy of the cheletropic-TS, making it the least kinetically favourable pathway.

(You should show evidence for effects such as secondary orbital overlap [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:48, 16 March 2018 (UTC))

{| class="wikitable" border="1"
|+ Electronic + Thermal Free energies
! Molecule !! Sum of electronic and thermal Free energies/ (Hartee/particle)
|-
| Sulfur dioxide || -0.118614
|-
| o-xylylene || 0.178073
|-
| Endo-TS || 0.090562
|-
| Exo-TS || 0.092078
|-
| Cheletropic-TS || 0.098102
|-
| Endo-Product || 0.021698
|-
| Exo-Product || 0.021454
|-
| Cheletropic-Product || 0.000005
|}

{| class="wikitable" border="1"
|+ Reaction Barrier and Energies
! Reaction Pathway !! Reaction Barrier/(kJ/mol) !! Reaction Energy/(kJ/mol)
|-
| Exo || 85.641191 || -99.7821351
|-
| Endo || 81.6609327 || -99.14151305
|-
| Cheletropic || 101.457204 || -156.0964889
|}

The aromatisation of the xylylene to benzene is a major thermodynamic driving force of the reaction. This occurs in both Diels Alder chemistry and cheletropic reactions. The following animations illustrates that ortho-xylylene is highly unstable and readily converted to the aromatic product.

[[File:Endo IRC.gif|thumb|center|Figure 12: Endo-Reaction Pathway|550px]]

(It's pretty hard to tell that this is endo from this angle [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:48, 16 March 2018 (UTC))

[[File:Exo IRCsfrqewtrwe.gif|thumb|center|Figure 13: Exo-Reaction Pathway|550px]]

[[File:Cheletropic IRC.gif|thumb|center|Figure 14: Cheletropic-Reaction Pathway|550px]]

=== Reaction with alternate Butadiene component on xylylene ===

[[File:ReactionScheme15151515.jpg|thumb|centre|Figure 15: Reaction Scheme|450px]]

There is a second cis-diene unit found on xylylene which could possible undergo an alternative Diels Alder reaction with sulfur dioxide to produce exo/endo products as shown above. The same procedure was used to produce the optimised TS and the energy analysis is summarised in the tables given below.

{| class="wikitable" border="1"
|+ Electronic + Thermal Free energies
! Molecule !! Sum of electronic and thermal Free energies/ (Hartee/particle)
|-
| Sulfur dioxide || -0.118614
|-
| o-xylylene || 0.178073
|-
| Endo-TS || 0.095656
|-
| Exo-TS || 0.093577
|-
| Endo-Product || 0.065609
|-
| Exo-Product || 0.067306
|}

{| class="wikitable" border="1"
|+ Reaction Barrier and Energies
! Reaction Pathway !! Reaction Barrier/(kJ/mol) !! Reaction Energy/(kJ/mol)
|-
| Exo || 89.5768158 || 20.6023001
|-
| Endo || 95.0352307 || 16.146826
|}

Using the data obtained, it can be concluded that this alternate Diels-Alder pathway is both kinetically and thermodynamically unfavourable. This has a larger reaction barrier for both endo/exo TS due to the high approach trajectory for sulfur dioxide towards the sterically hindered cis-diene component within the xylylene ring compared to the exocyclic reaction pathway. The reaction energies for this pathway are both positive as it does not involve the aromatisation of the xylylene ring, raising the energy of the final product.

=== LOG Files ===

[[Media:CHELETROPIC PRODUCT MIN PM6.LOG| Optimised Cheletropic-Product]]

[[Media:ENDO Product OPT PM6.LOG| Optimised Endo-Product]]

[[Media:EXO PRODUCT OPT PM6.LOG| Optimised Exo-Product]]

[[Media:CHELETROPIC TS MIN PM6.LOG| Optimised Cheletropic-TS]]

[[Media:ENDO TS OPT PM6 1.LOG| Optimised Endo-TS]]

[[Media:EXO TS PM6 OPT 2.LOG| Optimised Exo-TS]]

[[Media:SO2 OPT PM6.LOG| Sulfur dioxide]]

[[Media:XYLYLENE OPT PM6.LOG| o-xylylene]]

[[Media:ENDO PRODUCT MIN.LOG| Alternative Endo-Product]]

[[Media:EXO PRODUCT MIN.LOG| Alternative Exo-Product]]

[[Media:ENDO TS OPT PM6 1.LOG| Alternative Endo-TS]]

[[Media:EXO TS PM6 OPT 3454.LOG| Alternative Exo-TS]]

== Conclusion ==

This study involved the use of Gaussian Software to locate the TS of three different pericyclic reactions. This information was in turn used to calculate reaction energies and reaction barrier energies.

The first reaction was a [4+2] cycloaddition between betadiene and ethene and the MOs that were involved in the reaction between the two species were investigated along with the TS. The second reaction was another [4+2] cycloaddition between 1,3-dioxole and cyclohexadiene which consisted of an inverse electron demand compared to general Diels-Alder reactions. The two different reaction pathways, exo and endo were studied and the location of the TS and the final products indicated that the endo-pathway produced both the kinetic and thermodynamic product. The final study involved the comparison between the cheletropic and Diels-Alder reaction pathways for the same reactants, Sulfur dioxide and ortho-xylylene. It was concluded that the Diels-Alder reactions for both endo and exo pathways produced the kinetic product via the lower energy TS whereas the cheletropic reaction generated the thermodynamic product with the lowest energy final product.

The experiment could be improved with the use of B3LYP method for all three reactions with better accuracy.

Rep:Mod:hnt14Y3

2018-03-16T15:46:16Z

Tam10: /* Future Work */

== Introduction ==

In this project, a series of pericyclic reactions were explored. Diels-Alder cycloaddition, chelotropic and electrocyclic reactions were all studied. A Diels-Alder cycloaddition between a diene and a dienophile can be normal or inverse demand. A normal demand reaction occurs when the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of a transition state or product are formed from the diene HOMO and the dienophile LUMO. Inverse demand occurs as a result of interaction between the diene LUMO and dienophile HOMO. Both inverse and normal demand Diels-Alder cycloaddition were under investigation.

The reactants, products and transition states were built in GaussView and optimised using the semi-empirical PM6 method and Density Functional Theory (DFT) B3LYP method. This allowed the MOs (molecular orbitals) of each to be visualised and their relative energy levels to be determined. The MOs are built by linearly combining basis sets. Hence, this is a quantum mechanical approach to generating MOs. The PM6 optimisation is faster and thus offers an initial optimisation which can be more accurately optimised using the more complex B3LYP where necessary.

A potential energy surface (PES) shows how the potential energy of a system changes along numerous reaction coordinates. Along a particular coordinate, the transition state is a maximum, where the gradient is zero. Transition states occur at maxima because they are high in energy and unstable. However, the transition state is also a minimum in all other directions, thus making it a saddle point. The reactants and products along a reaction coordinate will be minima, also with a zero gradient. As the first derivative is zero in both cases, a second derivative (the curvature) is determined to distinguish between maxima and minima. The second derivative will have a negative value for a maximum and a positive value for a minimum. Thus, when trying to locate a transition state in GaussView by running a frequency calculation, a single negative frequency value will be an indication that a transition state has been found.

== Question 1ː Reaction of Butadiene with Ethylene ==

[[File:SchemeImage.PNG|400px|thumb|right|none|Figure 1-Reaction Scheme for [4+2] cycloaddition between butadiene and ethylene]]
[[File:MODiagramImageUPDATED.PNG|400px|thumb|right|none|Figure 2-MO diagram for the transition state of the [4+2] cycloaddition between butadiene and ethylene]]

Figure 1 shows the reaction scheme for the cycloaddition between butadiene and ethylene. In Figure 2, an MO diagram is constructed based on the interacting orbitals in the transition state of the Diels-Alder cycloaddition. These were determined by observing the relevant orbitals of the transition state formed from the HOMO and LUMO of each of the reactants in GaussView. The orbitals drawn in the MO diagram in Figure 2 correlate with those extracted from GaussView, which are shown in Table 1. It can be concluded from the resulting MOs in the transition state that only orbitals of the same symmetry are allowed to interact. Thus, there is a symmetry requirement for two interacting orbitals. In the case of orbitals with different symmetry, the interaction is forbidden and the orbital overlap integral will be zero. For orbitals of the same symmetry, the interaction is allowed and the overlap integral is non-zero. The results are summarised in Table 2.

{| class="wikitable" border="1"
|+ Table 1- Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <jmol>
<jmolApplet>
<title>Ethylene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_OPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Ethylene LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_OPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 36; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_BUTADIENEOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 36; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14_BUTADIENEOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" border="1"
|+ Table 2-Allowed and Forbidden Interactions
! !! Allowed !! Forbidden !! Orbital Overlap Integral
|-
| Symmetric-Symmetric || X || || Non-zero
|-
| Asymmetric-Asymmetric || X || || Non-zero
|-
| Symmetric-Asymmetric || || X || Zero
|}

In the reaction, the distances between atoms vary depending on whether a bond is being made or broken. Where a bond is being broken, its length will increase in the transition state until the bond eventually breaks. In the case of a bond being made, the distance between the atoms decreases as the bond forms. Where a bond is going from a single bond to a double bond, the bond length shortens and vice versa. The typical bond length for a single sp<sup>3</sup>-sp<sup>3</sup> C-C bond is 1.54 Å <ref name="Bond lengths"/> and 1.34 Å <ref name="Bond lengths"/> for a double sp<sup>3</sup>-sp<sup>2</sup> bond. In the transition state, the two bonds being formed are between C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub>. Both have a length of 2.11 Å between the carbon atoms in the transition state. This is considerably less than twice the Van der Waals radius of the carbon atom which is 3.4 Å. Hence, it can be concluded that there is an interaction between C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub> in the transition state. In the product, bonds are formed at these sites that have a length of 1.54 Å, as expected for carbon-carbon single bonds.
The overall change in bond lengths can be seen in Table 3.

{| class="wikitable" border="1"
|+ Table 3-Bond lengths (Å) in reactants, transition states and products
! !! Butadiene !! Ethylene !! Transition State !! Product !! Change in bond
|-
| C<sub>1</sub>-C<sub>2</sub> || 1.3335 || - || 1.3798 || 1.4926 || Longer
|-
| C<sub>2</sub>-C<sub>3</sub> || 1.4708 || - || 1.4111 || 1.3331 || Shorter
|-
| C<sub>3</sub>-C<sub>4</sub> || 1.3334 || - || 1.3798 || 1.4926 || Longer
|-
| C<sub>4</sub>-C<sub>5</sub> || - || - || 2.1146 || 1.5358 || -
|-
| C<sub>5</sub>-C<sub>6</sub> || - || 1.3273 || 1.3818 || 1.5376 || Longer
|-
| C<sub>1</sub>-C<sub>6</sub> || - || - || 2.1149 || 1.5358 || -
|}

The vibration shown below corresponds to the vibration along the reaction path that occurs at the transition state of the reaction. As the two new bonds at C<sub>4</sub>-C<sub>5</sub> and C<sub>1</sub>-C<sub>6</sub> form at the same time, the reaction is concerted and the formation of the two bonds is synchronous.

<jmol>
<jmolApplet>
<title> Figure 3-Vibration Mode at the Transition State</title>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 1;rotate x -20; </script>
<uploadedFileContents>HNT14_TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Files for the optimised reactants at PM6 levelː [[Media:HNT14_OPTMINPM6.LOG|Ethylene Optimisation]], [[Media:HNT14_BUTADIENEOPTMINPM6.LOG|Butadiene Optimisation]]

Files for the optimised transition state and the IRC at PM6 level: [[Media:HNT14_TSPM6.LOG|TS Optimisation]],[[Media:HNT14 IRC.LOG|IRC]]

File for the optimised product at PM6 levelː [[Media:HNT14 PRODUCTOPTPM6.LOG|Product Optimisation]]

== Question 2ː Reaction of Cyclohexadiene and 1,3-Dioxole ==

[[File:ReactionSchemeImage2.PNG|400px|thumb|right|none|Figure 4-Reaction Scheme for [4+2] cycloaddition between cyclohexadiene and 1,3-dioxole]]

[[File:MODIAGRAMENDOEXO.PNG|400px|thumb|right|none|Figure 5-Exo and Endo MO Diagrams for [4+2] cycloaddition between cyclohexadiene and 1,3-dioxole Transition States]]

The MO's of both the exo and endo transition states can be seen in Figure 5. The relative energy levels were determined using the B3LYP optimisations of the reactants and transition states in GaussView. The orbitals in Table 4 correlate with the energy levels and MOs in figure 5.

This reaction is an inverse demand Diels-Alder reaction because the HOMOs and LUMOs of both the exo and endo transition states occur as a result of the interaction between the diene (cyclohexadiene) LUMO and the dienophile (1,3-dioxole) HOMO.

{| class="wikitable" border="1"
|+ Table 4-Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>Exo TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Exo TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Exo TS LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> ||<jmol>
<jmolApplet>
<title>Exo TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 EXOTSB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>Endo TS HOMO -1</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Endo TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <jmol>
<jmolApplet>
<title>Endo TS LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>Endo TS LUMO +1</title>
<color>white</color>
<size>160</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 ENDOTSB3LYPH.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Cyclohexadiene HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 CYCLOHEXADIENEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>Cyclohexadiene LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 CYCLOHEXADIENEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>1,3-Dioxole HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 OPTMINDIOXOLEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|| <jmol>
<jmolApplet>
<title>1,3-Dioxole LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 OPTMINDIOXOLEB3LYP.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" border="1"
|+ Table 5- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 166.30 || -65.15
|-
| Endo || 158.51 || -68.75
|}

The endo adduct has a lower reaction barrier (due to the endo ts being of lower energy) than the exo adduct, indicating the endo product will be the kinetically favourable product (faster formation). Furthermore, the endo adduct also has a lower reaction energy than the exo adduct, meaning the endo product is also the thermodynamically favourable product. The energies can be seen in Table 5.

The lower energy of the endo ts is due to the secondary orbital interactions arising from orbital overlap between the O p orbital and the diene pi system. TS Stabilisation is hence a result of conjugation. This can only be achieved in the endo conformation, where the orbitals are in the correct orientation for overlap, as opposed to the orbitals in the exo adduct. This is in accordance with the endo rule.

The energies in Table 5 were calculated using the free energies of the reactants, products and transition states of the endo and exo adducts, which can be found in the log files below extracted from GaussView.

Files for the optimised reactants at B3LYP levelː [[Media:HNT14 CYCLOHEXADIENEB3LYP.LOG |Cyclohexadiene Optimisation]], [[Media:HNT14 OPTMINDIOXOLEB3LYP.LOG |1,3-Dioxole Optimisation]]

Files for the optimised transition states at B3LYP levelː[[Media:HNT14 EXOTSB3LYP.LOG |Exo TS Optimisation]], [[Media:HNT14 ENDOTSB3LYPH.LOG |Endo TS Optimisation]]

Files for the IRCs of the optimised transition states at PM6 levelː [[Media:HNT14 IRCEXOTSPM6I.LOG |Exo IRC]], [[Media:HNT14 IRCENDOTSPM6I.LOG |Endo IRC]]

Files for the optimised products at B3LYP levelː [[Media:HNT14 PRODUCTEXOB3LYPXXY.LOG |Exo Product Optimisation]], [[Media:HNT14 PRODUCTENDOB3LYPXX.LOG |Endo Product Optimisation]]

== Question 3ː Diels-Alder vs Chelotropic ==

[[File:Q3imagereactionscheme4.PNG|400px|thumb|right|none|Figure 6-Reaction Scheme for Diels-Alder and chelotropic pathways for the reaction between Xylylene and SO<sub>2</sub>]]

The reaction scheme in Figure 6 shows both the Diels-Alder and chelotropic reaction pathways at one of the dienes in xylylene. The Diels-Alder reaction can result in both an endo and exo product.

[[File:Hnt14 ALTexoGIFXXX.gif|400px|thumb|none|Figure 7-Exo adduct IRC]]

[[File:Hnt14 altendoXXYGIF.gif|400px|thumb|none|Figure 8-Endo adduct IRC]]

[[File:Hnt14 chelotropicGIFXXX.gif|400px|thumb|none|Figure 9-Chelotropic adduct IRC]]

The IRCs of the exo, endo and chelotropic reactions can be seen in Figures 7, 8 and 9 respectively. These allow the reaction coordinates to be visualised. Xylylene is highly unstable because the ring prefers to be aromatic to lower the molecule's energy. Formation of the products would result in the formation of a benzenoid ring. This 'aromatisation' makes these reactions favourable and results in overall stabilisation. This can be observed in the IRCs, where the bond lengths in the six-membered ring become equal throughout the reaction, indicating the ring is aromatic.

{| class="wikitable" border="1"
|+ Table 5- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 87.19 || -98.23
|-
| Endo || 83.22 || -97.58
|-
| Chelotropic || 105.53 || -154.56
|}

In Table 5, the reaction barriers and energies are calculated for each of endo, exo and chelotropic adducts as before. As can be seen, the exo adduct has a lower reaction energy, making the exo product the more thermodynamically favourable product (compared to the endo product). This is because steric strain is minimised in the exo conformation. On the other hand,the endo adduct affords the lowest reaction barrier due to secondary orbital interactions, making the endo product the fastest forming (kinetically favourable) product. However, the exo and endo energies are only marginally different. In contrast, The chelotropic adduct has a much higher reaction barrier, meaning its formation is considerably slower than both the exo and endo products. The exo and endo adducts form stable six-membered ring transition states (resulting in faster formation), whereas the chelotropic transition state contains a 5-membered ring, making it sterically unfavourable due to ring strain. However, the chelotropic adduct has the lowest reaction energy by far, making it the most thermodynamically favourable product. The driving force is the formation of the double S=O bond compared with the much weaker single S-O bonds. This results in increased stabilisation and thus lower energy (thermodynamically stable) products. The relative reaction profiles for each of the two Diels-Alder reactions and the chelotropic reaction can be seen in figure 10.

[[File:ReactionprofileEX3.PNG|400px|thumb|right|none|Figure 10-Reaction profiles for endo, exo and chelotropic reactions]]

Files for the optimsed reactions at PM6 levelː [[Media:HNT14 XYLYLENEOPTMINPM6.LOG |Xylylene optimisation]], [[Media:HNT14 SO2OPTMINPM6.LOG |SO<sub>2</sub> optimisation]]

File for the optimised transition states at PM6 levelː [[Media:HNT14 EXODIELSALDERT1EXOTS2PM6.LOG |Exo TS optimisation]], [[Media:HNT14 DIELSALDERENDOTSPM6FINALPM6.LOG |Endo TS optimisation]], [[Media:HNT14 chelotropicTSPM6.LOG |Chelotropic TS optimisation]]

Files for IRCs at PM6 levelː [[Media:HNT14 IRCEXODIELSALDERPM6.LOG |Exo TS IRC]], [[Media:HNT14 IRCDIELSALDERENDOPM6.LOG |Endo TS IRC]], [[Media:HNT14 IRCCHELOTROPICPM6.LOG |Chelotropic TS IRC]]

Files for the optimised products at PM6 levelː [[Media:HNT14 EXODIELSALDERPRODUCTPM6.LOG |Exo product optimisation]], [[Media:HNT14 PRODUCTENDODIELSALDEROPTMINPM6.LOG |Exo product optimisation]], [[Media:HNT14 PRODUCTCHELOTROPICOPTMINPM6.LOG |Chelotropic product optimisation]]

=== Reaction at Cyclic Diene ===

Both the Diels-Alder and chelotropic reactions can occur at the cyclic diene as well. This will also result in exo, endo and chelotropic products. The reaction barriers and energies are reported in Table 6.

{| class="wikitable" border="1"
|+ Table 6- Reaction Barriers and Energies
! Adduct !! Reaction Barrier (kJ/mol) !! Reaction Energy (kJ/mol)
|-
| Exo || 121.27 || 22.15
|-
| Endo || 113.42 || 17.70
|-
| Chelotropic || 142.14 || 48.74
|}

As can be observed, the reaction barriers for all three adducts are very high, meaning reaction at the cyclic diene is kinetically unfavourable. Furthermore, the reaction energies of all three adducts are very high, probably due to the non-aromatic product formation. Hence reaction at this diene is also thermodynamically unfavourable.

Files for the optimised transition states at PM6 levelː[[Media:HNT14 ALTEXOTSPM6.LOG |Alternative exo TS optimisation]], [[Media:HNT14 ALTENDOTSPM6.LOG |Alternative endo TS optimisation]],
[[Media:HNT14 ALTTYPE2TSPM6.LOG |Alternative chelotropic TS optimisation]]

Files for the IRCs at PM6 levelː [[Media:HNT14 IRCALTEXOTSPM6HNZT.LOG |Alternative exo IRC]], [[Media:HNT14 IRCALTENDOTSPM6.LOG |Alternative endo IRC]], [[Media:HNT14 IRCALTTYPE2TSPM6.LOG |Alternative chelotropic IRC]]

Files for the optimised products at PM6 levelː [[Media:HNT14 PRODUCTALTEXOOPTMINPM6.LOG |Alternative exo product optimisation]], [[Media:HNT14 ALTENDOPRODUCTOPTMINPM6.LOG |Alternative endo product optimisation]], [[Media:HNT14 PRODUCTALTTYPE2OPTMINPM6.LOG |Alternative chelotropic product optimisation]]

== Future Work ==

[[File:Futureworkscheme.PNG|500px|thumb|right|none|Figure 11-Reaction Scheme for electrocylic reaction]]

[[File:Disrotationhnt14.PNG|500px|thumb|right|none|Figure 12-Electrocyclic reaction by disrotation]]

The scheme shown in Figure 11 represents an electrocyclic reaction occuring by disrotation. The bond formation is suprafacial, as seen in Figure 12.
The LUMO of the reactant and the HOMO of the transition state that are visualised with Gaussview are consistent with those in figure 12, confirming that the reaction proceeds by disrotation. The visualised MOs are observed in Table 7.

{| class="wikitable" border="1"
|+ Table 7- Interacting Orbitals
|-
| <jmol>
<jmolApplet>
<title>Reactant LUMO</title>
<color>white</color>
<size>160</size>
<script>frame 20; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 FUTUREREACTANTOPTMINPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<title>TS HOMO</title>
<color>white</color>
<size>160</size>
<script>frame 94; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HNT14 FUTURETSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(This reaction is conrotation under thermal conditions, which it will be under PM6. Confirm this by visualising the IRC [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:46, 16 March 2018 (UTC))

File for optimised reactant at PM6 levelː [[Media:HNT14 FUTUREREACTANTOPTMINPM6.LOG |Reactant optimisation]]

File for optimised TS at PM6 levelː [[Media:HNT14 FUTURETSPM6.LOG |TS optimisation]]

File for IRC at PM6 levelː [[Media:HNT14 IRCFUTURETSPM6.LOG |IRC]]

File for optimised product at PM6 levelː [[Media:HNT14 FUTUREPRODUCTOPTMINPM6.LOG |Product optimisation]]

== Conclusion ==

Gaussview was used to visualise a series of pericyclic reactionsː Diels-Alder, chelotropic and electrocyclic reactions. With Gaussian, molecules and transition states for a large range of reactions can be optimised. Furthermore, MOs and reaction coordinates can be visualised and free energies extracted which can then be used for finding reaction barriers and energies. In this project, this data was extracted for well known reactions. However, the same software and methods can be used for reactions of which the outcome is less well known. This means computational methods can be used to predict the outcome and likelihood of a reaction, giving quantitative results on how a reaction may proceed. Hence, invaluable information can be extracted using these techniques, highlighting the importance of computational chemistry.

== References ==

<references>
<ref name="Bond lengths">Zavitsas, A. (2003). The Relation between Bond Lengths and Dissociation Energies of Carbon−Carbon Bonds. The Journal of Physical Chemistry A, 107(6), pp.897-898. </ref>

Rep:FD915 TRANSITION

2018-03-16T15:41:53Z

Tam10: /* Further Work */

= Transition Structure and Reactivity =

Felix de Courcy-Ireland
01062960
Transition States and Reactivity Computational Lab

==Introduction ==

Stationary points on potential energy surfaces (or ‘hypersurfaces’) are defined by a value of zero for the first derivative at that point<sup>(1)</sup>. However, it is through the use of second derivatives that the distinction can be made between the various types of stationary points, including reactants, transition states, intermediates and products<sup>(1)</sup>.

Products, reactants and intermediates are all minima on a potential energy surface. They are characterised by the fact that all paths through these points have a positive second derivative<sup>(1)</sup>.

Transition states are characterised by having a single normal coordinate for which the second derivative is negative, with all other paths through the transition state giving a positive second derivative at this point<sup>(1)</sup>. They are known as ‘saddle-points’. If a point on a potential energy surface is a maximum in more than one normal coordinate, it is diagnostic that there is a lower energy path for the reaction to proceed in the vicinity of this point<sup>(1)</sup>.

The calculations carried out were effectively an interrogation of the potential energy surface of a simple reaction. The aims of the calculations were to locate the stationary points of the potential energy surfaces. This was done through using the Gaussian software, which traced paths across the potential energy surface, iteratively calculating the second derivative of each point on the path until a point with a zero first derivative was reached.

In this laboratory, a successfully located transition state was denoted by there being a single negative frequency in the frequency calculation, which when animated, showed the desired reaction coordinate for the reaction.

In the relatively simple reactions investigated, where the reactants pass through only one transition state, it is simple to calculate important quantities such as the activation energy and the reaction energy, from knowledge of the free energies of the reactants, products and transition states.

In this laboratory, two computational methods were used; the semi-empirical PM6 method and the DFT method B3LYP/6-31(d).

The semi-empirical PM6 is a less accurate method but not as computationally expensive. Therefore, it proved useful in optimising structures, be they reactants, products or transition states, in preparation for the use of the more accurate and expensive B3LYP method.
B3LYP/6-31(d) is based in density functional theory (DFT)<sup>(1)</sup>. DFT finds approximate solutions to unsolvable many-electron wave functions by analysis of functionals of the one electron density, ρ(r), of the molecule<sup>(1)</sup>.

In some instances, use of chemical intuition in the location of transition states was most useful. There were cases where it proved fruitful to optimise a product or reactant(s) at the PM6 level, and then freeze the atoms immediately involved in the transition and further minimise the molecule around this frozen ‘transition state’ at the B3LYP level. A final calculation to find the transition state of at the B3LYP level was often more successful when using this ‘bond freezing’ technique.

==Exercise 1 ==

=== Reaction Scheme ===

[[File:Reaction_scheme.png|550px|center]]

=== Log Files ===

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Butadiene + Ethene
! colspan = "2" style="background: #0D4F8B; color: white;" | Log Files - Butadiene + Ethene
|-
| Minimisation of butadiene (PM6)
| [[Media:CIS_BUTADIENE_ATTEMPT3.LOG| Minimisation of butadiene (PM6)]]
|-
| Minimisation of ethene (PM6)
| [[Media:ETHENE_MINIMISATION_ATTEMPT1.LOG|Minimisation of ethene (PM6)]]
|-
| Minimisation of cyclohexene (PM6)
| [[Media:CYCLOHEXENE_OPTIMISATION_ATTEMPT4.LOG|Minimisation of cyclohexene (PM6)]]
|-
| Transition State (PM6)
| [[Media:BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG|Transition State (PM6)]]
|-
| IRC (PM6)
| [[Media:IRC_FROM_CYCLOHEXENE_ATTEMPT1_BOTH_WAYS.LOG|IRC (PM6)]]
|}

=== MO diagram ===

[[File:Ex1_MO_diagram.png|500px|center| MO diagram for reaction of butadiene and ethene]]

The above molecular orbital diagram shows the interaction between the HOMOs and LUMOs of the ethene and butadiene. Each MO is assigned a symmetry value (assignments were based on the phasing of orbitals) - from these assignments it can be seen that only orbitals of like symmetry interact. The orbital overlap integral is zero for the case of a symmetric-(anti-symmetric) interaction and non-zero for either a symmetric-symmetric or (anti-symmetric)-(anti-symmetric) interaction. The orbital energies are relative to one another rather than being absolute. An attempt has been made to draw the MOs of the transition state - the calculated MOs can be found in the table below.

=== Jmols of the HOMOs and LUMOS of Butadiene and Ethene ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 1 showing the HOMO and LUMO of ethene with relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Ethene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<title>Ethene HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_MINIMISATION_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.39228 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<title>Ethene LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_MINIMISATION_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.04256 E<sub>h</sub>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 2 showing the HOMO and LUMO of butadiene, with relative energies in Hartrees.
! colspan = "3" style="background: #0D4F8B; color: white;" | Butadiene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS_BUTADIENE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.35899 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS_BUTADIENE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01943 E<sub>h</sub>
|}

=== Jmols of the MOs in the Transition State ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 3 showing the four MOs produced from the interaction of the ethene and butadiene MOs with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 16
| <jmol>
<jmolApplet>
<title> MO 16 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.32754 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 17
| <jmol>
<jmolApplet>
<title> MO 17 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.32532 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 18
| <jmol>
<jmolApplet>
<title> MO 18 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.03</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01732 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 19
| <jmol>
<jmolApplet>
<title> MO 19 </title>
<color>white</color>
<size>300</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.03 </script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.03066 E<sub>h</sub>
|}

=== C-C Bond Lengths of Reactants, Transition State and Products ===

[[File:Reaction_scheme.png|550px|center]]

Reaction Scheme repeated for clarity when analysing the bond lengths below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 4 showing bond distances in the reactants.
! colspan = "2" style="background: #0D4F8B; color: white;" | Reactants
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.33344
|-
| C2-C3
| 1.47077
|-
| C3-C4
| 1.33344
|-
| C5-C6
| 1.32731
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 5 showing bond distances in the transition state
! colspan = "2" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.37978
|-
| C2-C3
| 1.41104
|-
| C3-C4
| 1.37981
|-
| C4-C5
| 2.11452
|-
| C5-C6
| 1.38177
|-
| C6-C1
| 2.11469
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 6 showing bond distances in the product
! colspan = "2" style="background: #0D4F8B; color: white;" | Cyclohexene
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.49118
|-
| C2-C3
| 1.36309
|-
| C3-C4
| 1.49118
|-
| C4-C5
| 1.58345
|-
| C5-C6
| 1.56027
|-
| C6-C1
| 1.58345
|}

==== Discussion of carbon-carbon (C-C) bond lengths ====

The C-C single bond length of typical n-hydrocarbon is 1.533 Å, and the bond length of a typical C-C double bond is 1.33 Å<sup>(2)</sup>. These lengths will be used as a point of comparison in the following discussion.

The two pairs of carbon atoms which make up the two alkene bonds in the butadiene (C1-C2 and C3-C4) lengthen from a separation of 1.33 Å to a separation of 1.49 Å. This can be rationalised by observing that these two double bonds in the butadiene reactant will be present in the cyclohexene product as single bonds in the cyclohexene ring.

The internal C-C bond in butadiene (C2-C3) shortens from a distance of 1.47 Å to a distance of 1.36 Å. Again, although this bond is shorter than a typical C-C single bond due to the conjugation of the butadiene, it shortens to a distance more typical of a C-C double bond which it adopts in the cyclohexene product.

The ethene C-C double bond lengthens from 1.327 Å to 1.560 Å. This is due to the carbons moving from the sp<sup>2</sup> hybridised environment of the ethene molecule to the sp<sup>3</sup> hybridised environment of the cyclohexene ring.

The two new C-C bonds which are formed upon the Diels-Alder [4+2] cycloaddition between the butadiene and ethene have a value of 2.115 Å in the transition state, which shortens to a value of 1.583 Å in the cyclohexene product. This change in bond distance shows a shortening of bond lengths from an effectively infinite value in the reactants, through to a bond distance of 1.583 Å in the cyclohexene product.

Van der Waals radius of a carbon atom is 1.7 Å <sup>(3)</sup>, and this can be used in discussion of the partially formed bond between the ethene and butadiene in the transition state.

The length of the partly formed C-C bonds between butadiene and ethene is 2.115 Å. This is less than two times the van der Waals radius of carbon. Therefore, although there is not formally a bond formed between the atoms, the atoms are close enough to interact through van der Waals forces.

==== Vibration corresponding to the transition state ====

<jmol>
<jmolApplet>
<title> Reaction Path Vibration </title>
<color>white</color>
<size>500</size>
<script>frame 15; vibration 2;rotate x -20;</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Jmol above shows the vibration that corresponds to the reaction path at the transition state. It shows that the formation of the two bonds is synchronous - both bonds form simultaneously<sup>(4)</sup>.

==Exercise 2 ==

=== Reaction Scheme ===

[[File:Ex2_reaction_scheme.png|500px|center]]

=== Log files ===

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - 1,3-Dioxole + Cyclohexadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Log Files - 1,3-Dioxole + Cyclohexadiene
|-
| Minimised Cyclohexadiene (B3LYP/6-31G(d))
| [[Media:CYCLOHEXADIENE_REPEAT_AGAIN_B3LYP_MINIMISATION.LOG|Minimised Cyclohexadiene (B3LYP/6-31G(d))]]
|-
| Minimised 1,3-Dioxole (B3LYP/6-31G(d))
| [[Media:13DIOXOLE_PROPER_MINIMISATION_B3LYP_ATTEMPT3.LOG|Minimised 1,3-Dioxole (B3LYP/6-31G(d))]]
|-
| Minimised exo-product (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_MINIMISATION.LOG|Minimised exo-product (B3LYP/6-31G(d))]]
|-
| Minimised endo-product (B3LYP/6-31G(d))
| [[Media:ENDO_FULL_MOLECULE_INITIAL_MINIMISATION_B3LYP.LOG|Minimised endo-product (B3LYP/6-31G(d))]]
|-
| Minimised exo-transition state (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG|Minimised exo-transition state (B3LYP/6-31G(d))]]
|-
| Minimised endo-transition state (B3LYP/6-31G(d))
| [[Media:ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG|Minimised endo-transition state (B3LYP/6-31G(d))]]
|-
| IRC on Exo Transition State (PM6)
| [[Media:EXO_FULL_MOLECULE_IRC_ATTEMPT1.LOG|IRC on Exo Transition State (PM6)]]
|-
| IRC on Endo Transition State (PM6)
| [[Media:ENDO_MOLECULE_PM6_IRC_ATTEMPT1.LOG|IRC on Endo Transition State (PM6)]]
|-
| Single Point Energy on Exo Transition State (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_SINGLEPOINTENERGY.LOG|Single Point Energy on Exo Transition State (B3LYP/6-31G(d))]]
|-
| Single Point Energy on Endo Transition State (B3LYP/6-31G(d))
| [[Media:ENDO_MOLECULE_B3LYP_SINGLEPOINTENERGY.LOG|Single Point Energy on Endo Transition State (B3LYP/6-31G(d))]]
|}

=== Jmols and Molecular Orbital Diagram for the Endo Reaction of Cyclohexadiene and 1,3-Dioxole ===

[[File:Ex2_MO_diagram_endo.png|500px|right| MO diagram for reaction with endo arrangement between 1,3-dioxole and cyclohexadiene]]

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Table 7 showing the MOs of the endo transition state with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 40 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 40 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19648 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 41 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 41 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19052 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 42 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 42 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.00462 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 43 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 43 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01543 E<sub>h</sub>
|}

Above is the new MO diagram from the endo reaction of cyclohexadiene and 1,3-dioxole. The endo reaction involves the two oxygen atoms of the 1,3-dioxole tucking under the cyclohexadiene. This leads to a stabilising secondary orbital interaction which shall be discussed later. The MO's produced by the interaction of the cyclohexadiene and 1,3-dioxole orbitals are shown in Table 7.

=== Jmols and Molecular Orbital Diagram for the Exo Reaction of Cyclohexadiene and 1,3-Dioxole ===

[[File:Ex2_MO_diagram_exo.png|500px|right| MO diagram for reaction with exo arrangement between 1,3-dioxole and cyclohexadiene]]

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Table 8 showing the MOs of the exo transition state with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 40 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 40 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19801 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 41 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 41 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.18560 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 42 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 42 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.00699 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 43 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 43 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01019 E<sub>h</sub>
|}

Above is the MO diagram from the exo transition state, with the MOs produced from interaction of the reactant HOMOs and LUMOs shown in Table 8. It should be noted that, similarly to the previous Diels-Alder reaction of butadiene and ethene, that only orbitals of like symmetry interact to give MOs in the transition state.

=== Inverse and Normal Electron Demand Diels-Alder Reactions ===

The reaction between 1,3-dioxole and cyclohexadiene is an inverse electron demand Diels-Alder reaction. Inverse electron demand Diels-Alder reactions are characterised by there being a smaller energy gap between the HOMO of the dienophile (1,3-dioxole) and the LUMO of the diene (cyclohexadiene) than the energy gap between the HOMO of the diene and the LUMO of the dienophile<sup>(5)</sup>.

[[File:Inverse_normal_DA.png|400px|center|Figure highlighting the relative energy differences that lead to definition of normal and inverse electron demand Diels-Alder reactions.]]

=== Thermochemistry ===

If the formation of more than one product is possible from a given set of reactants, knowledge of reaction energies and activation energies can lead to assignment of the kinetic and thermodynamic products. The kinetically favourable product is that from the reaction which has the lowest energy barrier to conversion between reactants and products. The thermodynamically favourable product is the lower energy product relative to the reactant(s).

In the case that there are two possible products of a reaction, as is the situation in this Diels-Alder reaction between 1,3-dioxole and cyclohexadiene, it is not necessary for one product to be the thermodynamic product and the other product to be the kinetic product. It may be the case that one of the products is both the thermodynamic and kinetic product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Energies Endo Reaction
|-
! style="background: #0D4F8B; color: white;" | Molecule
! style="background: #0D4F8B; color: white;" | Gibbs Free Energy (kJ/mol)
|-
| 1,3dioxole
| -701,188.414
|-
| cyclohexadiene
| -612,592.877
|-
| 1,3dioxole and cyclohexadiene
| -1,313,781.291
|-
| Endo Transition State
| -1,313,621.479
|-
| Endo Product
| -1,313,848.695
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Endo Reaction Parameters
|-
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
| 159.811
|-
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
| -67.404
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Energies Exo Reaction
|-
! style="background: #0D4F8B; color: white;" | Molecule
! style="background: #0D4F8B; color: white;" | Gibbs Free Energy (kJ/mol)
|-
| 1,3dioxole
| -701,188.414
|-
| cyclohexadiene
| -612,592.877
|-
| 1,3dioxole and cyclohexadiene
| -1,313,781.291
|-
| Exo Transition State
| -1,313,613.639
|-
| Exo Product
| -1,313,845.098
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Exo Reaction Parameters
|-
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
| 167.651
|-
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
| -63.807
|}

As shown in the above tables, the reaction barrier for the exo reaction is higher at a value of 167.651 kJ/mol, due to the transition state through which the reaction proceeds being of higher energy. Therefore, due to the lower reaction barrier of 159.811 kJ/mol, the endo product is kinetic product.

The endo product proceeds through a lower energy transition state due to the secondary orbital interactions between the oxygen p orbitals and the p orbitals of the internal carbons of the cis-butadiene fragment<sup>(5)</sup>.

The Jmol of the HOMO of the endo transition state is repeated here, where it can be seen that there is a stabilising interaction between the orbitals which lie on the oxygens of 1,3-dioxole and the two carbons which eventually form the double bond in the product, for the portion of the orbital located in these areas is the same phase.

<jmol>
<jmolApplet>
<title> MO 41 - Endo Transition State </title>
<color>white</color>
<size>350</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The endo product is again the thermodynamic product, as the energy of the endo product (-67.404 kJ/mol) is lower than that of the exo product (-63.807) - although the difference in energy is less in the products than in the reactants. This reason for the greater stabilisation of the endo product is possibly due to this same orbital interaction between the p orbitals on the oxygens with the alkene pi system. The fact that the difference in energy between the products is less than the difference in energy of the transition states is a consequence of this orbital interaction being poorer in the products.

==Exercise 3 ==

[[File:Ex3_reaction_scheme.png|500px|center]]

=== Log Files ===

==== Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Dioxide + Exo-Cyclic Butadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment
|-
| Xylylene Minimisation (PM6)
|[[File:XYLYLENE_MINIMISATION_PM6.LOG| Xylylene Minimisation (PM6)]]
|-
| Sulfur Dioxide Minimisation (PM6)
| [[File:SULFUR_DIOXIDE.LOG| Sulfur Dioxide Minimisation (PM6)]]
|-
| Cheletropic Transition State (PM6)]
| [[File:CHELETROPIC_PM6_PRODUCT_TRANSITIONSTATE_NOTFROZEN.LOG| Cheletropic Transition State (PM6)]]
|-
| Cheletropic Product (PM6)]
| [[File:CHELETROPIC_PRODUCT_INITIAL_MINIMISATION_2.LOG| Cheletropic Product (PM6)]]
|-
| Endo (Xylylene-SO2) Transition State (PM6)
| [[File:DA_ENDO_PM6_TRANSITIONSTATE_ATTEMPT1.LOG| Endo (Xylylene-SO2) Transition State (PM6)]]
|-
| Endo (Xylylene-SO2) Product (PM6)]
| [[File:DA_ENDO_PM6_PRODUCT_ATTEMPT1_NOTFROZEN_MINIMISATION.LOG| Endo (Xylylene-SO2) Product (PM6)]]
|-
| Exo (Xylylene-SO2) Transition State (PM6)]
| [[File:DA_EXO_PM6_TRANSITIONSTATE_SECOND.LOG| Exo (Xylylene-SO2) Transition State (PM6)]]
|-
| Cheletropic IRC (PM6)]
| [[File:CHELETROPIC_PM6_IRC_ATTEMPT1.LOG | Cheletropic IRC (PM6)]]
|-
| Endo (Xylylene-SO2) IRC (PM6)
| [[File:DA_ENDO_PM6_IRC_ATTEMPT1.LOG| Endo (Xylylene-SO2) IRC (PM6)]]
|-
| Exo (Xylylene-SO2) IRC (PM6)]
| [[File:DA_EXO_PM6_IRC_ATTEMPT1.LOG| Exo (Xylylene-SO2) IRC (PM6)]]
|}

==== Reaction of Sulfur with Alternate, Endo-Cyclic Cis-Butadiene Fragment of Xylylene ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Dioxide + Endo-Cyclic Butadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment
|-
| Endo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]
|[[File:ENDO EXTRA NEW TRANSITIONSTATE ATTEMPT2.LOG| Endo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Endo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:ENDO_EXTRA_NEW_MINIMISATION_ATTEMPT1.LOG| Endo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Exo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:EXO_EXTRA_TRANSITIONSTATE_ATTEMPT1.LOG| Exo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Exo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:EXO_EXTRA_MINIMISATION_ATTEMPT1.LOG| Exo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Cheletropic Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:CHELETROPIC_EXTRA_TRANSITIONSTATE_NOTFROZEN_ATTEMPT2.LOG| Cheletropic Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Cheletropic Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:CHELETROPIC_PRODUC_MINIMISATION_HOPEFULLY_ATTEMPT2.LOG| Cheletropic Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|}

=== GIFs of IRC for Reaction of Sulfur Dioxide and Xylylene ===

It can be seen in all of the GIFs of the reactions below that the 6-membered ring of the highly unstable xylylene molecule becomes aromatic on reaction with sulfur dioxide.

==== GIF for Endo Reaction ====

[[File:Endo_IRC_GIF.gif]]

==== GIF for Exo Reaction ====

[[File:Exo_IRC_GIF.gif]]

This reaction goes from products to reactants.

==== GIF for Cheletropic Reaction ====

[[File:Cheletropic_IRC_GIF.gif]]

=== Thermochemistry ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "3" style="background: #0D4F8B; color: white;" | Reaction Parameters For Reaction of Sulfur Dioxide With Xylylene
|-
! style="background: #0D4F8B; color: white;" | Reaction Type
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
|-
| style="background: #0D4F8B; color: white;" | Endo
| 81.724
| -99.050
|-
| style="background: #0D4F8B; color: white;" | Exo
| 85.709
| -99.714
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| 104.049
| -156.041
|}

The data above shows that the kinetic product is the endo product, due to it having the lowest reaction barrier of 111.946 kJ/mol. This is probably a consequence of the secondary orbitals interactions that were previously discussed, between the second sulfur oxygen and the carbon p orbitals that eventually form the alkene. The cheletropic reaction has the highest reaction barrier of 140.666 kJ/mol. This is potentially due to the 5-membered transition states that forms being of higher energy than that of the 6-membered transition states that form in the endo and exo forms of the reaction.

(The barriers in this text refer to the alternate reactions [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:32, 16 March 2018 (UTC))

The thermodynamic product is also that from the endo reaction, due to it having the lowest energy (-156.041 kJ/mol). This is best explained in terms of bond enthalpies. In the endo and exo reactions, a sulfur-oxygen bond is broken and a carbon-oxygen and sulfur-carbon bond are formed, whereas in the cheletropic reaction, no bonds are broken, and two bonds are formed.

Although the cheletropic reaction proceeds through a higher energy transition states, the formation of two bonds with the loss of none leads to a lower energy product.

=== Reaction Profile for the Reaction of Sulfur Dioxide and the Exo-Cyclic Cis-Butadiene Fragment of Xylylene ===

[[File:Reaction_Profile_for_Exercise_3.png|500px|center]]

=== Further Comment ===

==== Discussion of Stability of Xylylene ====

Xylylene is an 8 electron system, and therefore anti-aromatic (Huckel's 4n rule, with n=2)<sup>(5)</sup>. These systems are often bent to avoid planarity of the p orbitals of the molecule, however xylylene is somewhat constrained to a planar configuration due to the sp<sup>2</sup>) nature of the 6 ring carbons. This makes for a very strained molecule with a high relative energy of 467.460 kJ/mol.

=== Reaction at the Endo-Cyclic, Cis-Butadiene Fragment ===

[[File:Ex3 reaction scheme extension.png|500px|center]]

Reaction scheme above shows the same reactions are possible at the endo-cyclic cis-butadiene fragment of xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "3" style="background: #0D4F8B; color: white;" | Reaction Parameters For Reaction at the Alternate Cis-Butadiene Site of Xylylene
|-
! style="background: #0D4F8B; color: white;" | Reaction Type
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
|-
| style="background: #0D4F8B; color: white;" | Endo
| 111.946
| 16.197
|-
| style="background: #0D4F8B; color: white;" | Exo
| 119.783
| 20.668
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| 140.666
| 47.238
|}

The values for activation energy (reaction barrier) and reaction energy above show these reactions are far less favoured. All the reactions are endothermic, and also have larger reactions barriers than the reactions at the original cis-butadiene fragment.

The reason for the positive values for the reaction energy is due to the fact that there is no gain of aromaticity in these reactions, like there was previously.

The reason for the higher activation barrier is potentially a consequence of the endo-cyclic cis-butadiene fragment being harder to access, therefore the molecules need to adopt higher energy conformations in the transition states to yield the products

== Further Work ==

=== Ring Opening of the Dimethyl Ester Cyclobutene ===

[[File:Cyclobutene.png|500px|center]]

==== Log Files ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Ring Opening of the Dimethyl Ester Cyclobutene
! colspan = "2" style="background: #0D4F8B; color: white;" | Ring Opening of the Dimethyl Ester Cyclobutene
|-
| Dimethyl Ester of Cyclobutene
| [[Media:CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG|Dimethyl Ester of Cyclobutene]]
|-
| Transition State
| [[Media:FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG|Transition State]]
|-
| Diene Product
| [[Media:DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG|Diene Product]]
|-
| IRC Calculation
| [[Media:BIS_CYCLOHEXENE_IRC_ATTEMPT1.LOG| IRC Calculations]]
|}

==== Jmols of MOs ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Jmols of MOs for Ring Opening of the Dimethyl Ester Cyclobutene
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
|-
| Reactant (ring closed)
| <jmol>
<jmolApplet>
<title> Reactant HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Reactant LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Transition State
| <jmol>
<jmolApplet>
<title> Transition State HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Transition State LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product (ring open)
| <jmol>
<jmolApplet>
<title> Product HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Product LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Disrotatory or Conrotatory? ====

Due to running out of time, I have not been able to put the correct MO for the transition state into the table above (I am doing something wrong, but I am sure that the marker will be able to work out what it is I have done). However, the reaction proceeds in a conrotatory fashion, as expected due to it being a 4n cyclisation under thermal conditions<sup>(5)</sup>.

(So what's happened is that you're showing the MOs of the initial geometries of the calculations eg product frame should be 64 not 2. Yes this reaction is conrotatory as you're on the ground state [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:41, 16 March 2018 (UTC))

=== Cyclisation of [1,1']bicyclohexyl-1,1'-diene ===

[[File:Diene_one.png|500px|center]]

==== Log Files ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Cyclisation of [1,1']bicyclohexyl-1,1'-diene
! colspan = "2" style="background: #0D4F8B; color: white;" | Cyclisation of [1,1']bicyclohexyl-1,1'-diene
|-
| [1,1']bicyclohexyl-1,1'-diene
| [[Media:REACTANT_EXTENSION_MINIMISATION.LOG|[1,1']bicyclohexyl-1,1'-diene]]
|-
| Transition State
| [[Media:PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG|Transition State]]
|-
| Cyclised Product
| [[Media:PRODUCT_INITIAL_MINIMISATION.LOG|Cyclised Product]]
|-
| IRC Calculation
| [[Media:FRESHCYCLOBUTENE_PM6_IRC_ATTEMPT1.LOG|IRC Calculation]]
|}

==== Jmols of MOs ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Jmols of MOs for Cyclisation of [1,1']bicyclohexyl-1,1'-diene
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
|-
| Reactant (ring open)
| <jmol>
<jmolApplet>
<title> Reactant HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REACTANT_EXTENSION_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Reactant LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REACTANT_EXTENSION_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Transition State
| <jmol>
<jmolApplet>
<title> Transition State HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Transition State LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product (ring closed)
| <jmol>
<jmolApplet>
<title> Product HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_INITIAL_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Product LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_INITIAL_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(The same problem as before, but perhaps worse here. You've started with geometries that have a plane of symmetry, which in this case have favoured MOs with the same symmetry (just happen to correspond to the orbitals that would be populated under photochemical conditions). If you use the correct frame you'll see that it is all conrotation. Also observing the IRC should show the same result. Perhaps important to know is PM6 is a ground state, single-reference method [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:41, 16 March 2018 (UTC))

==== Disrotatory or Conrotatory? ====

As can be seen from the MOs of the transition state structures for the cyclisation of this [1,1']bicyclohexyl-1,1'-diene, the cyclisation proceeds in a disrotatory fashion, with either end of the butadiene fragment twisting in the opposite direction. This is anticipated due to it being a 4n cyclisation performed under photochemical conditions<sup>(5)</sup>.

==Conclusion==

A computational analysis of three different reactions of increasingly complexity were studied. Through the introduction to Gaussian, two computational methods were used (PM6 and B3LYP/6-31(d)) to optimise both the reactants and products of a reaction. From these initial minimisations, and using chemical intuition, the transition states for these reactions were located.

From using the relative energies of the transition states, reactants and products, thermodynamic properties of the systems were calculated (the activation energy (reaction barrier) and reaction energy). These values were used in discussion of the thermodynamic and kinetic products of the reaction.

Further work was carried out on two electrocyclic reactions, however the student ran out of time to conduct a full analysis of these reactions, for said was enjoying carrying out the calculations too much.

The tutorial and further reading provided facilitated an introduction to potential energy surfaces and the underlying quantum mechanics of the Gaussian code. A computational chemist must marry a working knowledge of the computational methods (and underlying approximations) with the savoir-faire of an experimental chemist.

==References==
{{Reflist}}

1. W. J. Ot, Computational quantum chemistry, 1990, vol. 207.

2. L. S. Bartell, J. Am. Chem. Soc., 1959, 81, 3497–3498.

3. A. Bondi, J. Phys. Chem., 1964, 68, 441–451.

4. B. R. Beno, K. N. Houk and D. A. Singleton, J. Am. Chem. Soc., 1996, 118, 9984–9985.

5. J.Clayden, Organic Chemistry, OUP, Oxford, 2001

6. E. Białkowska-Jaworska, M. Jaworski and Z. Kisiel, J. Mol. Struct., 1995, 350, 247–254.

Rep:FD915 TRANSITION

2018-03-16T15:32:15Z

Tam10: /* Exercise 3 */

= Transition Structure and Reactivity =

Felix de Courcy-Ireland
01062960
Transition States and Reactivity Computational Lab

==Introduction ==

Stationary points on potential energy surfaces (or ‘hypersurfaces’) are defined by a value of zero for the first derivative at that point<sup>(1)</sup>. However, it is through the use of second derivatives that the distinction can be made between the various types of stationary points, including reactants, transition states, intermediates and products<sup>(1)</sup>.

Products, reactants and intermediates are all minima on a potential energy surface. They are characterised by the fact that all paths through these points have a positive second derivative<sup>(1)</sup>.

Transition states are characterised by having a single normal coordinate for which the second derivative is negative, with all other paths through the transition state giving a positive second derivative at this point<sup>(1)</sup>. They are known as ‘saddle-points’. If a point on a potential energy surface is a maximum in more than one normal coordinate, it is diagnostic that there is a lower energy path for the reaction to proceed in the vicinity of this point<sup>(1)</sup>.

The calculations carried out were effectively an interrogation of the potential energy surface of a simple reaction. The aims of the calculations were to locate the stationary points of the potential energy surfaces. This was done through using the Gaussian software, which traced paths across the potential energy surface, iteratively calculating the second derivative of each point on the path until a point with a zero first derivative was reached.

In this laboratory, a successfully located transition state was denoted by there being a single negative frequency in the frequency calculation, which when animated, showed the desired reaction coordinate for the reaction.

In the relatively simple reactions investigated, where the reactants pass through only one transition state, it is simple to calculate important quantities such as the activation energy and the reaction energy, from knowledge of the free energies of the reactants, products and transition states.

In this laboratory, two computational methods were used; the semi-empirical PM6 method and the DFT method B3LYP/6-31(d).

The semi-empirical PM6 is a less accurate method but not as computationally expensive. Therefore, it proved useful in optimising structures, be they reactants, products or transition states, in preparation for the use of the more accurate and expensive B3LYP method.
B3LYP/6-31(d) is based in density functional theory (DFT)<sup>(1)</sup>. DFT finds approximate solutions to unsolvable many-electron wave functions by analysis of functionals of the one electron density, ρ(r), of the molecule<sup>(1)</sup>.

In some instances, use of chemical intuition in the location of transition states was most useful. There were cases where it proved fruitful to optimise a product or reactant(s) at the PM6 level, and then freeze the atoms immediately involved in the transition and further minimise the molecule around this frozen ‘transition state’ at the B3LYP level. A final calculation to find the transition state of at the B3LYP level was often more successful when using this ‘bond freezing’ technique.

==Exercise 1 ==

=== Reaction Scheme ===

[[File:Reaction_scheme.png|550px|center]]

=== Log Files ===

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Butadiene + Ethene
! colspan = "2" style="background: #0D4F8B; color: white;" | Log Files - Butadiene + Ethene
|-
| Minimisation of butadiene (PM6)
| [[Media:CIS_BUTADIENE_ATTEMPT3.LOG| Minimisation of butadiene (PM6)]]
|-
| Minimisation of ethene (PM6)
| [[Media:ETHENE_MINIMISATION_ATTEMPT1.LOG|Minimisation of ethene (PM6)]]
|-
| Minimisation of cyclohexene (PM6)
| [[Media:CYCLOHEXENE_OPTIMISATION_ATTEMPT4.LOG|Minimisation of cyclohexene (PM6)]]
|-
| Transition State (PM6)
| [[Media:BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG|Transition State (PM6)]]
|-
| IRC (PM6)
| [[Media:IRC_FROM_CYCLOHEXENE_ATTEMPT1_BOTH_WAYS.LOG|IRC (PM6)]]
|}

=== MO diagram ===

[[File:Ex1_MO_diagram.png|500px|center| MO diagram for reaction of butadiene and ethene]]

The above molecular orbital diagram shows the interaction between the HOMOs and LUMOs of the ethene and butadiene. Each MO is assigned a symmetry value (assignments were based on the phasing of orbitals) - from these assignments it can be seen that only orbitals of like symmetry interact. The orbital overlap integral is zero for the case of a symmetric-(anti-symmetric) interaction and non-zero for either a symmetric-symmetric or (anti-symmetric)-(anti-symmetric) interaction. The orbital energies are relative to one another rather than being absolute. An attempt has been made to draw the MOs of the transition state - the calculated MOs can be found in the table below.

=== Jmols of the HOMOs and LUMOS of Butadiene and Ethene ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 1 showing the HOMO and LUMO of ethene with relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Ethene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<title>Ethene HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_MINIMISATION_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.39228 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<title>Ethene LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_MINIMISATION_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.04256 E<sub>h</sub>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 2 showing the HOMO and LUMO of butadiene, with relative energies in Hartrees.
! colspan = "3" style="background: #0D4F8B; color: white;" | Butadiene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS_BUTADIENE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.35899 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS_BUTADIENE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01943 E<sub>h</sub>
|}

=== Jmols of the MOs in the Transition State ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 3 showing the four MOs produced from the interaction of the ethene and butadiene MOs with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 16
| <jmol>
<jmolApplet>
<title> MO 16 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.32754 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 17
| <jmol>
<jmolApplet>
<title> MO 17 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.32532 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 18
| <jmol>
<jmolApplet>
<title> MO 18 </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.03</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01732 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 19
| <jmol>
<jmolApplet>
<title> MO 19 </title>
<color>white</color>
<size>300</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.03 </script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.03066 E<sub>h</sub>
|}

=== C-C Bond Lengths of Reactants, Transition State and Products ===

[[File:Reaction_scheme.png|550px|center]]

Reaction Scheme repeated for clarity when analysing the bond lengths below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 4 showing bond distances in the reactants.
! colspan = "2" style="background: #0D4F8B; color: white;" | Reactants
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.33344
|-
| C2-C3
| 1.47077
|-
| C3-C4
| 1.33344
|-
| C5-C6
| 1.32731
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 5 showing bond distances in the transition state
! colspan = "2" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.37978
|-
| C2-C3
| 1.41104
|-
| C3-C4
| 1.37981
|-
| C4-C5
| 2.11452
|-
| C5-C6
| 1.38177
|-
| C6-C1
| 2.11469
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Table 6 showing bond distances in the product
! colspan = "2" style="background: #0D4F8B; color: white;" | Cyclohexene
|-
! style="background: #0D4F8B; color: white;" | Bond
! style="background: #0D4F8B; color: white;" | C-C Bond Distance (Å)
|-
| C1-C2
| 1.49118
|-
| C2-C3
| 1.36309
|-
| C3-C4
| 1.49118
|-
| C4-C5
| 1.58345
|-
| C5-C6
| 1.56027
|-
| C6-C1
| 1.58345
|}

==== Discussion of carbon-carbon (C-C) bond lengths ====

The C-C single bond length of typical n-hydrocarbon is 1.533 Å, and the bond length of a typical C-C double bond is 1.33 Å<sup>(2)</sup>. These lengths will be used as a point of comparison in the following discussion.

The two pairs of carbon atoms which make up the two alkene bonds in the butadiene (C1-C2 and C3-C4) lengthen from a separation of 1.33 Å to a separation of 1.49 Å. This can be rationalised by observing that these two double bonds in the butadiene reactant will be present in the cyclohexene product as single bonds in the cyclohexene ring.

The internal C-C bond in butadiene (C2-C3) shortens from a distance of 1.47 Å to a distance of 1.36 Å. Again, although this bond is shorter than a typical C-C single bond due to the conjugation of the butadiene, it shortens to a distance more typical of a C-C double bond which it adopts in the cyclohexene product.

The ethene C-C double bond lengthens from 1.327 Å to 1.560 Å. This is due to the carbons moving from the sp<sup>2</sup> hybridised environment of the ethene molecule to the sp<sup>3</sup> hybridised environment of the cyclohexene ring.

The two new C-C bonds which are formed upon the Diels-Alder [4+2] cycloaddition between the butadiene and ethene have a value of 2.115 Å in the transition state, which shortens to a value of 1.583 Å in the cyclohexene product. This change in bond distance shows a shortening of bond lengths from an effectively infinite value in the reactants, through to a bond distance of 1.583 Å in the cyclohexene product.

Van der Waals radius of a carbon atom is 1.7 Å <sup>(3)</sup>, and this can be used in discussion of the partially formed bond between the ethene and butadiene in the transition state.

The length of the partly formed C-C bonds between butadiene and ethene is 2.115 Å. This is less than two times the van der Waals radius of carbon. Therefore, although there is not formally a bond formed between the atoms, the atoms are close enough to interact through van der Waals forces.

==== Vibration corresponding to the transition state ====

<jmol>
<jmolApplet>
<title> Reaction Path Vibration </title>
<color>white</color>
<size>500</size>
<script>frame 15; vibration 2;rotate x -20;</script>
<uploadedFileContents>BUTADIENE_ETHENE_TRANSITIONSTATE_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Jmol above shows the vibration that corresponds to the reaction path at the transition state. It shows that the formation of the two bonds is synchronous - both bonds form simultaneously<sup>(4)</sup>.

==Exercise 2 ==

=== Reaction Scheme ===

[[File:Ex2_reaction_scheme.png|500px|center]]

=== Log files ===

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - 1,3-Dioxole + Cyclohexadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Log Files - 1,3-Dioxole + Cyclohexadiene
|-
| Minimised Cyclohexadiene (B3LYP/6-31G(d))
| [[Media:CYCLOHEXADIENE_REPEAT_AGAIN_B3LYP_MINIMISATION.LOG|Minimised Cyclohexadiene (B3LYP/6-31G(d))]]
|-
| Minimised 1,3-Dioxole (B3LYP/6-31G(d))
| [[Media:13DIOXOLE_PROPER_MINIMISATION_B3LYP_ATTEMPT3.LOG|Minimised 1,3-Dioxole (B3LYP/6-31G(d))]]
|-
| Minimised exo-product (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_MINIMISATION.LOG|Minimised exo-product (B3LYP/6-31G(d))]]
|-
| Minimised endo-product (B3LYP/6-31G(d))
| [[Media:ENDO_FULL_MOLECULE_INITIAL_MINIMISATION_B3LYP.LOG|Minimised endo-product (B3LYP/6-31G(d))]]
|-
| Minimised exo-transition state (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG|Minimised exo-transition state (B3LYP/6-31G(d))]]
|-
| Minimised endo-transition state (B3LYP/6-31G(d))
| [[Media:ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG|Minimised endo-transition state (B3LYP/6-31G(d))]]
|-
| IRC on Exo Transition State (PM6)
| [[Media:EXO_FULL_MOLECULE_IRC_ATTEMPT1.LOG|IRC on Exo Transition State (PM6)]]
|-
| IRC on Endo Transition State (PM6)
| [[Media:ENDO_MOLECULE_PM6_IRC_ATTEMPT1.LOG|IRC on Endo Transition State (PM6)]]
|-
| Single Point Energy on Exo Transition State (B3LYP/6-31G(d))
| [[Media:EXO_FULL_MOLECULE_B3LYP_SINGLEPOINTENERGY.LOG|Single Point Energy on Exo Transition State (B3LYP/6-31G(d))]]
|-
| Single Point Energy on Endo Transition State (B3LYP/6-31G(d))
| [[Media:ENDO_MOLECULE_B3LYP_SINGLEPOINTENERGY.LOG|Single Point Energy on Endo Transition State (B3LYP/6-31G(d))]]
|}

=== Jmols and Molecular Orbital Diagram for the Endo Reaction of Cyclohexadiene and 1,3-Dioxole ===

[[File:Ex2_MO_diagram_endo.png|500px|right| MO diagram for reaction with endo arrangement between 1,3-dioxole and cyclohexadiene]]

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Table 7 showing the MOs of the endo transition state with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 40 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 40 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19648 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 41 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 41 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19052 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 42 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 42 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.00462 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 43 - Endo Transition State
| <jmol>
<jmolApplet>
<title> MO 43 - Endo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01543 E<sub>h</sub>
|}

Above is the new MO diagram from the endo reaction of cyclohexadiene and 1,3-dioxole. The endo reaction involves the two oxygen atoms of the 1,3-dioxole tucking under the cyclohexadiene. This leads to a stabilising secondary orbital interaction which shall be discussed later. The MO's produced by the interaction of the cyclohexadiene and 1,3-dioxole orbitals are shown in Table 7.

=== Jmols and Molecular Orbital Diagram for the Exo Reaction of Cyclohexadiene and 1,3-Dioxole ===

[[File:Ex2_MO_diagram_exo.png|500px|right| MO diagram for reaction with exo arrangement between 1,3-dioxole and cyclohexadiene]]

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Table 8 showing the MOs of the exo transition state with associated relative energies in Hartrees
! colspan = "3" style="background: #0D4F8B; color: white;" | Transition State
|-
! style="background: #0D4F8B; color: white;" | MO 40 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 40 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.19801 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 41 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 41 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.18560 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 42 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 42 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| -0.00699 E<sub>h</sub>
|-
! style="background: #0D4F8B; color: white;" | MO 43 - Exo Transition State
| <jmol>
<jmolApplet>
<title> MO 43 - Exo Transition State </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.02 </script>
<uploadedFileContents>EXO_FULL_MOLECULE_B3LYP_TRANSITIONSTATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| 0.01019 E<sub>h</sub>
|}

Above is the MO diagram from the exo transition state, with the MOs produced from interaction of the reactant HOMOs and LUMOs shown in Table 8. It should be noted that, similarly to the previous Diels-Alder reaction of butadiene and ethene, that only orbitals of like symmetry interact to give MOs in the transition state.

=== Inverse and Normal Electron Demand Diels-Alder Reactions ===

The reaction between 1,3-dioxole and cyclohexadiene is an inverse electron demand Diels-Alder reaction. Inverse electron demand Diels-Alder reactions are characterised by there being a smaller energy gap between the HOMO of the dienophile (1,3-dioxole) and the LUMO of the diene (cyclohexadiene) than the energy gap between the HOMO of the diene and the LUMO of the dienophile<sup>(5)</sup>.

[[File:Inverse_normal_DA.png|400px|center|Figure highlighting the relative energy differences that lead to definition of normal and inverse electron demand Diels-Alder reactions.]]

=== Thermochemistry ===

If the formation of more than one product is possible from a given set of reactants, knowledge of reaction energies and activation energies can lead to assignment of the kinetic and thermodynamic products. The kinetically favourable product is that from the reaction which has the lowest energy barrier to conversion between reactants and products. The thermodynamically favourable product is the lower energy product relative to the reactant(s).

In the case that there are two possible products of a reaction, as is the situation in this Diels-Alder reaction between 1,3-dioxole and cyclohexadiene, it is not necessary for one product to be the thermodynamic product and the other product to be the kinetic product. It may be the case that one of the products is both the thermodynamic and kinetic product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Energies Endo Reaction
|-
! style="background: #0D4F8B; color: white;" | Molecule
! style="background: #0D4F8B; color: white;" | Gibbs Free Energy (kJ/mol)
|-
| 1,3dioxole
| -701,188.414
|-
| cyclohexadiene
| -612,592.877
|-
| 1,3dioxole and cyclohexadiene
| -1,313,781.291
|-
| Endo Transition State
| -1,313,621.479
|-
| Endo Product
| -1,313,848.695
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Endo Reaction Parameters
|-
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
| 159.811
|-
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
| -67.404
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Energies Exo Reaction
|-
! style="background: #0D4F8B; color: white;" | Molecule
! style="background: #0D4F8B; color: white;" | Gibbs Free Energy (kJ/mol)
|-
| 1,3dioxole
| -701,188.414
|-
| cyclohexadiene
| -612,592.877
|-
| 1,3dioxole and cyclohexadiene
| -1,313,781.291
|-
| Exo Transition State
| -1,313,613.639
|-
| Exo Product
| -1,313,845.098
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "2" style="background: #0D4F8B; color: white;" | Exo Reaction Parameters
|-
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
| 167.651
|-
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
| -63.807
|}

As shown in the above tables, the reaction barrier for the exo reaction is higher at a value of 167.651 kJ/mol, due to the transition state through which the reaction proceeds being of higher energy. Therefore, due to the lower reaction barrier of 159.811 kJ/mol, the endo product is kinetic product.

The endo product proceeds through a lower energy transition state due to the secondary orbital interactions between the oxygen p orbitals and the p orbitals of the internal carbons of the cis-butadiene fragment<sup>(5)</sup>.

The Jmol of the HOMO of the endo transition state is repeated here, where it can be seen that there is a stabilising interaction between the orbitals which lie on the oxygens of 1,3-dioxole and the two carbons which eventually form the double bond in the product, for the portion of the orbital located in these areas is the same phase.

<jmol>
<jmolApplet>
<title> MO 41 - Endo Transition State </title>
<color>white</color>
<size>350</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01 </script>
<uploadedFileContents>ENDO_MOLECULE_B3LYP_FRESH_TRANSITIONSTATE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The endo product is again the thermodynamic product, as the energy of the endo product (-67.404 kJ/mol) is lower than that of the exo product (-63.807) - although the difference in energy is less in the products than in the reactants. This reason for the greater stabilisation of the endo product is possibly due to this same orbital interaction between the p orbitals on the oxygens with the alkene pi system. The fact that the difference in energy between the products is less than the difference in energy of the transition states is a consequence of this orbital interaction being poorer in the products.

==Exercise 3 ==

[[File:Ex3_reaction_scheme.png|500px|center]]

=== Log Files ===

==== Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Dioxide + Exo-Cyclic Butadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment
|-
| Xylylene Minimisation (PM6)
|[[File:XYLYLENE_MINIMISATION_PM6.LOG| Xylylene Minimisation (PM6)]]
|-
| Sulfur Dioxide Minimisation (PM6)
| [[File:SULFUR_DIOXIDE.LOG| Sulfur Dioxide Minimisation (PM6)]]
|-
| Cheletropic Transition State (PM6)]
| [[File:CHELETROPIC_PM6_PRODUCT_TRANSITIONSTATE_NOTFROZEN.LOG| Cheletropic Transition State (PM6)]]
|-
| Cheletropic Product (PM6)]
| [[File:CHELETROPIC_PRODUCT_INITIAL_MINIMISATION_2.LOG| Cheletropic Product (PM6)]]
|-
| Endo (Xylylene-SO2) Transition State (PM6)
| [[File:DA_ENDO_PM6_TRANSITIONSTATE_ATTEMPT1.LOG| Endo (Xylylene-SO2) Transition State (PM6)]]
|-
| Endo (Xylylene-SO2) Product (PM6)]
| [[File:DA_ENDO_PM6_PRODUCT_ATTEMPT1_NOTFROZEN_MINIMISATION.LOG| Endo (Xylylene-SO2) Product (PM6)]]
|-
| Exo (Xylylene-SO2) Transition State (PM6)]
| [[File:DA_EXO_PM6_TRANSITIONSTATE_SECOND.LOG| Exo (Xylylene-SO2) Transition State (PM6)]]
|-
| Cheletropic IRC (PM6)]
| [[File:CHELETROPIC_PM6_IRC_ATTEMPT1.LOG | Cheletropic IRC (PM6)]]
|-
| Endo (Xylylene-SO2) IRC (PM6)
| [[File:DA_ENDO_PM6_IRC_ATTEMPT1.LOG| Endo (Xylylene-SO2) IRC (PM6)]]
|-
| Exo (Xylylene-SO2) IRC (PM6)]
| [[File:DA_EXO_PM6_IRC_ATTEMPT1.LOG| Exo (Xylylene-SO2) IRC (PM6)]]
|}

==== Reaction of Sulfur with Alternate, Endo-Cyclic Cis-Butadiene Fragment of Xylylene ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Log Files - Dioxide + Endo-Cyclic Butadiene
! colspan = "2" style="background: #0D4F8B; color: white;" | Reaction of Sulfur Dioxide with Exo-Cyclic Cis-Butadiene Fragment
|-
| Endo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]
|[[File:ENDO EXTRA NEW TRANSITIONSTATE ATTEMPT2.LOG| Endo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Endo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:ENDO_EXTRA_NEW_MINIMISATION_ATTEMPT1.LOG| Endo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Exo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:EXO_EXTRA_TRANSITIONSTATE_ATTEMPT1.LOG| Exo Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Exo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:EXO_EXTRA_MINIMISATION_ATTEMPT1.LOG| Exo Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Cheletropic Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:CHELETROPIC_EXTRA_TRANSITIONSTATE_NOTFROZEN_ATTEMPT2.LOG| Cheletropic Transition State - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|-
| Cheletropic Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE
| [[File:CHELETROPIC_PRODUC_MINIMISATION_HOPEFULLY_ATTEMPT2.LOG| Cheletropic Product Minimisation - OTHER CIS-BUTADIENE FRAGMENT OF XYLYLENE]]
|}

=== GIFs of IRC for Reaction of Sulfur Dioxide and Xylylene ===

It can be seen in all of the GIFs of the reactions below that the 6-membered ring of the highly unstable xylylene molecule becomes aromatic on reaction with sulfur dioxide.

==== GIF for Endo Reaction ====

[[File:Endo_IRC_GIF.gif]]

==== GIF for Exo Reaction ====

[[File:Exo_IRC_GIF.gif]]

This reaction goes from products to reactants.

==== GIF for Cheletropic Reaction ====

[[File:Cheletropic_IRC_GIF.gif]]

=== Thermochemistry ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "3" style="background: #0D4F8B; color: white;" | Reaction Parameters For Reaction of Sulfur Dioxide With Xylylene
|-
! style="background: #0D4F8B; color: white;" | Reaction Type
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
|-
| style="background: #0D4F8B; color: white;" | Endo
| 81.724
| -99.050
|-
| style="background: #0D4F8B; color: white;" | Exo
| 85.709
| -99.714
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| 104.049
| -156.041
|}

The data above shows that the kinetic product is the endo product, due to it having the lowest reaction barrier of 111.946 kJ/mol. This is probably a consequence of the secondary orbitals interactions that were previously discussed, between the second sulfur oxygen and the carbon p orbitals that eventually form the alkene. The cheletropic reaction has the highest reaction barrier of 140.666 kJ/mol. This is potentially due to the 5-membered transition states that forms being of higher energy than that of the 6-membered transition states that form in the endo and exo forms of the reaction.

(The barriers in this text refer to the alternate reactions [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:32, 16 March 2018 (UTC))

The thermodynamic product is also that from the endo reaction, due to it having the lowest energy (-156.041 kJ/mol). This is best explained in terms of bond enthalpies. In the endo and exo reactions, a sulfur-oxygen bond is broken and a carbon-oxygen and sulfur-carbon bond are formed, whereas in the cheletropic reaction, no bonds are broken, and two bonds are formed.

Although the cheletropic reaction proceeds through a higher energy transition states, the formation of two bonds with the loss of none leads to a lower energy product.

=== Reaction Profile for the Reaction of Sulfur Dioxide and the Exo-Cyclic Cis-Butadiene Fragment of Xylylene ===

[[File:Reaction_Profile_for_Exercise_3.png|500px|center]]

=== Further Comment ===

==== Discussion of Stability of Xylylene ====

Xylylene is an 8 electron system, and therefore anti-aromatic (Huckel's 4n rule, with n=2)<sup>(5)</sup>. These systems are often bent to avoid planarity of the p orbitals of the molecule, however xylylene is somewhat constrained to a planar configuration due to the sp<sup>2</sup>) nature of the 6 ring carbons. This makes for a very strained molecule with a high relative energy of 467.460 kJ/mol.

=== Reaction at the Endo-Cyclic, Cis-Butadiene Fragment ===

[[File:Ex3 reaction scheme extension.png|500px|center]]

Reaction scheme above shows the same reactions are possible at the endo-cyclic cis-butadiene fragment of xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! colspan = "3" style="background: #0D4F8B; color: white;" | Reaction Parameters For Reaction at the Alternate Cis-Butadiene Site of Xylylene
|-
! style="background: #0D4F8B; color: white;" | Reaction Type
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJ/mol)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ/mol)
|-
| style="background: #0D4F8B; color: white;" | Endo
| 111.946
| 16.197
|-
| style="background: #0D4F8B; color: white;" | Exo
| 119.783
| 20.668
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| 140.666
| 47.238
|}

The values for activation energy (reaction barrier) and reaction energy above show these reactions are far less favoured. All the reactions are endothermic, and also have larger reactions barriers than the reactions at the original cis-butadiene fragment.

The reason for the positive values for the reaction energy is due to the fact that there is no gain of aromaticity in these reactions, like there was previously.

The reason for the higher activation barrier is potentially a consequence of the endo-cyclic cis-butadiene fragment being harder to access, therefore the molecules need to adopt higher energy conformations in the transition states to yield the products

== Further Work ==

=== Ring Opening of the Dimethyl Ester Cyclobutene ===

[[File:Cyclobutene.png|500px|center]]

==== Log Files ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Ring Opening of the Dimethyl Ester Cyclobutene
! colspan = "2" style="background: #0D4F8B; color: white;" | Ring Opening of the Dimethyl Ester Cyclobutene
|-
| Dimethyl Ester of Cyclobutene
| [[Media:CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG|Dimethyl Ester of Cyclobutene]]
|-
| Transition State
| [[Media:FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG|Transition State]]
|-
| Diene Product
| [[Media:DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG|Diene Product]]
|-
| IRC Calculation
| [[Media:BIS_CYCLOHEXENE_IRC_ATTEMPT1.LOG| IRC Calculations]]
|}

==== Jmols of MOs ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Jmols of MOs for Ring Opening of the Dimethyl Ester Cyclobutene
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
|-
| Reactant (ring closed)
| <jmol>
<jmolApplet>
<title> Reactant HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Reactant LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOBUTENE_REMINIMISATION_PM6_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Transition State
| <jmol>
<jmolApplet>
<title> Transition State HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Transition State LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>FRESHCYCLOBUTENE_PM6_TRANSITIONSTATE_ATTEMPT3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product (ring open)
| <jmol>
<jmolApplet>
<title> Product HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Product LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENE_PRODUCT_MINIMISED_ATTEMPT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Disrotatory or Conrotatory? ====

Due to running out of time, I have not been able to put the correct MO for the transition state into the table above (I am doing something wrong, but I am sure that the marker will be able to work out what it is I have done). However, the reaction proceeds in a conrotatory fashion, as expected due to it being a 4n cyclisation under thermal conditions<sup>(5)</sup>.

=== Cyclisation of [1,1']bicyclohexyl-1,1'-diene ===

[[File:Diene_one.png|500px|center]]

==== Log Files ====

{| class="wikitable"
|+ align="bottom" style="caption-side: bottom" | Cyclisation of [1,1']bicyclohexyl-1,1'-diene
! colspan = "2" style="background: #0D4F8B; color: white;" | Cyclisation of [1,1']bicyclohexyl-1,1'-diene
|-
| [1,1']bicyclohexyl-1,1'-diene
| [[Media:REACTANT_EXTENSION_MINIMISATION.LOG|[1,1']bicyclohexyl-1,1'-diene]]
|-
| Transition State
| [[Media:PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG|Transition State]]
|-
| Cyclised Product
| [[Media:PRODUCT_INITIAL_MINIMISATION.LOG|Cyclised Product]]
|-
| IRC Calculation
| [[Media:FRESHCYCLOBUTENE_PM6_IRC_ATTEMPT1.LOG|IRC Calculation]]
|}

==== Jmols of MOs ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ align="bottom" style="caption-side: bottom" | Jmols of MOs for Cyclisation of [1,1']bicyclohexyl-1,1'-diene
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
|-
| Reactant (ring open)
| <jmol>
<jmolApplet>
<title> Reactant HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REACTANT_EXTENSION_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title> Reactant LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REACTANT_EXTENSION_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Transition State
| <jmol>
<jmolApplet>
<title> Transition State HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Transition State LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_TRANSITIONSTATE_ATTEMPT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product (ring closed)
| <jmol>
<jmolApplet>
<title> Product HOMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 33; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_INITIAL_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title> Product LUMO </title>
<color>white</color>
<size>400</size>
<script>frame 2; mo 34; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT_INITIAL_MINIMISATION.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Disrotatory or Conrotatory? ====

As can be seen from the MOs of the transition state structures for the cyclisation of this [1,1']bicyclohexyl-1,1'-diene, the cyclisation proceeds in a disrotatory fashion, with either end of the butadiene fragment twisting in the opposite direction. This is anticipated due to it being a 4n cyclisation performed under photochemical conditions<sup>(5)</sup>.

==Conclusion==

A computational analysis of three different reactions of increasingly complexity were studied. Through the introduction to Gaussian, two computational methods were used (PM6 and B3LYP/6-31(d)) to optimise both the reactants and products of a reaction. From these initial minimisations, and using chemical intuition, the transition states for these reactions were located.

From using the relative energies of the transition states, reactants and products, thermodynamic properties of the systems were calculated (the activation energy (reaction barrier) and reaction energy). These values were used in discussion of the thermodynamic and kinetic products of the reaction.

Further work was carried out on two electrocyclic reactions, however the student ran out of time to conduct a full analysis of these reactions, for said was enjoying carrying out the calculations too much.

The tutorial and further reading provided facilitated an introduction to potential energy surfaces and the underlying quantum mechanics of the Gaussian code. A computational chemist must marry a working knowledge of the computational methods (and underlying approximations) with the savoir-faire of an experimental chemist.

==References==
{{Reflist}}

1. W. J. Ot, Computational quantum chemistry, 1990, vol. 207.

2. L. S. Bartell, J. Am. Chem. Soc., 1959, 81, 3497–3498.

3. A. Bondi, J. Phys. Chem., 1964, 68, 441–451.

4. B. R. Beno, K. N. Houk and D. A. Singleton, J. Am. Chem. Soc., 1996, 118, 9984–9985.

5. J.Clayden, Organic Chemistry, OUP, Oxford, 2001

6. E. Białkowska-Jaworska, M. Jaworski and Z. Kisiel, J. Mol. Struct., 1995, 350, 247–254.

Rep:MOD:TS Yiming Xu

2018-03-16T15:14:31Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

The potential energy surface (PES) is the mathematical relationship between the energy of a molcule and its geometry. <ref>E. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics, Springer Netherlands, Dordrecht, 2nd edn., 2011.</ref> By taking advantage of the Born-Oppenheimer approximation, the PES represents the electronic energy of the molecule at all possible arrangements of the atoms. Vibrational zero-point energy is sometimes added to the PES for increased accuracy.

For a molecule with N atoms, this represents a surface with 3N-6 dimensions (degrees of freedom for a non-linear molecule). Naïvely, this could be found by evaluating the energy of the molecule over all points in space using specific methods suitable for the molecule at hand. However, the effectively infinite number of possible configurations renders this approach computationally impossible. Luckily, during a reaction, only a limited "patch" of the PES is explored by the molecule, and any analysis of a reaction can be reasonably limited to studies of the reactants, products, and any surface that they traversed from the reactants to products (the reaction profile).

The reactants and products are (relatively) stable chemical species. Intuitively, they reside in minima on the PES - as stable chemical species, they tend to return to their configuration from slight perturbations. On the other hand, a reaction path is physical, and must necessarily be continuous and differentiable (where the PES itself might not be). In this case, a reaction profile joining two minima (i.e. reactants and products) will pass through one (or more) maxima along the reaction coordinate. These properties can be used to deduce structures from the PES.

== Critical points on the PES ==

Both minima and maxima are stationary points on the PES. For a stationary point at <math>\vec{q}</math>, the following relationship must hold:

<math display="block"> \nabla U(\vec{q})= 0</math>,

where <math>\nabla</math> is the gradient function, <math>\vec{q}</math> is any geometric parameter (e.g. mass-weighted coordinates), and <math>U(\vec{q})</math> is the potential energy surface. In order to determine if it is a local maximum or minimum, the second derivative test must be conducted. First, a square <math>n\times n</math> matrix, where <math>n</math> is the number of geometric parameters, can be defined:

<math display="block"> H_{i,j} = \frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}}</math>

where <math>H_{i,j}</math> is the i-th and j-th term of the Hessian matrix, <math>H</math>. The second partial derivative test is conducted by looking at the eigenvalue of the Hessian matrix at the stationary points <math>\vec{q}</math>, assuming that <math>H</math> is invertible: - If all eigenvalues are positive, <math>\vec{q}</math> is at a local maximum. - If all eigenvalues are negative, <math>\vec{q}</math> is at a local minimum. - If there is a mix of positive and negative eigenvalues, <math>\vec{q}</math> is at a saddle point. - And inconclusive otherwise.

In essence, the second partial derivative test is looking at direction of the local curvature at the station points.

== Harmonic Approximation and the Transition State ==

When deviation from equilibrium stationary points are small, the harmonic approximation can be used. The general expression of the harmonic approximation is as follows:

<math display="block">U \approx \frac{1}{2}\sum_{i,j=1}\frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}} q_i q_j</math>

As the force is related to energy as well as position,

<math display="block">\begin{align}
\vec{F} &= -\nabla U\\
& = -k\vec{X}
\end{align}
</math>

where <math>\vec{F}</math> is the column vector of the forces <math>[\vec{F_1},\vec{F_2}, ...]^T</math>, <math>X</math> is the column displacement vector of the coordinates <math>[\vec{q_1},\vec{q_2}, ...]^T</math>, and <math>k</math> is the force tensor connecting the force to the displacement of the atoms from their equilibrium positions. The differential equation admits a solution of the form:

<math display="block"> \vec{F} = -\omega ^2 \vec{X}</math>

where <math>\omega</math> is the frequency of vibration of the harmonic oscillator. It is obvious that it is an eigenvalue problem to obtain values of <math>\omega</math>, with the associated eigenvectors being the normal modes of vibrations. In practice, this is often referred to diagonalising the Hessian matrix, as the elements of the diagonalised matrix are the eigenvalues of the matrix. If we compare the form of the harmonic approximation with the second partial derivative test, it could be immediately seen that:

<math display="block"> k_{i,j} = H_{i,j} = \frac{\partial ^2 U}{\partial \vec{q_i} \partial \vec{q_j}}</math>

We could then restate the relationship between curvature and vibration as follows:

# The frequency of vibration is proportional to the square root of the local curvature at the point.
# A local minimum along coordinate <math>q_i</math> will have a positive frequency of vibration along coordinate <math>q_i</math>; and
# A local maximum along coordinate <math>q_i</math> will have an imaginary frequency of vibration (<math>\sqrt{-x} = i\sqrt{x}</math>); and
# A saddle point will have a mixture of positive and imaginary vibrational frequencies.

A transition state is defined to be a point on the PES that lies at the minimum along all coordinates, except for the reaction coordinate along which it lies at the maximum. <ref>E. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics, Springer Netherlands, Dordrecht, 2nd edn., 2011.</ref> In this case, a transition state will have one and only one imaginary vibrational frequency in its structure.

From the transition state, optimization of the structure along the coordinate following the steepest descent (as informed by the imaginary vibration frequency or negative force constant) allows one to reach the reactant and product state. The path traced out by such a procedure is called the Intrinsic Reaction Coordinate (IRC), and may or may not represent an actual physical reactive path due to other energy contributions (e.g. vibrational, kinetic, etc.). In either case, the IRC allows us to understand the changes in the molecular geometry, along with its electronic properties and molecule wavefunction, through the course of an reaction.

== Computational Approaches ==

In quantum mechanics, all information about a quantum system is encoded In its wavefunction, <math>\Psi</math>. The wavefunction obeys the Schrödinger equation, generally stated (in its time-independent form) ss below:

<math display="block">\hat{H} \Psi = E \Psi</math>

where <math>\hat{H}</math> is the Hamiltonian operator and <math> E </math> is the energy of the system. The Schrödinger equation is not analytically solvable in general, and many techniques have been developed since to find an approximate solution to the Schrödinger equation. One of the earliest approaches was the Hartree–Fock method. It was an ''ab initio'' computational method to directly compute the molecule wavefunction. Along with post-Hartree–Fock methods and alternatives approaches such as the Density Functional Theory (DFT). The different approaches share broadly similar features.

One of the most useful computational methods for finding the ground state solution is the variational method, based on the variational principle. It requires the use of trial solutions (''ansatz''), often a basis set of orbitals, to evaluate the energy eigenvalue. As the variational principle states that the true ground state has the lowest energy, the wavefunction (or rather coefficients to the basis set) can be found by locating the global minimum of the ansatz. Often, the basis set of orbitals are orthogonal to each other and uses either Slater Type Orbitals (STOs) or Gaussian Type Orbitals (GTOs) to save computation time.

Different methods employ different formalism and assumptions to simplify calculations. For example, Hartree–Fock implies the mean-field assumption and ignores electron correlation. The ansatz for the variational method is the Slater determinant of the basis sets and solves for the molecular wavefunction directly. DFT works by recognising the equivalence of finding the electron density of the molecule with its ground state wavefunction, allowing the optimizing of a single electron Schrödinger equation, shortening computation time. Modern methods with hybrid functionals (e.g. B3LYP) may use features from both to obtain more accurate results.

Unlike the ''ab initio'' methods above, semi-empirical methods drastically shorten computation time by making assumptions and correcting for them using parameters. These can include the zero differential overlap assumption, reducing the computational complexity scaling from <math>N^4</math> to <math>N^2</math>, where <math>N</math> is the number of electrons. One common semi-empirical method is the Huckle method for π-electrons. However, the parametrization requirement means that different parameters or assumptions must be used for different systems (valence electron vs п-electrons, transition metals, small vs heavy elements, etc.). When properly parameterized, semi-empirical methods can produce results more accurately than ''ab initio'' methods with much greater computation efficiency. Even if general purpose semi-empiricle methods (e.g. PM6) are less accurate than ''ab initio'' methods, its computational efficiency means that it is often used as an initial step in an optimization.

= Experimental Methods =

In this experiment, the Diels-Alder reaction was investigated in 3 different systems: reaction of butadiene with ethylene, reaction of cyclohexadiene with 1,3-dioxole, and reaction between o-xylylene and sulphur dioxide. The calculations are carried out with Gaussian 09 on Windows 7. Unless otherwise specified, initial geometry optimizations and IRC calculations were carried out in PM6 at default settings, with IRC calculations allowed to carry out to PES minima. Reactant, product and transition state molecular orbital calculations were carried out with B3LYP/6-31G(d) unless otherwise specified.

Results were extracted and analysed with GuassView (v5.0.9), as well as with cclib (v1.5) on Jupyter Notebook using Python (v3.6.4). Python analysis script is available on request. Surfaces were visualized via generation of Cube files from Gaussian, then converted to .jvxl files for faster loading and subsequently visualized on JSmol.

= Exercise 1: Reaction of Butadiene with Ethylene =

[[File:Yx6015 mechanism butadiene ethene.png|thumb|300px|'''Figure 1'''. Arrow-pushing mechanism of the Diels-Alder reaction between buta-1,3-diene and ethene showing concerted addition.]]

The reaction between buta-1,3-diene with ethene is the simplest example of a Diels-Alder reaction. The Diels-Alder reaction is a concerted pericyclic reaction between a diene (i.e. buta-1,3-diene) and a dieneophile (i.e. ethene). It in general proceeds via a single transition state with no intermediates, and is thus classified as a [4π<sub>S</sub>+2π<sub>S</sub>], and is thermally allowed under the Woodward-Hoffmann rules.

[[File:Yx6015 modiagram TS butadiene ethene.png|center|thumb|800px|'''Figure 2''': Molecular orbital diagram for the reaction between buta-1,3-diene in s-cis conformation (left) and ethene (right), along with the predicted transition state (middle).]]

Using the Hückel method, we could restrict our analysis to only π-electrons. An illustration of the molecular orbitals is found in Figure 2. It is important to note that there are additional interactions betwene the sigma and pi frameworks of the molecules. From the MO diagram, it could be seen that there are significant interactions throughout the pi system. For example, the TS orbital
π<sub>3s</sub> is due to the net interaction of 3 orbitals: butadiene π<sub>1s</sub> and π<sub>3s</sub>, and ethene π<sub>1s</sub>. Using frontier orbital molecular theory, we could further simplify analysis by, looking at only the HOMO/LUMO of the reactants and their interactions.

{| class="wikitable" style="text-align: center; margin: auto;"
|
!Buta-1,3-diene
!colspan = 2| Transition State
!Ethene
|- style="vertical-align:bottom;"
! scope="row" style="vertical-align:middle;"| LUMOs
| [[File:Yx6015 butadiene lumo.png|center|thumb|200px|'''Figure 3a''': Molecular orbital of the LUMO of buta-1,3-diene (MO 12, energy = +0.01104 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS4.png|center|thumb|200px|'''Figure 5a''': Molecular orbital of the LUMO of the TS (MO 16, energy = -0.32755 a.u.). Corresponds to π<sub>5a</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS3.png|center|thumb|200px|'''Figure 5b''': Molecular orbital of the LUMO+1 of the TS (MO 17, energy = -0.32533 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 ethene lumo.png|center|thumb|200px|'''Figure 4a''': Molecular orbital of the LUMO of ethene (MO 7, energy = +0.04256 a.u.). Corresponds to π<sub>4s</sub> from Fig 2.]]
|- style="vertical-align:bottom;"
! scope="row" style="vertical-align:middle;"| HOMOs
| [[File:Yx6015 butadiene homonew.png|center|thumb|200px|'''Figure 3b''': Molecular orbital of the HOMO of buta-1,3-diene(MO 11, energy = -0.35169 a.u.). Corresponds to π<sub>2a</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS2.png|center|thumb|200px|'''Figure 5c''': Molecular orbital of the HOMO-1 of the TS MO 18, energy = +0.01732 a.u.). Corresponds to π<sub>3s</sub> from Fig 2.]]
| [[File:Yx6015 butadiene ethene TS1.png|center|thumb|200px|'''Figure 5d''': Molecular orbital of the HOMO of the TS (MO 19, energy = +0.03067 a.u.). Corresponds to π<sub>2a</sub> from Fig 2.]]
| [[File:Yx6015 ethene homo.png|center|thumb|200px|'''Figure 4b''': Molecular orbital of the HOMO of ethene (MO 6, energy = -0.39228a.u.). Corresponds to π<sub>1s</sub> from Fig 2.]]
|}

For Figures 3, 4, and 5, only the MOs that would be directly relevant from the frontier orbitals are shown. It can be obviously seen that the frontier orbital theory is sufficient for this case - MO 16 and MO 18 cannot be generated from the HOMO and LUMO of the reactants only. A more correct interpretatin and diagram is depicted in Figure 2. In addition, it is clear the symmetry of the orbitals are important for their interaction and for a reaction to proceed - with orbitals only interacting with each other if they have the same symmetry. This can be formalized by the orbital overlap integral:

<math display = "block">
S_{AB} = <\psi^*_A|\psi_B>
</math>

where <math>S_{AB}</math> is the overlap integral for wavefunctions A and B, <math>\psi^*_A</math> is the Hermitian adjoint of wavefunction A, and <math>\psi_B</math> is wavefunction B. It is immediately evident that where <math>\psi_A</math> and <math>\psi_B</math> are of opposite phase, <math>\psi_A \times \psi_B</math> is an odd function and <math>S_{AB}</math> evaluates to 0. Specifically:

* the overlap integral is zero for a symmetric-antisymmetric interaction;
* the overlap integral is non-zero for a symmetric-symmetric interaction; and
* the overlap integral is non-zero for a antisymmetric-antisymmetric interaction.

The transition state for this reaction could be quite easily found as it is a simple molecular system. As detailed above, it was verified to be correct as it contains only 1 imaginary frequency, and the vibration corresponds to the desired reaction path. The transition state is visualized below.

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015_TS_reaction_path.gif|center|frame|300px|'''Figure 6a''': Transition state vibration at 948.67i cm<sup>-1</sup>. Calculated E(RPM6] = 0.11286018 at ultrafine grid.]]
| [[File:Yx6015 anim irc butadiene ethene.gif|center|frame|300px|'''Figure 6b''': IRC path for reaction between buta-1,3-diene and ethene.]]
|}

From the transition, an IRC optimization was carried out to find the reaction path, and to confirm that the transition state is indeed the transition state. The IRC path is also shown above, illustrating the correct TS and transition state is found. The changes to the bond lengths of the products and reactants could be visualized from the IRC.

| [[File:Yx6015 ccbonds butadiene ethene.png|center|thumb|800px|'''Figure 7a''': All bond lengths over the reaction coordiante. Reactant on negative reaction coordinate.]]
| [[File:Yx6015 chbonds butadiene ethene.png|center|thumb|800px|'''Figure 7b''': C-H bond lengths over the reaction coordinate. Reactant on negative reaction coordinate.]]

As can be seen from Figure 7, the bond lengths of the various C-C and C-H bonds vary across the reaction coordinate as expected. In general, variation comes from the change in hybridization of the terminal carbons bonds on butadiene and ethene from double bond to single bond, and the change from 'middle' carbons on butadiene from single to double bond. Similar variations are seen for C-H bonds, although the trend is not as straightforward. Notably, differences in the products are seen depending on the position of the hydrogen - axial vs equitorial, bowspirit vs flagpole. The two forming C-C bonds could also be seen approaching each other over time.

From the animation as well as the overlapped nature of the graph (each line has another line underneath), it is clear that the formation of the two bonds was synchronous. This was to be expected as the reactants, transition state and product all have the same plane of symmetry.

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

[[File:Yx6015 mechanism cyclohexadiene dioxole.png|thumb|300px|'''Figure 8'''. Arrow-pushing mechanism of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole showing concerted addition.]]

The reaction is another example of a Diels-Alder reaction. Changing the dienenophile from ethene to dioxole allowed the possibility of the product having two stereoisomers - the endo product and the exo product. The IRC paths for the respective products are as follow:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc cyclohexadiene dioxole exo.gif|center|frame|300px|'''Figure 9a''': IRC path for the reaction between cyclohexadiene and 1,3-dioxole with the exo product.]]
| [[File:Yx6015 anim irc cyclohexadiene dioxole endo.gif|center|frame|300px|'''Figure 9b''': IRC path for the reaction between cyclohexadiene and 1,3-dioxole with the endo product.]]
|}

From Figure 9, it could be seen that the transition state leading to the different products had different transition structures. The reactants' MO should however be identical:

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Cyclohexadiene
! 1,3-Dioxole
|-
! scope = "row"| LUMO
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/c/c1/Yx6015_cyclohexadiene_631Gd_mo23.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 cyclohexadiene 631Gd mo22.cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 23, energy = -0.01710 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/3/30/Yx6015_Dioxole_631Gd_mo20.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 Dioxole 631Gd mo20cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 20, energy = +0.03794 a.u., symmetric
|-
! scope = "row"| HOMO
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/c/cc/Yx6015_cyclohexadiene_631Gd_mo22.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 cyclohexadiene 631Gd mo22.cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 22, energy = -0.20551 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/60/Yx6015_Dioxole_631Gd_mo19.cub.jvxl" nodots nomesh fill translucent; rotate BEST;</script>
<uploadedFileContents>Yx6015 Dioxole 631Gd mo20cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
MO 19, energy = -0.19594 a.u., antisymmetric
|}

From the molecular orbitals of the reactants, the transition state MO could be inferred. As with the previous section, only orbitals with the same symmetry have significant interactions. The reactant molecules overlap in either an endo or exo orientation. The molecular orbitals of the transition state is visualized as below:

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Endo Transition State
! Exo Transition State
|-
! scope = "row"| LUMO +1 (MO43)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/65/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo43.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = +0.01550 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/e/e6/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo43.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = +0.01024 a.u., antisymmetric
|-
! scope = "row"| LUMO (MO42)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/3/3f/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo42.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.00466 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/b/b2/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo42.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.00703 a.u., symmetric
|-
! scope = "row"| HOMO (MO41)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/6/69/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo41.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19047 a.u., symmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/8/85/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo41.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.18561 a.u., symmetric
|-
! scope = "row"| HOMO-1 (MO40)
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/b/bf/Yx6015_ENDOOPT_PM6_TS_PM6_TS_631GD_mo40.cub.jvxl" nodots nomesh fill translucent;</script>
<uploadedFileContents>Yx6015 ENDOOPT PM6 TS PM6 TS 631GD mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19650 a.u., antisymmetric
| <jmol><jmolApplet>
<size>300</size>
<script>isosurface sign "images/4/48/Yx6015_EXOOPT_PM6_TS_PM6_TS_631G_mo40.cub.jvxl" nodots nomesh fill translucent;rotate x 90;</script>
<uploadedFileContents>Yx6015 EXOOPT PM6 TS PM6 TS 631G mo43cub.xyz</uploadedFileContents>
</jmolApplet> </jmol>
energy = -0.19803 a.u., antisymmetric
|}

The relevant endo and exo TS MOs show similar characteristics, with the exception of the HOMO. For the endo TS, in addition to the normal overlap between the reacting carbons as shown on the exo TS, there were secondary orbital overlaps between the oxygen with the middle two carbon atoms of the diene. This stabilizes the interactions, lowering the overall TS energy. In addition, additional repulsive non-covation interactions (i.e. steric clash) can be seen in the exo transition state. The energy difference can be seen in the energy profile of the reaction as below:

[[File:Yx6015_energyprofile_endo_exo.png|center|frame|700px|'''Figure 10''': Energy profile of the reaction over the IRC path. Reactants on the left.]]

From the reaction profile, it could be seen that the endo pathway has slightly lower energy at transition state, as discussed above. According to the Arrhenius equation, <math> k = Ae^{\frac{-E_a}{RT}} </math>, a lower activation energy would lend to a fastor rate of reaction, thus the endo product would be formed preferentially. However, it is noted that the endo product has a lower energy than the exo product - this would imply that the endo product is thermodynamically more stable. This is the opposite of what was expected - the exo product is usually the more thermodynamically stable one due to the steric clash present in the endo product. In this case, steric clash is seen in both products. The thermodynamics of the reaction was calculated using B3LYP/6-31G(d) and is given below. The results correspond with what was seen from PM6 above.

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Cyclohexadiene
! Dioxole
! Sum of Reactants
! Endo TS
! Exo TS
! Endo Product
! Exo Product
|-
! <math>\Delta G^o </math>/kJ mol<sup>-1</sup>
| -612591
| -701188
| -1313780
| -1313622
| -1313614
| -1313849
| -1313845
|}

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Reaction Energy /kJ mol<sup>-1</sup>
! Reaction Barrier /kJ mol<sup>-1</sup>
|-
! Endo
| -69
| +158
|-
! Exo
| -65
| +166
|}

Using results from the MO calculations, a MO diagram for the formation of the TS could be plotted. As previously mentioned, only orbitals of the same symmetry can interact with each other.

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 energy level endo cyclohexadiene dioxole.png|center|thumb|400px|'''Figure 11a''': MO diagram for the endo TS. Secondary orbital interactions in red.]]
| [[File:Yx6015 energy level exo cyclohexadiene dioxole.png|center|thumb|400px|'''Figure 11b''': MO diagram for the exo TS.]]
|}

From the MO diagrams, it can be seen that the dienenopphile, 1,3-dioxole, has a HOMO of a higher energy due to electron donation by the oxygens. This reaction is thus an inverse-demand Diels-Alder reaction.

= Exercise 3: Diels-Alder vs Cheletropic =

The reaction between o-xylylene and SO<sub>2</sub> form two different types of bicyclic products - a Diels-Alder product with two six-membered rings, and a cheletropic product with one six-membered ring and one five-membered ring:

[[File:Yx6015 mechanism so2.png|center|thumb|600px|'''Figure 12'''. Arrow-pushing mechanism of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole showing concerted addition.]]

The hallmark of a chelotropic reaction is both bond form reactions happen on the same atom. In this case, both bond formation occur on the sulphur atom. Together with the two stereoisomers from the Diels-Alder reaction, a total of 3 products could be obtained with 3 different reaction paths:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc so2 exo.gif|center|frame|400px|'''Figure 13a''': IRC path for the Diels-Alder reaction resulting in the exo product.]]
| [[File:Yx6015 anim irc so2 endo.gif|center|frame|400px|'''Figure 13b''': IRC path for the Diels-Alder reaction resulting in the endo product.]]
|-
| colspan=2|[[File:Yx6015 anim irc cheletropic.gif|center|frame|400px|'''Figure 13c''': IRC path for the cheletropic reaction.]]
|}

From the IRC animation, it could be seen that the new bonds are formed asynchronously. This is due to the lack of the mirror plane, as could be found in the previous two exercises. However, as symmetry was maintained in the cheletropic reaction, the bonds were formed synchronously.

The energy along the reaction path could be followed in a similar manner:
[[File:Yx6015_energyprofile_so2.png|center|thumb|800px|'''Figure 14''': Energy profile of the reactions along the IRC path. Reactants on the left.]]

(The problem with overlaying IRCs is that they don't exist in the same reference frame. The reaction coordinate is different for all three. Another issue is the IRC gives you the electronic energy when we want the free energies of the stationary points. However it's ok to get a qualitative comparison of the three. [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:14, 16 March 2018 (UTC))

While PM6 was not able to give accurate results for the reactant and product energies, the overall trend in the reactions was clear. As with other Diels-Alder reactions investigated above, the endo TS showed a slightly energy than the exo TS, making the endo TS the kinetic product. The cheletropic product showed significantly higher transition state energies, and may not be readily observed. More accurate results were obtained using B3LYP/6-31G(d):

{| class="wikitable" style="text-align: center; margin: auto;"
|
! o-xylylene
! SO<sub>2</sub>
! Sum of Reactants
! Endo TS
! Exo TS
! Cheletropic TS
! Endo Product
! Exo Product
! Cheletropic Product
|-
! <math>\Delta G^o </math>/kJ mol<sup>-1</sup>
| -812870
| -1440316
| -2253186
| -2253200
| -2253200
| -2253181
| -2253333
| -2253335
| -2253324
|}

{| class="wikitable" style="text-align: center; margin: auto;"
|
! Reaction Energy /kJ mol<sup>-1</sup>
! Reaction Barrier /kJ mol<sup>-1</sup>
|-
! Endo
| -147
| -14
|-
! Exo
| -149
| -14
|-
! Cheletropic
| -138
| +5
|}

(You should definitely not be getting negative barriers! There must be a minimum in between your reactants and TS, or, more likely, your SO2 energy is wrong [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:14, 16 March 2018 (UTC))

Calculation using B3LYP/6-31G(d) show different trend as compared to PM6 previously. The energy TS for the endo and exo products are essentially identical, possibly owing to minimal sterics and interaction due to the small SO<sub>2</sub> size. In addition, they appear below the energy of the reactants. This could be a quirk of the optimization or due to the aromatization energy. However, as expected, the exo product is the most thermodynamic product, with the cheletropic pathway being quite unfavourable. The generated reaction profile is as follow:

[[File:Yx6015 final rxn profile.png|center|thumb|800px|'''Figure 15''': Reaction profile of the reactions.]]

== The ''Other'' Diels-Alder Reaction ==
[[File:Yx6015 mechanism other.png|thumb|300px|'''Figure 16''': Arrow-pushing mechanism for the ''other'' Diels-Alder reaction.]]

The Diels-Alder reaction could also take place at the other pair (non-terminal) of diene to form another two (exo and endo) products. The reactions proceed as below:

{| style="text-align: center; margin: auto;"
|- style="vertical-align:top;"
| [[File:Yx6015 anim irc otherexo.gif|center|frame|400px|'''Figure 17a''': IRC path for the ''other'' Diels-Alder reaction resulting in the exo product.]]
| [[File:Yx6015 anim irc otherendo.gif|center|frame|400px|'''Figure 17b''': IRC path for the ''other'' Diels-Alder reaction resulting in the endo product.]]
|}

Due to the loss of the free energy of aromatization in this reaction, the reaction was expected to be much more unfavourable. The energy from IRC was plotted and compared to the normal positions above:

[[File:Yx6015_energyprofile_other.png|center|thumb|800px|'''Figure 18''': Energy profile of different possible reactions between o-xylylene and SO<sub>2</sub> along the IRC path. Reactants on the left.]]

From the graph, it could be clearly seen that the Diels-Alder reactions at the non-terminal dienes are kinetically much less favourable. Due to the loss in aromaticity, the products are also less thermodynamically stable. As such, Diels-Alder reactions would not happen at this position.

= Conclusion =

Some examples of Diels-Alder reactions were investigated in this experiment. The reaction proceed in a single step with a single transition state, without intermediates. In general, the bond-forming reaction proceed in a synchronous manner. The reaction barrier for the reaction may be reduced through secondary orbital interactions, preferring endo products over exo products where secondary orbital interactions are possible. Additional interactions, such as sterics or aromatization may also promote specific regio or stereoisomers of the Diels-Alder product. The cheletropic reaction was also investigated, and was found to have higher reaction barrier, but produces more stable 5-membered adduct.

= References =

Rep:Zw4415:TSexercise

2018-03-16T15:03:50Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

=Introduction=

===The Transition State===

According to '''Computational Quantum Chemistry''' the reaction coordinate was functionalised by all 3N<sub>atoms</sub>-6 internal coordinates.

Potenyial energy surface describes the energy of a specific system where energy was tabulated by a set of reaction coordinates. [1]

The reactant and product with stationary structure are the minimum points on the potential energy surface.It could be calculated by :

[[File:Zinan_Wang_eq1.png|thumb|center|Equation. 1 [1] ]]

where '''R''' is a set of all internal coordinates and q is normal coordinates which is a linear combination of all internal coordinates.

The transition state is the point with the highest energy along the reaction pathway. The second derivative should be all positive except the one along the reaction coordinate.
Thus it could be calculated as below.
[[File:Zinan_Wang_eq2.png|thumb|center|Equation. 2 [1] ]]
[[File:Zinan_Wang_eq3.png|thumb|center|Equation. 3 [1] ]]

===The computational method===
In this exercise, PM6 and B3LYP/6-31G(d) methods have been used to calculate the optimized structure of the reactants, products and the transition state. PM6 method is generally a faster method to give a rough approximation of the structure. A more precise optimization could be carried out by B3LYP with basis set of 6-31G(d) while it often takes quite a long time.

===Freqrency check===
All the normal modes for stationary structure ,thus the reactants and products, should have positive values as they represent the minimum energy points on the PES.
For all the transition state structures, only 1 negative value should be seen. It is because when calculating from a harmonic oscillator with negative force constant (The negative value of the second derivative along the reaction coordinate), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate the imaginary number (e.g. 526.7i).

===IRC check===
IRC was obtained with the same basis set used to calculate the transition structrue. The gradient of the energy graph (thus the first derivative along the reaction coordinate) shows 0 at the Transition state, reactants and product, which confirms the success of obtaining transition state.

=Exercise 1: Reaction of Butadiene with Ethylene=
In exercise 1, the simplest Diels-Alder reaction between butadiene and ethene was calculated.

The net reaction was visualized by the bond length measurment which represent the change of bond order.

===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level with frequency checked to only have one negative value at around -930.

[[File: Zinan_Wang_EX1_IRC.PNG|thumb|The IRC for optimized transition state|300px]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The MO energy level of both reactant was obtained by Energy calculation using PM6 method. For this specific Diels-Alder reaction between butadiene and ethene with no substituents, the electrons are in normal demand (Diene being electron rich and ethene being electron poor).

The Transition state MO generated by both reactant has higher energy then the HOMO of ethene. That is due to the fact that it is MO for transition state (not the product) which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

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

This is a reaction between cyclohexadiene and 1,3-Dioxole. There are 2 pathways of Diels-Alder reaction, Endo and Exo. For both pathway, reactants, TS and products were approximated using PM6 method then reoptimized by B3LYP method with 6-31G(d) basis set. Frequencies were checked, Gibbs free energies were extracted and MO diagrams were constructed and adjusted.

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy (Hatree)
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===Secondary orbital interactions===

In the endo position, there are 2 oxygen p orbitals from oxygen lone pair which has the silimar energy and same symmetry of the cyclohexadiene LUMO, therefore they would have non-zero overlap integral. This interaction would lower the energy of LUMO producing a stabalising effect for the whole structrue. Thus more thermodynamically favored.

In the exo position, the two orbitals mentioned above were too far apart, thus almost no overlap integral. Moreover, there is a steric clash between the ring structure of 1,3-Dioxole and the half of the ring structure of cyclohexadiene, which rise up the energy of the net structure, thus less stable.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise 3: Diels-Alder vs Cheletropic=

In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.

The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is most thermodynamic favored.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

(Too many significant figures. You need to think about the errors related to to the convergence criteria you are using [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:03, 16 March 2018 (UTC))

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

In this computational lab, 3 pericyclic reactions were investigated. Gaussian was used to optimized the structure of the reactants, products and transition states using either PM6 or B3LYP method with IRC and frequency checked to confirm the transition states. Gibbs free energy was extracted from the log file for each species and the reaction barriers and reaction energies were calculated from them. The kinetic favored pathway were determined by the lowest reaction barrier and thermodynamic favored pathway was determined by the lowest reaction energy.

This computational method could be carried out for more reactions to determine the reaction route under different conditions.

=Reference=

[1] J. J. W. McDouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, The Royal Society of Chemistry, London,
2013, ch. 1, pp. 1-62.

Rep:PS4615 Transition States and Reactivity

2018-03-16T14:49:13Z

Tam10: /* Extension: Electrocyclic reaction */

=Introduction=

In this experiment, the reactivity of different Diels-Alder reactions were explored computationally by carrying out energy calculations of the reactants, products and more importantly the transition states. The two computational methods used are the PM6 (semi-empirical) and B3LYP (Density Functional Theory).

==<i>Potential Energy Surface (PES) and Transition States</i>==

A potential energy surface (PES) describes the potential energy of a system, especially a collection of atoms or molecules, in terms of certain parameters. In this case, the PES describes the potential energy of the system when it is in different geometries. Its dimensionality depends on the number of atoms in the system. Using 3-dimensional cartesian coordinates to describe the position of the atoms in the system, it can be deduced that the dimensionality would be <math>3N</math>. Although, the potential energy, hence the PES does not depend on the absolute position of the atoms, but only their relative positions. As a result, the translational and rotational degrees of freedom (3 each) can be removed from the dimensionality of the PES. As a result, the dimensionality of the PES becomes:

<center><math>3N - 6 </math> <b>(1)</b></center>

where N is the number of atoms in the system.

The most interesting points on PES's are stationary points. A stationary point on a PES is a point with nuclear configuration where all the forces vanish. In other words, it is where every component of the gradient in all directions/dimensions <math>\alpha</math> is zero.

<center><math>\frac{{\delta}V(X)}{{\delta}X_{\alpha}} = 0</math> <b>(2)</b></center>

where <math>V(X)</math> represents the potential energy of a particular coordinate <math>X</math>. <math>\alpha</math> represents a particular dimension in the PES where <math>\alpha \epsilon [3N-6]</math>. The following summarises the three points:

<b>1. Minima</b>: corresponds to stable (global minimum) species or quasi-stable (local minima) species. Examples include the reactants, intermediates and products.

<b>2. Transition states</b>: saddle points which are minimum in all dimensions in the PES except for one, where it is a maximum in that dimension. In other words, the transition state is the true kinetic barrier of a reaction.

<b>3. Higher-order saddle points</b>: a minimum in all dimensions except for <math>n</math> number of dimensions, where <math>n > 1</math>. It is the maximum points in the <math>n</math> dimensions.

At the stationary point, since the first derivative of the potential energy (which is the force) is zero, the leading terms of a Taylor expansion of the potential energy <math>V(Q)</math> at a stationary point <math>M</math>, where <math>Q = X - M</math> are quadratic.

<center><math> V(Q) = \frac{1}{2}\sum^{3N-6}_{\alpha=1}\omega^2_{\alpha}Q^2_{\alpha} + K</math> <b>(3)</b></center>

where <math>Q_{\alpha}</math> represents the <math>\alpha</math> component of <math>Q</math>, <math>\omega_\alpha </math> represents the Hessian eigenvalues of <math>\alpha</math> of <math>Q</math> and <math>K</math> represents the higher order terms in the Taylor expansion (Harmonic Approximation).

The Hessian eigenvalues determine the characteristic of the stationary points. More importantly, the Hessian index, which is the number of negative Hessian eigenvalues, determines whether the stationary point is a minimum, transition state or high order saddle point. It also corresponds to the number of imaginary (negative) vibrational frequencies. For minimum points, the Hessian index is zero. This means all the vibrational frequencies must be positive. On the other hand, a transition state is a stationary point with a Hessian index of 1. This means that the frequency analysis of the transition state must result in one imaginary/negative vibrational frequency. A saddle point has a Hessian index of more than 1, which again can be observed from the output frequencies after running a vibrational analysis.<ref>D. J. Wales, Energy landscapes, Cambridge University Press, Cambridge, UK, 2003, ch. 4</ref>

[[File:PS615_TS_PES.GIF|thumb|center|700px|alt=|<b>Figure 1</b>. The transition state (TS) indicated on a sample PES. MEP stands for the minimum energy path, which in this case is the IRC.<ref>Nino Runeberg, 2018.
</ref>]]

In this experiment, the energies of the reactants, transition states and the products of different pericyclic reactions were computed. The difference between the energy of the reactions' transition state and reactants were used to quantify the kinetic barriers of the reactions. In addition, the minimum energy paths that connect the reactants, transition states and products were visualised to show the reaction coordinate of the reactions (IRC).

==<I>Methods</i>==

Gaussian was used for the computations in this experiment, where GaussView was used as a user interface and visualisation of the molecular orbitals. There are three methods that can be used to compute the transition state geometries and energies of the pericyclic reactions in this experiment. The following outlines the methods available:

<b>Method 1</b>. This method only work for small systems, where a guessed transition state is optimised in one single step with the PM6 method. This only work for simple systems because for complex systems with many atoms, the PES will be very complex with multiple higher order saddle points around the true transition state. It is the fastest method but at the same time the least reliable as the converged structure might actually be a higher order saddle point due to the complex PES.

<b>Method 2</b>. Again, this method requires guessing the transition state structure. Although, the atoms that is involved in the reaction are frozen, with the resulting structure optimised to a minimum before the whole guessed transition state is optimised to find the converged structure. This ensures that the guessed structure is as close to the transition state as possible in the PES, providing the fastest reliable method for computing the geometry of transition states.

<b>Method 3</b>. Compared to the other 2, this method does not require the guessing of the transition state. It is the most reliable method of the three, but take the longest time due to additional steps required. The product or the reactants of the reaction is optimised individually to a minima. This is followed by altering the bond lengths so that the structure resembles the transition state. The atoms involved in the reactions are then frozen like Method 2, optimised to a minimum before being optimised again to get the converged structure.

From earlier, it was mentioned how the PES can be used to determine the geometries and energies of transition states, but not how they can be generated. For very simple systems, the PES can be fitted to experimental data. For more complex and reactive systems, the PES must be generated by quantum mechanical calculations (eg. semi-empirical, DFT, etc).

The <b>Parameterisation Method 6 (PM6)</b> method, which is a semi-emipirical method, is an approximate version of the Hartree-Fock method. Many approximations are made to calculate the Hamiltonian of the Schrodinger equation of the system. Namely, some two-electron and sometimes one-electron integrals are neglected to speed up the computation and reduce the computation cost. To make up for this, empirical parameters are used to make up for these approximations. For the remaining integrals, some are computed exactly, but some are computed using parameters obtained from experiments (hence semi-empirical). This means that the method will work well for systems that experimental parameters are available, but not reliable otherwise.

The <b>B3LYP</b> method used in this experiment is a hybrid method that contains elements from Density Functional Theory (DFT) and Hartree-Fock theory. The 'B3' part specifies the exchange functional (Hartree-Fock) used to run the computation, whereas the 'LYP' specifies the correlation functional (DFT). In other words, it utilises the Hartree-Fock theory to calculate the exchange integral terms in the Hamiltonian. In addition to that, it uses DFT to approximate the correlated motions of electrons in the system. 6-31G basis set was used to model the electronic wavefunctions. Overall, B3LYP carry out calculations more accurately compared to PM6, but takes longer time and computation cost. <ref>J. J. W. McDouall, Computational quantum chemistry: molecular structure and properties in silico, Royal Society of Chemistry, Cambridge, 2013, ch. 1</ref>

=Exercise 1: Reaction of Butadiene with Ethylene=

[[File:Ex1_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 2</b>. The reaction scheme between butadiene and ethylene to make cyclohexene.]]

<b>Corresponding Log files</b>

[[Media:PS4615_1_ETHENE_MIN_OPT_FREQ_PM6.LOG|PS4615_1_ETHENE_MIN_OPT_FREQ_PM6.LOG]]

[[Media:PS4615_1_BUTADIENE_MIN_OPT_FREQ_PM6_AGAIN_BREAK_SYM.LOG|PS4615_1_BUTADIENE_MIN_OPT_FREQ_PM6_AGAIN_BREAK_SYM.LOG]]

[[Media:PS4615_1_CYCLOHEXENE_MIN_PM6.LOG|PS4615_1_CYCLOHEXENE_MIN_PM6.LOG]]

[[Media:PS4615_1_TS_BERNY_PM6_2.LOG|PS4615_1_TS_BERNY_PM6_2.LOG]]

[[Media:PS4615_1_TS_IRC_PM6.LOG|PS4615_1_TS_IRC_PM6.LOG]]

==<i>Transition State MO diagram</i>==

[[File:Exercise_1_MO.png|thumb|center|1000px|alt=|<b>Figure 3</b>. The transition state MO diagram of the reaction. Note that the energies of the MOs are obtained (in Hartrees) from Gaussian.]]

The MO diagram as shown in <b>figure 3</b> was constructed using the MOs from the reactants optimised using Gaussian. In addition, the MOs of the transition state were obtained using <b>Method 3</b>, where they were used to correlate the reactants' MOs that interacted to make up the TS MOs. The MOs obtained from the calculation are shown below in <b>table 1</b>. The symmetry of the MOs were determined by following the steps as described below:

1. Identify a plane of symmetry in the MOs.

2. If the phase of the atomic orbitals on both sides of the plane are the same, then the MO is symmetric (S). If it is in the opposite phase, then it must be antisymmetric (A).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 1</b>. The HOMO and LUMO of butadiene, ethylene and the transition state of the reaction.'''

!Butadiene HOMO

!Butadiene LUMO

!Ethylene HOMO

!Ethylene LUMO

|-

|<jmol>
<jmolApplet>
<color>white</color>
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|-

!'''Transition State HOMO-1'''

!Transition State HOMO

!Transition State LUMO

!Transition State LUMO + 1

|-

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Firstly, the HOMO and LUMO of the transition structure was analysed. It can be seen from the MOs that it is a result of the interaction between the HOMO of the reactant ethylene and LUMO of butadiene, both of which are symmetric. As a result, the transition state MOs must be symmetric. This was further confirmed by carrying the symmetry analysis described on the TS MOs. As for the HOMO-1 and LUMO+1 of the TS, it was determined that they are the result of the interaction between the LUMO of ethylene and HOMO of the butadiene. The reactants' MOs are all antisymmetric, which resulted in antisymmetric HOMO-1 and LUMO+1 of the TS.

From this, it can be concluded that only orbitals with the same symmetry can interact to produce molecular orbitals. Furthermore, it is possible to draw up the conclusion that in order to determine whether the reaction is forbidden or allowed, the MOs of the reactants must be analysed. For an allowed reaction, the orbitals of the reactants must have the same symmetry. On the other hand, if the orbitals of the reactants does not have the same symmetry, the reaction is then said to be forbidden. This can be explained further by considering the overlap integrals <math>S_{AB}</math> of the orbitals. It is a quantitative way of analysing the extent of interaction between the orbitals. For symmetric-symmetric or antisymmetric-antisymmetric orbital interaction, the overall overlap integral is non-zero, leading to two new MOs (the TS MOs in this case). As for antisymmetric-symmetric orbital interaction, the overlap integral is zero leading to no MOs formed.

==<i>Carbon-Carbon Bond Length Analysis</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 2</b>. The Carbon-Carbon bond lengths for the reaction obtained from the calculation.'''
!
! colspan="4" style="text-align: center; font-weight: bold;" | Bond Length (Å)
|-
| style="text-align: center; font-weight: bold;" | C-C Bond
| style="text-align: center; font-weight: bold;" | Butadiene (Reactant)
| style="text-align: center; font-weight: bold;" | Ethylene (Reactant)
| style="text-align: center; font-weight: bold;" | Transition State
| style="text-align: center; font-weight: bold;" | Cyclohexene (Product)
|-
| style="text-align: center; font-weight: bold;" | C1-C2
| style="text-align: center;" | 1.333
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.380
| style="text-align: center;" | 1.491
|-
| style="text-align: center; font-weight: bold;" | C2-C3
| style="text-align: center;" | 1.471
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.411
| style="text-align: center;" | 1.363
|-
| style="text-align: center; font-weight: bold;" | C3-C4
| style="text-align: center;" | 1.333
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.380
| style="text-align: center;" | 1.491
|-
| style="text-align: center; font-weight: bold;" | C4-C5
| style="text-align: center;" | N/A
| style="text-align: center;" | N/A
| style="text-align: center;" | 2.116
| style="text-align: center;" | 1.583
|-
| style="text-align: center; font-weight: bold;" | C5-C6
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.327
| style="text-align: center;" | 1.382
| style="text-align: center;" | 1.560
|-
| style="text-align: center; font-weight: bold;" | C6-C1
| style="text-align: center;" | N/A
| style="text-align: center;" | N/A
| style="text-align: center;" | 2.113
| style="text-align: center;" | 1.583
|}

During the course of the reaction, the different C-C bonds change as it progresses from the reactant to the transition state and finally the product. Firstly, the hybridisation of the carbons in the reactants and products must be discussed to make the explanation easier. It is clear from the reaction scheme that all of the carbons in the reactants are <math>sp^2</math> hybridised. After the reaction has proceeded to the product, the hybridisation of C2 and C3 stays the same, whereas the rest of the carbons changed their hybridisation to <math>sp^3</math>.

The analysis of the hybridisation of the carbons are essentially for identifying the change in the bond lengths. From <b>Table 2</b>, it can seen that C1-C2/ C3-C4 bond lengths (they are the same due to symmetry) changes from 1.333 Å (double bond) to 1.491 Å (<math>sp^{2}-sp^{3}</math> single bond), with the bond length of 1.380 Å for the transition state. One of the reasons why the bond length increases is because the bond length changes from being a double bond to being a single bond. Moreover, the hybridisation of the carbons that make up the bonds changes from being <math>sp^{2}-sp^{2}</math> to <math>sp^{2}-sp^{3}</math>. Having less s-character in the hybridisation increases the bond length, as s-orbital electron densities are closer to the nucleus.

As for C5-C6, the bond changes from 1.327 Å (double bond) to 1.560 Å (<math>sp^{3}-sp^{3}</math> single bond), with the bond length of 1.382 Å for the transition state. Again, the same analysis can be made for the discussion of the changes in the C-C bond lengths. Although, it is worth noting that the C5-C6 bond length is greater than the C1-C2 / C3-C4 bond lengths in product. One possible explanation is that even though both of the bonds has a bond order of 1, the hybridisation of C5-C6 bond is <math>sp^3-sp^3</math>. Hence, there is less s-character in the bond, making it longer. For C2-C3, the bond length changes from 1.471 Å (<math>sp^{2}-sp^{2}</math> single bond) to 1.362 Å (double bond) with the bond length of 1.411 Å for the transition state. For this case, the transition state bond length is observed to be shorter than the reactants compare to the other cases discussed. This is because for this case, instead of the double bonds in the reactant partially breaking (decreasing in electron density) in the transition state, a double bond is partially forming (increasing electron density) here, making the bond length decrease.

As for the new bonds created (C1-C6 and C4-C5), the corresponding bond lengths for both of them is 1.583 Å (<math>sp^{3}-sp^{3}</math> single bond). As for the transition states, the corresponding partially formed bond lengths are 2.113 Å and 2.116 Å for C1-C6 and C4-C5 respectively. This is shorter than Van der Waals radii between two carbons of 3.4 Å (each being 1.7 Å) but at the same time longer than a typical C-C single bond. This indicates that the orbitals in the carbons involved are drawn together, interacting, and about to form new bonds in the transition state.

From this, it can be approximated that the typical bond length for C-C double bonds is 1.3 Å (lit. 1.34 Å), 1.6 Å (lit. 1.54 Å) for <math>sp^{3}-sp^{3}</math> single bonds, and 1.5 Å for <math>sp^{2}-sp^{3}</math>/<math>sp^{2}-sp^{2}</math> single bonds, with <math>sp^{2}-sp^{2}</math> single bonds slightly shorter than <math>sp^{2}-sp^{3}</math> single bonds (lit. 1.50 Å for <math>sp^{2}-sp^{3}</math> and 1.47 Å for <math>sp^{2}-sp^{2}</math>) <ref>Fox, Marye Anne., and James K. Whitesell. Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen. Heidelberg: Spektrum Akademischer Verlag, 1995.</ref>.

==<i>Transition State Vibrations</I>==

[[File:PS4615_IRC_exersize_1.PNG|thumb|center|600px|alt=|<b>Figure 4</b>. The IRC of the reaction.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

!<b>Figure 5</b> shows the vibration of the transition state.
|-
|

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|
|}

By running an IRC calculation, the vibration calculation was confirmed to be successful (see <b>Figure 4</b>). In addition, vibration corresponding to the transition state is illustrated (<b>Figure 5</b>). As described in the introduction, the frequency of this particular vibration of the transition state is negative. From the IRC of the reaction, it can be deduced that the bond formation between terminal carbons in butadiene and ethylene is synchronous, as the bond formation occurred at the same time. Also, it can be seen from the Jmol that the carbons involved in forming the new bonds approach each other at the same time and synchronously. This results in synchronous bond formation.

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

[[File:ex2_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 6</b>. The reaction scheme of the reaction. Note that there are two possible products from the reaction.]]

<b>Corresponding Log files</b>

Reactants:

[[Media:PS4615_2_CYCLOHEXADIENE_MIN_PM6.LOG|PS4615_2_CYCLOHEXADIENE_MIN_PM6.LOG]]

[[Media:PS4615_2_CYCLOHEXADIENE_MIN_B3LYP.LOG|PS4615_2_CYCLOHEXADIENE_MIN_B3LYP.LOG]]

[[Media:PS4615_2_1_3_DIOXOLE_MIN_PM6.LOG|PS4615_2_1_3_DIOXOLE_MIN_PM6.LOG]]

[[Media:PS4615_2_1_3_DIOXOLE_MIN_B3LYP.LOG|PS4615_2_1_3_DIOXOLE_MIN_B3LYP.LOG]]

ENDO TS and products:

[[Media:PS4615_2_TS_BERNY_ENDO_PM6.LOG|PS4615_2_TS_BERNY_ENDO_PM6.LOG]]

[[Media:PS4615_2_TS_BERNY_ENDO_B3LYP.LOG|PS4615_2_TS_BERNY_ENDO_B3LYP.LOG]]

[[Media:PS4615_2_PRODUCT_ENDO_MIN_PM6.LOG|PS4615_2_PRODUCT_ENDO_MIN_PM6.LOG]]

[[Media:PS4615_2_PRODUCT_ENDO_MIN_B3LYP.LOG|PS4615_2_PRODUCT_ENDO_MIN_B3LYP.LOG]]

[[Media:PS4615_2_TS_IRC_ENDO_PM6.LOG|PS4615_2_TS_IRC_ENDO_PM6.LOG]]

EXO TS and products:

[[Media:PS4615_2_TS_BERNY_EXO_PM6.LOG|PS4615_2_TS_BERNY_EXO_PM6.LOG]]

[[Media:PS4615_2_TS_BERNY_EXO_B3LYP.LOG|PS4615_2_TS_BERNY_EXO_B3LYP.LOG]]

[[Media:PS4615_2_PRODUCT_EXO_MIN_PM6.LOG|PS4615_2_PRODUCT_EXO_MIN_PM6.LOG]]

[[Media:PS4615_2_PRODUCT_EXO_MIN_B3LYP.LOG|PS4615_2_PRODUCT_EXO_MIN_B3LYP.LOG]]

[[Media:PS4615_2_TS_EXO_IRC_PM6.LOG|PS4615_2_TS_EXO_IRC_PM6.LOG]]

==<i>Transition State MO Diagram and Analysis</i>==

[[File:PS4615_Ex2MO_ENDO.png|thumb|center|600px|alt=|<b>Figure 7</b>. The transition state MO diagram of the reaction (ENDO). Note that the energies of the MOs are obtained (in Hartree) from Gaussian.]]
[[File:PS4615_Ex2ExoMO.png|thumb|center|600px|alt=|<b>Figure 8</b>. The transition state MO diagram of the reaction (EXO). Note that the energies of the MOs are obtained (in Hartree) from Gaussian.]]

<b>Figure 7</b> illustrates the molecular orbital diagram of the transition states for the Diels-Alder reaction. The MO diagrams were constructed by carrying out the same analysis on the relevant MOs of the reaction's transition states (see <b>table 3</b> for the MOs of the transition states). Again, it was observed that MOs that has the same symmetry interact to form the TS MOs. It can be seen that for each case, the overall energy of the transition state for the ENDO case is lower compared to the transition state for the EXO product. Qualitatively speaking, this indicates that the kinetic barrier/activation energy for the EXO case is higher, resulting in the pathway being kinetically stable compared to the ENDO pathway. A more quantitative analysis is discussed in the <I>Thermochemistry</I> section below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 3</b>. The relevant molecular orbitals of the transition states of the Diels-Alder reaction.'''

!TS ENDO HOMO-1

!TS ENDO HOMO

!TS ENDO LUMO

!TS ENDO LUMO+1

|-

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!'''TS ENDO HOMO-1'''

!TS ENDO HOMO

!TS ENDO LUMO

!TS ENDO LUMO+1

|-

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Diels-Alder reactions such as this case can be classified as either normal or inverse electron-demand. For a qualitative analysis, it can be said that for a normal electron-demand Diels-Alder reaction, the diene is electron rich whereas the dienophile is electron deficient. On the other hand, the diene is required to be electron deficient, where the dienophile is electron rich for an inverse electron-demand Diels-Alder reaction. For a more quantitative analysis, whether the reaction is normal or inverse electron-demand depends on the relative energies of the HOMO and LUMO of the reactants involved in the reaction. For a normal electron-demand reaction, the HOMO and LUMO of the dienophile is lower in energy compared to the respective HOMO and LUMO of the diene. As a result, there is a strong interaction between the HOMO of the diene and the LUMO of the dienenophile as they have similar energies, forming the HOMO and LUMO of the product. An example of this is the Diels-Alder reaction in Exercise 1 (see <b>figure 3</b> for the MO diagram). For an inverse electron-demand reaction, the HOMO and LUMO of the dienophile is higher in energy compared to the respective HOMO and LUMO of the diene. For this case, the HOMO of the dienophile and LUMO of the diene interact strongly to produce the HOMO and LUMO of the product. For the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the reaction is an inverse electron-demand reaction, with explanations as described above. One of the reasons why the HOMO and LUMO of the dienophile has such high energies, surpassing the MOs of the diene, is because of the electron donating effect of the two oxygens next to the alkene, raising the energy of MOs of the dienophile. <b>Figure 9</b> illustrates the inverse electron-demand characteristic of the (ENDO) reaction nicely, with the energies of the product MOs calculated by running an optimisation on the product structure (B3LYP).

[[File:PS4615_Ex2MO_ENDO_product_INV.png|thumb|center|600px|alt=|<b>Figure 9</b>. A simplified MO diagram (ENDO product) illustrating the inverse electron demand nature of the reaction.]]

==<i>Thermochemistry</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 4</b> The table shows activation energies and the Gibbs free energies of the ENDO and EXO Diels-Alder reaction.'''
! style="text-align: center;" |
! style="text-align: center; font-weight: bold;" | Activation Energy / <math>kJmol^{-1}</math>
! style="text-align: center; font-weight: bold;" | Gibbs Free Energy / <math>kJmol^{-1}</math>
|-
| style="text-align: center; font-weight: bold;" | ENDO
| style="text-align: center;" | +159.8
| style="text-align: center;" | -67.4
|-
| style="text-align: center; font-weight: bold;" | EXO
| style="text-align: center;" | +167.7
| style="text-align: center;" | -63.8
|}

From <b>table 4</b>, it can be seen that the ENDO pathway has a lower activation energy compared to the EXO pathway, making it kinetically favourable. This is because the HOMO of the ENDO transition state is further stabilised by secondary orbital interactions. From <b>table 5</b>, it can be seen that the p orbitals on the oxygens of the dienophile interacts with the delocalised π orbitals on the diene, which has a stabilising effect on the transition state. Secondary orbital interaction is absent in the EXO pathway, as transition state does not have the correct geometry for it. This makes the energy of the ENDO transition state lower than that of the EXO pathway, making it kinetically favoured.

In addition, the ENDO pathway is more exothermic compared to the EXO pathway, making it the thermodynamically favoured compared to the other pathway. As a result, this makes the ENDO product thermodynamically more stable than the EXO product. Secondary orbital interactions within the ENDO product is one of the factors that make the energy of the ENDO product lower than the EXO product. This is the same interaction as described above, with the EXO product lacking in the stabilising interaction due to its geometry. Furthermore, unfavourable steric interactions between the dioxole group and the ethylene bridgehead in the EXO product may have played a significant role in increasing its energy, making it less exothermic. This effect is likely to be less significant for the ENDO product, as the dioxole is closest to the saturated bridgehead, resulting in less interaction with the hydrogen atoms (see <b>table 6</b> for illustration).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 5</b> The table shows the HOMO of the transition states with the isovalue set to 0.01 to show secondary orbital interactions.'''

!TS ENDO HOMO

!TS EXO HOMO

|-

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{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 6</b> The table shows the steric interactions in the ENDO and EXO product.'''

!ENDO product

!EXO product

|-

|[[File:PS4615_Sterics_ENDO_product.png|500px]]|
|[[File:PS4615_Sterics_EXO_product.png|500px]]|

|}

=Exercise 3: Diels-Alder vs Cheletropic=

[[File:PS4615_ex3_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 10</b>. The reaction scheme of the reaction. Note that there are two possible reaction pathways, including Diels-ALder and Cheletropic.]]

<b>Corresponding Log files</b>

Reactants:

[[Media:PS4615_3_REACTANT_DIENE_MIN_PM6.LOG|PS4615_3_REACTANT_DIENE_MIN_PM6.LOG]]

[[Media:PS4615_3_REACTANT_SO2_MIN_PM6.LOG|PS4615_3_REACTANT_SO2_MIN_PM6.LOG]]

Diels-Alder ENDO TS and products:

[[Media:PS4615_3_DA_TS_BERNY_ENDO_PM6.LOG|PS4615_3_DA_TS_BERNY_ENDO_PM6.LOG]]

[[Media:PS4615_3_DA_TS_IRC_ENDO_PM6.LOG|PS4615_3_DA_TS_IRC_ENDO_PM6.LOG]]

[[Media:PS4615_3_DA_PRODUCT_MIN_ENDO_PM6.LOG|PS4615_3_DA_PRODUCT_MIN_ENDO_PM6.LOG]]

Diels-Alder EXO TS and products:

[[Media:PS4615_3_DA_EXO_TS_BERNY_PM6.LOG|PS4615_3_DA_EXO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_DA_EXO_TS_IRC_PM6.LOG|PS4615_3_DA_EXO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_DA_EXO_PRODUCT_MIN_PM6.LOG|PS4615_3_DA_EXO_PRODUCT_MIN_PM6.LOG]]

Cheletropic TS and products:

[[Media:PS4615_3_CHELETROPIC_TS_BERNY_PM6.LOG|PS4615_3_CHELETROPIC_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_CHELETROPIC_TS_IRC_PM6.LOG|PS4615_3_CHELETROPIC_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_CHELETROPIC_PRODUCT_MIN_PM6.LOG|PS4615_3_CHELETROPIC_PRODUCT_MIN_PM6.LOG]]

Alternative Diels-Alder ENDO TS and products:

[[Media:PS4615_3_ALT_DA_ENDO_TS_BERNY_PM6.LOG|PS4615_3_ALT_DA_ENDO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_ENDO_TS_IRC_PM6.LOG|PS4615_3_ALT_DA_ENDO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_ENDO_PRODUCT_MIN_PM6.LOG|PS4615_3_ALT_DA_ENDO_PRODUCT_MIN_PM6.LOG]]

Alternative Diels-Alder EXO TS and products:

[[Media:PS4615_3_ALT_DA_EXO_TS_BERNY_PM6.LOG|PS4615_3_ALT_DA_EXO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_EXO_TS_IRC_PM6.LOG|PS4615_3_ALT_DA_EXO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_EXO_PRODUCT_MIN_PM6.LOG|PS4615_3_ALT_DA_EXO_PRODUCT_MIN_PM6.LOG]]

==<i>IRC</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 7</b> The table shows the different IRC of the Diels-Alder and Cheletropic reaction. Note that the IRC of the Diels-Alder EXO IRC is in the opposite direction.'''

!Diels-Alder ENDO IRC

!Diels-Alder EXO IRC

!Cheletropic IRC

!Alternative Diels-Alder ENDO IRC

!Alternative Diels-Alder EXO IRC

|-

|[[File:PS4615_endo_DA_IRC.png|400px]]|
|[[File:PS4615_exo_DA_IRC.png|400px]]|
|[[File:PS4615_cheletropic_IRC.png|400px]]|
|[[File:PS4615_ALT_endo_DA_IRC.png|400px]]|
|[[File:PS4615_ALT_exo_DA_IRC.png|400px]]|

|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 8</b> visualises the IRC path of the Diels-Alder and Cheletropic reactions. Click on the links to see the animations.'''

!Diels-Alder ENDO IRC

!Diels-Alder EXO IRC

!Cheletropic IRC

!Alternative Diels-Alder ENDO IRC

!Alternative Diels-Alder EXO IRC

|-

|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ENDO_DA_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_EXO_DA_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_cheletropic_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ALT_ENDO_DA_IRC_movie_NEW.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ALT_EXO_DA_IRC_movie_NEW.gif]]|

|}

<b>Table 7</b> and <b>table 8</b> Shows the IRC (described in the Introduction section) of the reaction pathways of this exercise, including the movie file links that illustrates the nature of bond formations of the pathways. From the movies, it can be seen that all the Diels-Alder reaction pathways (including the reaction at the high energy site) form new bonds asynchronously. On the other hand, the bond formation of the cheletropic pathway is synchronous. It is worth noting that xylylene is an extremely reactive species, as it is only one oxidation state away from forming a 6-membered aromatic ring. In fact, this can be seen during the reaction of xylylene with sulphur dioxide (see the IRC animation), where the ring becomes aromatised when transition states are formed. This is not the case for the alternative pathway at the inner diene site, resulting in the reaction being highly unfavourable.

==<i>Thermochemistry</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 9</b> shows the activation energies and Gibbs free energies of the different reaction pathways.'''

!
! style="text-align: center; font-weight: bold;" | Activation Energy / <math>kJmol^{-1}</math>
! style="font-weight: bold;" | Gibbs Free Energy / <math>kJmol^{-1}</math>
|-
| style="text-align: center; font-weight: bold;" | DA ENDO
| style="text-align: center;" | +84.4
| style="text-align: center;" | -96.4
|-
| style="text-align: center; font-weight: bold;" | DA EXO
| style="text-align: center;" | +88.4
| style="text-align: center;" | -97.0
|-
| style="text-align: center; font-weight: bold;" | Cheletropic
| style="text-align: center;" | +106.7
| style="text-align: center;" | -153.4
|-
| style="text-align: center; font-weight: bold;" | Alternative DA ENDO
| style="text-align: center;" | +114.7
| style="text-align: center;" | +18.9
|-
| style="text-align: center; font-weight: bold;" | Alternative DA EXO
| style="text-align: center;" | +122.5
| style="text-align: center;" | +23.4
|}

(This is really a change in free energy. Best to just call it a reaction energy [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:42, 16 March 2018 (UTC))

[[File:PS4615_3_energy_diagram_FULL.png|thumb|center|1000px|alt=|<b>Figure 11</b>. The energy diagram illustrating the relative activation energies and Gibbs free energies of the Diels-Alder and Cheletropic reaction.]]

From <b>figure 11</b>, it can be seen that out of all the reaction pathways (excluding the alternative Diels-Alder), the cheletropic pathway has the greatest activation energy, making it the most kinetically stable compared to the other 2 pathways. One of the possible explanation for this is the fact that the reaction forms a new 5-membered ring, compared to 6-membered rings for the other pathways. The ring strain in the 5-membered ring raises the energy of the transition state, raising its activation energy. Even though it is the most kinetically inert compared to the other three, the cheletropic path is the most thermodynamically favourable, as it is the most exothermic pathway (most negative Gibbs free energy of reaction). This is because of the stabilisation of the product by the 2 strong S=O bonds (bond enthalpy of 518 kJ/mol each <ref>Luo, Yu-Ran. Comprehensive handbook of chemical bond energies. Boca Raton, Fla.: CRC Press, 2007.
</ref>) compared to only one S=O and one S-O (S-O contributes 348 kJ/mol <ref>Cottrell, T. L. The strengths of chemical bonds. New York: Academic Press, 1961.
</ref>) in the Diels-Alder products. The two S=O bonds has a much greater effect than the ring strain in the 5-membered ring, making it the most exothermic reaction of the three.

Contrarily, the ENDO Diels-Alder pathway has the lowest activation energy, making it the fastest kinetically compared to the other two paths. This is due to the stabilisation of the transition state by secondary orbital interactions (similar to Exercise 2 case). This involves the interaction between the p orbital of the oxygen in sulphur dioxide and the delocalised π orbitals of xylylene. This is not possible for the EXO case as it does not have the correct geometry for the interaction, making its activation energy higher (but still lower than cheletropic path) than the ENDO transition state. Due to steric repulsions between the oxygen in the S=O and the rest of the molecule, the ENDO product energy is slightly above the EXO product. This makes the EXO path more thermodynamically favourable than the ENDO pathway, as it is slightly more exothermic. If the reaction is carried out under equilibrating conditions, the cheletropic product will be the major product of the reaction between sulphur dioxide and xylylene, as it is the most thermonamically favourable pathway.

The energy diagram (<b>figure 11</b>) shows that the alternative Diels-Alder reaction at the inner site is both thermodynamically and kinetically unfavourable. Firstly, the activation energy of the reaction is greater than any of the pathways described before. The reactions (EXO and ENDO) are endothermic, which means that they require energy to convert from reactants to product overall. The ENDO product here is both the kinetic and thermodynamic product compared to the EXO case. The transition states for this alternative pathway is higher in energy than the preferred path because it lacks the aromatic ring formed at the 6-membered ring. This also explains the why the reaction is endothermic, as the products does not have the aromatic 6-membered ring in it like the normal Diels-Alder and cheletropic products.

=Extension: Electrocyclic reaction=

[[File:Ext_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 12</b>. The reaction scheme of the electrocyclic reaction of cyclobutene.]]

<b>Corresponding Log Files</b>

[[Media:PS4615_EXT_CYCLOBUTENE_MIN_PM6.LOG|PS4615_EXT_CYCLOBUTENE_MIN_PM6.LOG]]

[[Media:PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG|PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG]]

[[Media:PS4615_EXT_TS_BERNY_PM6.LOG|PS4615_EXT_TS_BERNY_PM6.LOG]]

[[Media:PS4615_EXT_TS_BERNY_B3LYP.LOG|PS4615_EXT_TS_BERNY_B3LYP.LOG]]

[[Media:PS4615_EXT_TS_IRC_PM6.LOG|PS4615_EXT_TS_IRC_PM6.LOG]]

[[Media:PS4615_EXT_PRODUCT_B3LYP.LOG|PS4615_EXT_PRODUCT_B3LYP.LOG]]

In this extension, the thermal electrocyclic ring opening of the molecule shown in the reaction scheme above was studied. Since electrocyclic reactions is a class of a pericyclic reaction, the stereochemistry of the product can be determined using the Woodward-Hoffman rules. From this, it was determined that the reaction undergoes conrotatory electrocyclic ring opening, which agrees with the calculations carried out using B3LYP (see the animation in <b>table 10</b> and the vibrations of the transition state at <b>figure 13</b>). The activation energy of the reaction was found to be <math> +122.4 kJmol^{-1} </math>, with the Gibbs free energy of the reaction at <math>-64.1 kJmol^{-1}</math>. This shows that the reaction has a significantly high activation energy, making it kinetically inert. One possible explanation to this is the raise in the TS energy due to steric interactions between the bulky methyl ester groups during the transition from the reactant to product (see animations). Since the reaction is significantly exothermic, the reaction is considered thermodynamically favourable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

!<b>Figure 13</b> shows the vibration of the transition state.
|-
|

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size><align>centre</align>
<uploadedFileContents>PS4615_EXT_TS_BERNY_B3LYP.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 29; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>EXT_TS_VIBRATION</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>EXT_TS_VIBRATION</target>
</jmolbutton>
</jmol>

|
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 10</b> shows the IRC of the reaction, where the movie shows that the reaction is conrotatory.'''

!The reaction's IRC

|-

|[[File:PS4615_EXT_IRC.png|400px]]|

|-

!IRC movie. Click on the link for movie.

|-

|[[https://wiki.ch.ic.ac.uk/wiki/images/d/d1/PS4615_EXT_IRC_movie.gif]]|

|}

It is clear from the animations and the transition state vibrations that the reaction is a conrotatory electrocyclic ring opening. Aside from using the Woodward-Hoffmann rules, this can be determined and illustrated by looking the the HOMO of the reactants and products (see <b>table 11</b>). From the HOMO of the product, it can be seen that the only way that the reaction can proceed (working backwards) is through antarafacial interactions of the MOs at the terminal carbons, as this is the only way to achieve constructive interaction between the orbitals. In terms of the symmetry (when considering just the diene fragment), the HOMO is asymmetric. By following through with the reaction to the reactants, it can be seen that the terminal carbons rotate in the same direction to form the cyclobutene. This is illustrated in the in <b>figure 14</b>.

[[File:PS4615_EXT_orbitals_interaction_NEW.png|thumb|center|600px|alt=|<b>Figure 14</b>. This illustrates the Frontier orbital (HOMO) approach to determining the stereochemistry of the reaction.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 11</b>. The relevant molecular orbitals of the reaction.'''

!Cyclobutene HOMO

!Transition state HOMO

!Product HOMO

|-

|<jmol>
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|-

!Cyclobutene LUMO

!Transition state LUMO

!Product LUMO

|-

|<jmol>
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</jmolApplet>
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|-
|}

(It is actually the HOMO-1 in the TS that has the orbitals that you are looking for [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:49, 16 March 2018 (UTC))

=Conclusion=

In this experiment, a semi-empirical method PM6 and a hybrid method B3LYP were used to calculate the geometries and vibrations of 4 different transition states of 4 different pericyclic reactions successfully. Method three was used for all of the calculations, as it is the most accurate method out of the three. Starting with the first exercise, the C-C bond lengths involved in the reaction were analysed as the reaction progresses from the reactants, to the transition states and finally the product. It was also found that the bond formation is synchronous, which is not the case for the reactions in exercise 3. The activation energies and Gibbs free energies of the ENDO and EXO Diels-Alder reactions were calculated in exercise 2 up to the B3LYP level of accuracy. The relevant MOs were visualised to qualitatively show the effect of secondary orbital interactions and steric repulsions on the thermochemistry of the reactions. From the energies of the relavant MOs, it was proven that the Diels-Alder reaction in exercise 2 is an inverse electron-demand reaction. As for exercise 3, the different reaction paths were investigated for the reaction between sulphur dioxide and xylylene. It was found that the most thermodynamically favourable pathway is the Cheletropic path, whereas the ENDO Diels-Alder reaction path is the most kinetically driven. Lastly, calculations up to B3LYP level of accuracy for a thermal electrocyclic ring opening of cyclobutene was carried out. The IRC animation and the transition state vibrations showed that the reaction is conrotatory, which is in agreement with the Woodward-Hoffmann rules.

=Bibliography=

Rep:PS4615 Transition States and Reactivity

2018-03-16T14:42:41Z

Tam10: /* Thermochemistry */

=Introduction=

In this experiment, the reactivity of different Diels-Alder reactions were explored computationally by carrying out energy calculations of the reactants, products and more importantly the transition states. The two computational methods used are the PM6 (semi-empirical) and B3LYP (Density Functional Theory).

==<i>Potential Energy Surface (PES) and Transition States</i>==

A potential energy surface (PES) describes the potential energy of a system, especially a collection of atoms or molecules, in terms of certain parameters. In this case, the PES describes the potential energy of the system when it is in different geometries. Its dimensionality depends on the number of atoms in the system. Using 3-dimensional cartesian coordinates to describe the position of the atoms in the system, it can be deduced that the dimensionality would be <math>3N</math>. Although, the potential energy, hence the PES does not depend on the absolute position of the atoms, but only their relative positions. As a result, the translational and rotational degrees of freedom (3 each) can be removed from the dimensionality of the PES. As a result, the dimensionality of the PES becomes:

<center><math>3N - 6 </math> <b>(1)</b></center>

where N is the number of atoms in the system.

The most interesting points on PES's are stationary points. A stationary point on a PES is a point with nuclear configuration where all the forces vanish. In other words, it is where every component of the gradient in all directions/dimensions <math>\alpha</math> is zero.

<center><math>\frac{{\delta}V(X)}{{\delta}X_{\alpha}} = 0</math> <b>(2)</b></center>

where <math>V(X)</math> represents the potential energy of a particular coordinate <math>X</math>. <math>\alpha</math> represents a particular dimension in the PES where <math>\alpha \epsilon [3N-6]</math>. The following summarises the three points:

<b>1. Minima</b>: corresponds to stable (global minimum) species or quasi-stable (local minima) species. Examples include the reactants, intermediates and products.

<b>2. Transition states</b>: saddle points which are minimum in all dimensions in the PES except for one, where it is a maximum in that dimension. In other words, the transition state is the true kinetic barrier of a reaction.

<b>3. Higher-order saddle points</b>: a minimum in all dimensions except for <math>n</math> number of dimensions, where <math>n > 1</math>. It is the maximum points in the <math>n</math> dimensions.

At the stationary point, since the first derivative of the potential energy (which is the force) is zero, the leading terms of a Taylor expansion of the potential energy <math>V(Q)</math> at a stationary point <math>M</math>, where <math>Q = X - M</math> are quadratic.

<center><math> V(Q) = \frac{1}{2}\sum^{3N-6}_{\alpha=1}\omega^2_{\alpha}Q^2_{\alpha} + K</math> <b>(3)</b></center>

where <math>Q_{\alpha}</math> represents the <math>\alpha</math> component of <math>Q</math>, <math>\omega_\alpha </math> represents the Hessian eigenvalues of <math>\alpha</math> of <math>Q</math> and <math>K</math> represents the higher order terms in the Taylor expansion (Harmonic Approximation).

The Hessian eigenvalues determine the characteristic of the stationary points. More importantly, the Hessian index, which is the number of negative Hessian eigenvalues, determines whether the stationary point is a minimum, transition state or high order saddle point. It also corresponds to the number of imaginary (negative) vibrational frequencies. For minimum points, the Hessian index is zero. This means all the vibrational frequencies must be positive. On the other hand, a transition state is a stationary point with a Hessian index of 1. This means that the frequency analysis of the transition state must result in one imaginary/negative vibrational frequency. A saddle point has a Hessian index of more than 1, which again can be observed from the output frequencies after running a vibrational analysis.<ref>D. J. Wales, Energy landscapes, Cambridge University Press, Cambridge, UK, 2003, ch. 4</ref>

[[File:PS615_TS_PES.GIF|thumb|center|700px|alt=|<b>Figure 1</b>. The transition state (TS) indicated on a sample PES. MEP stands for the minimum energy path, which in this case is the IRC.<ref>Nino Runeberg, 2018.
</ref>]]

In this experiment, the energies of the reactants, transition states and the products of different pericyclic reactions were computed. The difference between the energy of the reactions' transition state and reactants were used to quantify the kinetic barriers of the reactions. In addition, the minimum energy paths that connect the reactants, transition states and products were visualised to show the reaction coordinate of the reactions (IRC).

==<I>Methods</i>==

Gaussian was used for the computations in this experiment, where GaussView was used as a user interface and visualisation of the molecular orbitals. There are three methods that can be used to compute the transition state geometries and energies of the pericyclic reactions in this experiment. The following outlines the methods available:

<b>Method 1</b>. This method only work for small systems, where a guessed transition state is optimised in one single step with the PM6 method. This only work for simple systems because for complex systems with many atoms, the PES will be very complex with multiple higher order saddle points around the true transition state. It is the fastest method but at the same time the least reliable as the converged structure might actually be a higher order saddle point due to the complex PES.

<b>Method 2</b>. Again, this method requires guessing the transition state structure. Although, the atoms that is involved in the reaction are frozen, with the resulting structure optimised to a minimum before the whole guessed transition state is optimised to find the converged structure. This ensures that the guessed structure is as close to the transition state as possible in the PES, providing the fastest reliable method for computing the geometry of transition states.

<b>Method 3</b>. Compared to the other 2, this method does not require the guessing of the transition state. It is the most reliable method of the three, but take the longest time due to additional steps required. The product or the reactants of the reaction is optimised individually to a minima. This is followed by altering the bond lengths so that the structure resembles the transition state. The atoms involved in the reactions are then frozen like Method 2, optimised to a minimum before being optimised again to get the converged structure.

From earlier, it was mentioned how the PES can be used to determine the geometries and energies of transition states, but not how they can be generated. For very simple systems, the PES can be fitted to experimental data. For more complex and reactive systems, the PES must be generated by quantum mechanical calculations (eg. semi-empirical, DFT, etc).

The <b>Parameterisation Method 6 (PM6)</b> method, which is a semi-emipirical method, is an approximate version of the Hartree-Fock method. Many approximations are made to calculate the Hamiltonian of the Schrodinger equation of the system. Namely, some two-electron and sometimes one-electron integrals are neglected to speed up the computation and reduce the computation cost. To make up for this, empirical parameters are used to make up for these approximations. For the remaining integrals, some are computed exactly, but some are computed using parameters obtained from experiments (hence semi-empirical). This means that the method will work well for systems that experimental parameters are available, but not reliable otherwise.

The <b>B3LYP</b> method used in this experiment is a hybrid method that contains elements from Density Functional Theory (DFT) and Hartree-Fock theory. The 'B3' part specifies the exchange functional (Hartree-Fock) used to run the computation, whereas the 'LYP' specifies the correlation functional (DFT). In other words, it utilises the Hartree-Fock theory to calculate the exchange integral terms in the Hamiltonian. In addition to that, it uses DFT to approximate the correlated motions of electrons in the system. 6-31G basis set was used to model the electronic wavefunctions. Overall, B3LYP carry out calculations more accurately compared to PM6, but takes longer time and computation cost. <ref>J. J. W. McDouall, Computational quantum chemistry: molecular structure and properties in silico, Royal Society of Chemistry, Cambridge, 2013, ch. 1</ref>

=Exercise 1: Reaction of Butadiene with Ethylene=

[[File:Ex1_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 2</b>. The reaction scheme between butadiene and ethylene to make cyclohexene.]]

<b>Corresponding Log files</b>

[[Media:PS4615_1_ETHENE_MIN_OPT_FREQ_PM6.LOG|PS4615_1_ETHENE_MIN_OPT_FREQ_PM6.LOG]]

[[Media:PS4615_1_BUTADIENE_MIN_OPT_FREQ_PM6_AGAIN_BREAK_SYM.LOG|PS4615_1_BUTADIENE_MIN_OPT_FREQ_PM6_AGAIN_BREAK_SYM.LOG]]

[[Media:PS4615_1_CYCLOHEXENE_MIN_PM6.LOG|PS4615_1_CYCLOHEXENE_MIN_PM6.LOG]]

[[Media:PS4615_1_TS_BERNY_PM6_2.LOG|PS4615_1_TS_BERNY_PM6_2.LOG]]

[[Media:PS4615_1_TS_IRC_PM6.LOG|PS4615_1_TS_IRC_PM6.LOG]]

==<i>Transition State MO diagram</i>==

[[File:Exercise_1_MO.png|thumb|center|1000px|alt=|<b>Figure 3</b>. The transition state MO diagram of the reaction. Note that the energies of the MOs are obtained (in Hartrees) from Gaussian.]]

The MO diagram as shown in <b>figure 3</b> was constructed using the MOs from the reactants optimised using Gaussian. In addition, the MOs of the transition state were obtained using <b>Method 3</b>, where they were used to correlate the reactants' MOs that interacted to make up the TS MOs. The MOs obtained from the calculation are shown below in <b>table 1</b>. The symmetry of the MOs were determined by following the steps as described below:

1. Identify a plane of symmetry in the MOs.

2. If the phase of the atomic orbitals on both sides of the plane are the same, then the MO is symmetric (S). If it is in the opposite phase, then it must be antisymmetric (A).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 1</b>. The HOMO and LUMO of butadiene, ethylene and the transition state of the reaction.'''

!Butadiene HOMO

!Butadiene LUMO

!Ethylene HOMO

!Ethylene LUMO

|-

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|-

!'''Transition State HOMO-1'''

!Transition State HOMO

!Transition State LUMO

!Transition State LUMO + 1

|-

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Firstly, the HOMO and LUMO of the transition structure was analysed. It can be seen from the MOs that it is a result of the interaction between the HOMO of the reactant ethylene and LUMO of butadiene, both of which are symmetric. As a result, the transition state MOs must be symmetric. This was further confirmed by carrying the symmetry analysis described on the TS MOs. As for the HOMO-1 and LUMO+1 of the TS, it was determined that they are the result of the interaction between the LUMO of ethylene and HOMO of the butadiene. The reactants' MOs are all antisymmetric, which resulted in antisymmetric HOMO-1 and LUMO+1 of the TS.

From this, it can be concluded that only orbitals with the same symmetry can interact to produce molecular orbitals. Furthermore, it is possible to draw up the conclusion that in order to determine whether the reaction is forbidden or allowed, the MOs of the reactants must be analysed. For an allowed reaction, the orbitals of the reactants must have the same symmetry. On the other hand, if the orbitals of the reactants does not have the same symmetry, the reaction is then said to be forbidden. This can be explained further by considering the overlap integrals <math>S_{AB}</math> of the orbitals. It is a quantitative way of analysing the extent of interaction between the orbitals. For symmetric-symmetric or antisymmetric-antisymmetric orbital interaction, the overall overlap integral is non-zero, leading to two new MOs (the TS MOs in this case). As for antisymmetric-symmetric orbital interaction, the overlap integral is zero leading to no MOs formed.

==<i>Carbon-Carbon Bond Length Analysis</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 2</b>. The Carbon-Carbon bond lengths for the reaction obtained from the calculation.'''
!
! colspan="4" style="text-align: center; font-weight: bold;" | Bond Length (Å)
|-
| style="text-align: center; font-weight: bold;" | C-C Bond
| style="text-align: center; font-weight: bold;" | Butadiene (Reactant)
| style="text-align: center; font-weight: bold;" | Ethylene (Reactant)
| style="text-align: center; font-weight: bold;" | Transition State
| style="text-align: center; font-weight: bold;" | Cyclohexene (Product)
|-
| style="text-align: center; font-weight: bold;" | C1-C2
| style="text-align: center;" | 1.333
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.380
| style="text-align: center;" | 1.491
|-
| style="text-align: center; font-weight: bold;" | C2-C3
| style="text-align: center;" | 1.471
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.411
| style="text-align: center;" | 1.363
|-
| style="text-align: center; font-weight: bold;" | C3-C4
| style="text-align: center;" | 1.333
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.380
| style="text-align: center;" | 1.491
|-
| style="text-align: center; font-weight: bold;" | C4-C5
| style="text-align: center;" | N/A
| style="text-align: center;" | N/A
| style="text-align: center;" | 2.116
| style="text-align: center;" | 1.583
|-
| style="text-align: center; font-weight: bold;" | C5-C6
| style="text-align: center;" | N/A
| style="text-align: center;" | 1.327
| style="text-align: center;" | 1.382
| style="text-align: center;" | 1.560
|-
| style="text-align: center; font-weight: bold;" | C6-C1
| style="text-align: center;" | N/A
| style="text-align: center;" | N/A
| style="text-align: center;" | 2.113
| style="text-align: center;" | 1.583
|}

During the course of the reaction, the different C-C bonds change as it progresses from the reactant to the transition state and finally the product. Firstly, the hybridisation of the carbons in the reactants and products must be discussed to make the explanation easier. It is clear from the reaction scheme that all of the carbons in the reactants are <math>sp^2</math> hybridised. After the reaction has proceeded to the product, the hybridisation of C2 and C3 stays the same, whereas the rest of the carbons changed their hybridisation to <math>sp^3</math>.

The analysis of the hybridisation of the carbons are essentially for identifying the change in the bond lengths. From <b>Table 2</b>, it can seen that C1-C2/ C3-C4 bond lengths (they are the same due to symmetry) changes from 1.333 Å (double bond) to 1.491 Å (<math>sp^{2}-sp^{3}</math> single bond), with the bond length of 1.380 Å for the transition state. One of the reasons why the bond length increases is because the bond length changes from being a double bond to being a single bond. Moreover, the hybridisation of the carbons that make up the bonds changes from being <math>sp^{2}-sp^{2}</math> to <math>sp^{2}-sp^{3}</math>. Having less s-character in the hybridisation increases the bond length, as s-orbital electron densities are closer to the nucleus.

As for C5-C6, the bond changes from 1.327 Å (double bond) to 1.560 Å (<math>sp^{3}-sp^{3}</math> single bond), with the bond length of 1.382 Å for the transition state. Again, the same analysis can be made for the discussion of the changes in the C-C bond lengths. Although, it is worth noting that the C5-C6 bond length is greater than the C1-C2 / C3-C4 bond lengths in product. One possible explanation is that even though both of the bonds has a bond order of 1, the hybridisation of C5-C6 bond is <math>sp^3-sp^3</math>. Hence, there is less s-character in the bond, making it longer. For C2-C3, the bond length changes from 1.471 Å (<math>sp^{2}-sp^{2}</math> single bond) to 1.362 Å (double bond) with the bond length of 1.411 Å for the transition state. For this case, the transition state bond length is observed to be shorter than the reactants compare to the other cases discussed. This is because for this case, instead of the double bonds in the reactant partially breaking (decreasing in electron density) in the transition state, a double bond is partially forming (increasing electron density) here, making the bond length decrease.

As for the new bonds created (C1-C6 and C4-C5), the corresponding bond lengths for both of them is 1.583 Å (<math>sp^{3}-sp^{3}</math> single bond). As for the transition states, the corresponding partially formed bond lengths are 2.113 Å and 2.116 Å for C1-C6 and C4-C5 respectively. This is shorter than Van der Waals radii between two carbons of 3.4 Å (each being 1.7 Å) but at the same time longer than a typical C-C single bond. This indicates that the orbitals in the carbons involved are drawn together, interacting, and about to form new bonds in the transition state.

From this, it can be approximated that the typical bond length for C-C double bonds is 1.3 Å (lit. 1.34 Å), 1.6 Å (lit. 1.54 Å) for <math>sp^{3}-sp^{3}</math> single bonds, and 1.5 Å for <math>sp^{2}-sp^{3}</math>/<math>sp^{2}-sp^{2}</math> single bonds, with <math>sp^{2}-sp^{2}</math> single bonds slightly shorter than <math>sp^{2}-sp^{3}</math> single bonds (lit. 1.50 Å for <math>sp^{2}-sp^{3}</math> and 1.47 Å for <math>sp^{2}-sp^{2}</math>) <ref>Fox, Marye Anne., and James K. Whitesell. Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen. Heidelberg: Spektrum Akademischer Verlag, 1995.</ref>.

==<i>Transition State Vibrations</I>==

[[File:PS4615_IRC_exersize_1.PNG|thumb|center|600px|alt=|<b>Figure 4</b>. The IRC of the reaction.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

!<b>Figure 5</b> shows the vibration of the transition state.
|-
|

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size><align>centre</align>
<uploadedFileContents>PS4615_1_TS_BERNY_PM6_2.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>EX1_TS_VIBRATION</name>
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<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
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|
|}

By running an IRC calculation, the vibration calculation was confirmed to be successful (see <b>Figure 4</b>). In addition, vibration corresponding to the transition state is illustrated (<b>Figure 5</b>). As described in the introduction, the frequency of this particular vibration of the transition state is negative. From the IRC of the reaction, it can be deduced that the bond formation between terminal carbons in butadiene and ethylene is synchronous, as the bond formation occurred at the same time. Also, it can be seen from the Jmol that the carbons involved in forming the new bonds approach each other at the same time and synchronously. This results in synchronous bond formation.

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

[[File:ex2_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 6</b>. The reaction scheme of the reaction. Note that there are two possible products from the reaction.]]

<b>Corresponding Log files</b>

Reactants:

[[Media:PS4615_2_CYCLOHEXADIENE_MIN_PM6.LOG|PS4615_2_CYCLOHEXADIENE_MIN_PM6.LOG]]

[[Media:PS4615_2_CYCLOHEXADIENE_MIN_B3LYP.LOG|PS4615_2_CYCLOHEXADIENE_MIN_B3LYP.LOG]]

[[Media:PS4615_2_1_3_DIOXOLE_MIN_PM6.LOG|PS4615_2_1_3_DIOXOLE_MIN_PM6.LOG]]

[[Media:PS4615_2_1_3_DIOXOLE_MIN_B3LYP.LOG|PS4615_2_1_3_DIOXOLE_MIN_B3LYP.LOG]]

ENDO TS and products:

[[Media:PS4615_2_TS_BERNY_ENDO_PM6.LOG|PS4615_2_TS_BERNY_ENDO_PM6.LOG]]

[[Media:PS4615_2_TS_BERNY_ENDO_B3LYP.LOG|PS4615_2_TS_BERNY_ENDO_B3LYP.LOG]]

[[Media:PS4615_2_PRODUCT_ENDO_MIN_PM6.LOG|PS4615_2_PRODUCT_ENDO_MIN_PM6.LOG]]

[[Media:PS4615_2_PRODUCT_ENDO_MIN_B3LYP.LOG|PS4615_2_PRODUCT_ENDO_MIN_B3LYP.LOG]]

[[Media:PS4615_2_TS_IRC_ENDO_PM6.LOG|PS4615_2_TS_IRC_ENDO_PM6.LOG]]

EXO TS and products:

[[Media:PS4615_2_TS_BERNY_EXO_PM6.LOG|PS4615_2_TS_BERNY_EXO_PM6.LOG]]

[[Media:PS4615_2_TS_BERNY_EXO_B3LYP.LOG|PS4615_2_TS_BERNY_EXO_B3LYP.LOG]]

[[Media:PS4615_2_PRODUCT_EXO_MIN_PM6.LOG|PS4615_2_PRODUCT_EXO_MIN_PM6.LOG]]

[[Media:PS4615_2_PRODUCT_EXO_MIN_B3LYP.LOG|PS4615_2_PRODUCT_EXO_MIN_B3LYP.LOG]]

[[Media:PS4615_2_TS_EXO_IRC_PM6.LOG|PS4615_2_TS_EXO_IRC_PM6.LOG]]

==<i>Transition State MO Diagram and Analysis</i>==

[[File:PS4615_Ex2MO_ENDO.png|thumb|center|600px|alt=|<b>Figure 7</b>. The transition state MO diagram of the reaction (ENDO). Note that the energies of the MOs are obtained (in Hartree) from Gaussian.]]
[[File:PS4615_Ex2ExoMO.png|thumb|center|600px|alt=|<b>Figure 8</b>. The transition state MO diagram of the reaction (EXO). Note that the energies of the MOs are obtained (in Hartree) from Gaussian.]]

<b>Figure 7</b> illustrates the molecular orbital diagram of the transition states for the Diels-Alder reaction. The MO diagrams were constructed by carrying out the same analysis on the relevant MOs of the reaction's transition states (see <b>table 3</b> for the MOs of the transition states). Again, it was observed that MOs that has the same symmetry interact to form the TS MOs. It can be seen that for each case, the overall energy of the transition state for the ENDO case is lower compared to the transition state for the EXO product. Qualitatively speaking, this indicates that the kinetic barrier/activation energy for the EXO case is higher, resulting in the pathway being kinetically stable compared to the ENDO pathway. A more quantitative analysis is discussed in the <I>Thermochemistry</I> section below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 3</b>. The relevant molecular orbitals of the transition states of the Diels-Alder reaction.'''

!TS ENDO HOMO-1

!TS ENDO HOMO

!TS ENDO LUMO

!TS ENDO LUMO+1

|-

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|-

!'''TS ENDO HOMO-1'''

!TS ENDO HOMO

!TS ENDO LUMO

!TS ENDO LUMO+1

|-

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Diels-Alder reactions such as this case can be classified as either normal or inverse electron-demand. For a qualitative analysis, it can be said that for a normal electron-demand Diels-Alder reaction, the diene is electron rich whereas the dienophile is electron deficient. On the other hand, the diene is required to be electron deficient, where the dienophile is electron rich for an inverse electron-demand Diels-Alder reaction. For a more quantitative analysis, whether the reaction is normal or inverse electron-demand depends on the relative energies of the HOMO and LUMO of the reactants involved in the reaction. For a normal electron-demand reaction, the HOMO and LUMO of the dienophile is lower in energy compared to the respective HOMO and LUMO of the diene. As a result, there is a strong interaction between the HOMO of the diene and the LUMO of the dienenophile as they have similar energies, forming the HOMO and LUMO of the product. An example of this is the Diels-Alder reaction in Exercise 1 (see <b>figure 3</b> for the MO diagram). For an inverse electron-demand reaction, the HOMO and LUMO of the dienophile is higher in energy compared to the respective HOMO and LUMO of the diene. For this case, the HOMO of the dienophile and LUMO of the diene interact strongly to produce the HOMO and LUMO of the product. For the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the reaction is an inverse electron-demand reaction, with explanations as described above. One of the reasons why the HOMO and LUMO of the dienophile has such high energies, surpassing the MOs of the diene, is because of the electron donating effect of the two oxygens next to the alkene, raising the energy of MOs of the dienophile. <b>Figure 9</b> illustrates the inverse electron-demand characteristic of the (ENDO) reaction nicely, with the energies of the product MOs calculated by running an optimisation on the product structure (B3LYP).

[[File:PS4615_Ex2MO_ENDO_product_INV.png|thumb|center|600px|alt=|<b>Figure 9</b>. A simplified MO diagram (ENDO product) illustrating the inverse electron demand nature of the reaction.]]

==<i>Thermochemistry</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 4</b> The table shows activation energies and the Gibbs free energies of the ENDO and EXO Diels-Alder reaction.'''
! style="text-align: center;" |
! style="text-align: center; font-weight: bold;" | Activation Energy / <math>kJmol^{-1}</math>
! style="text-align: center; font-weight: bold;" | Gibbs Free Energy / <math>kJmol^{-1}</math>
|-
| style="text-align: center; font-weight: bold;" | ENDO
| style="text-align: center;" | +159.8
| style="text-align: center;" | -67.4
|-
| style="text-align: center; font-weight: bold;" | EXO
| style="text-align: center;" | +167.7
| style="text-align: center;" | -63.8
|}

From <b>table 4</b>, it can be seen that the ENDO pathway has a lower activation energy compared to the EXO pathway, making it kinetically favourable. This is because the HOMO of the ENDO transition state is further stabilised by secondary orbital interactions. From <b>table 5</b>, it can be seen that the p orbitals on the oxygens of the dienophile interacts with the delocalised π orbitals on the diene, which has a stabilising effect on the transition state. Secondary orbital interaction is absent in the EXO pathway, as transition state does not have the correct geometry for it. This makes the energy of the ENDO transition state lower than that of the EXO pathway, making it kinetically favoured.

In addition, the ENDO pathway is more exothermic compared to the EXO pathway, making it the thermodynamically favoured compared to the other pathway. As a result, this makes the ENDO product thermodynamically more stable than the EXO product. Secondary orbital interactions within the ENDO product is one of the factors that make the energy of the ENDO product lower than the EXO product. This is the same interaction as described above, with the EXO product lacking in the stabilising interaction due to its geometry. Furthermore, unfavourable steric interactions between the dioxole group and the ethylene bridgehead in the EXO product may have played a significant role in increasing its energy, making it less exothermic. This effect is likely to be less significant for the ENDO product, as the dioxole is closest to the saturated bridgehead, resulting in less interaction with the hydrogen atoms (see <b>table 6</b> for illustration).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 5</b> The table shows the HOMO of the transition states with the isovalue set to 0.01 to show secondary orbital interactions.'''

!TS ENDO HOMO

!TS EXO HOMO

|-

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{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 6</b> The table shows the steric interactions in the ENDO and EXO product.'''

!ENDO product

!EXO product

|-

|[[File:PS4615_Sterics_ENDO_product.png|500px]]|
|[[File:PS4615_Sterics_EXO_product.png|500px]]|

|}

=Exercise 3: Diels-Alder vs Cheletropic=

[[File:PS4615_ex3_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 10</b>. The reaction scheme of the reaction. Note that there are two possible reaction pathways, including Diels-ALder and Cheletropic.]]

<b>Corresponding Log files</b>

Reactants:

[[Media:PS4615_3_REACTANT_DIENE_MIN_PM6.LOG|PS4615_3_REACTANT_DIENE_MIN_PM6.LOG]]

[[Media:PS4615_3_REACTANT_SO2_MIN_PM6.LOG|PS4615_3_REACTANT_SO2_MIN_PM6.LOG]]

Diels-Alder ENDO TS and products:

[[Media:PS4615_3_DA_TS_BERNY_ENDO_PM6.LOG|PS4615_3_DA_TS_BERNY_ENDO_PM6.LOG]]

[[Media:PS4615_3_DA_TS_IRC_ENDO_PM6.LOG|PS4615_3_DA_TS_IRC_ENDO_PM6.LOG]]

[[Media:PS4615_3_DA_PRODUCT_MIN_ENDO_PM6.LOG|PS4615_3_DA_PRODUCT_MIN_ENDO_PM6.LOG]]

Diels-Alder EXO TS and products:

[[Media:PS4615_3_DA_EXO_TS_BERNY_PM6.LOG|PS4615_3_DA_EXO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_DA_EXO_TS_IRC_PM6.LOG|PS4615_3_DA_EXO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_DA_EXO_PRODUCT_MIN_PM6.LOG|PS4615_3_DA_EXO_PRODUCT_MIN_PM6.LOG]]

Cheletropic TS and products:

[[Media:PS4615_3_CHELETROPIC_TS_BERNY_PM6.LOG|PS4615_3_CHELETROPIC_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_CHELETROPIC_TS_IRC_PM6.LOG|PS4615_3_CHELETROPIC_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_CHELETROPIC_PRODUCT_MIN_PM6.LOG|PS4615_3_CHELETROPIC_PRODUCT_MIN_PM6.LOG]]

Alternative Diels-Alder ENDO TS and products:

[[Media:PS4615_3_ALT_DA_ENDO_TS_BERNY_PM6.LOG|PS4615_3_ALT_DA_ENDO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_ENDO_TS_IRC_PM6.LOG|PS4615_3_ALT_DA_ENDO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_ENDO_PRODUCT_MIN_PM6.LOG|PS4615_3_ALT_DA_ENDO_PRODUCT_MIN_PM6.LOG]]

Alternative Diels-Alder EXO TS and products:

[[Media:PS4615_3_ALT_DA_EXO_TS_BERNY_PM6.LOG|PS4615_3_ALT_DA_EXO_TS_BERNY_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_EXO_TS_IRC_PM6.LOG|PS4615_3_ALT_DA_EXO_TS_IRC_PM6.LOG]]

[[Media:PS4615_3_ALT_DA_EXO_PRODUCT_MIN_PM6.LOG|PS4615_3_ALT_DA_EXO_PRODUCT_MIN_PM6.LOG]]

==<i>IRC</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 7</b> The table shows the different IRC of the Diels-Alder and Cheletropic reaction. Note that the IRC of the Diels-Alder EXO IRC is in the opposite direction.'''

!Diels-Alder ENDO IRC

!Diels-Alder EXO IRC

!Cheletropic IRC

!Alternative Diels-Alder ENDO IRC

!Alternative Diels-Alder EXO IRC

|-

|[[File:PS4615_endo_DA_IRC.png|400px]]|
|[[File:PS4615_exo_DA_IRC.png|400px]]|
|[[File:PS4615_cheletropic_IRC.png|400px]]|
|[[File:PS4615_ALT_endo_DA_IRC.png|400px]]|
|[[File:PS4615_ALT_exo_DA_IRC.png|400px]]|

|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 8</b> visualises the IRC path of the Diels-Alder and Cheletropic reactions. Click on the links to see the animations.'''

!Diels-Alder ENDO IRC

!Diels-Alder EXO IRC

!Cheletropic IRC

!Alternative Diels-Alder ENDO IRC

!Alternative Diels-Alder EXO IRC

|-

|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ENDO_DA_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_EXO_DA_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_cheletropic_IRC_movie_FULL.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ALT_ENDO_DA_IRC_movie_NEW.gif]]|
|[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:PS4615_ALT_EXO_DA_IRC_movie_NEW.gif]]|

|}

<b>Table 7</b> and <b>table 8</b> Shows the IRC (described in the Introduction section) of the reaction pathways of this exercise, including the movie file links that illustrates the nature of bond formations of the pathways. From the movies, it can be seen that all the Diels-Alder reaction pathways (including the reaction at the high energy site) form new bonds asynchronously. On the other hand, the bond formation of the cheletropic pathway is synchronous. It is worth noting that xylylene is an extremely reactive species, as it is only one oxidation state away from forming a 6-membered aromatic ring. In fact, this can be seen during the reaction of xylylene with sulphur dioxide (see the IRC animation), where the ring becomes aromatised when transition states are formed. This is not the case for the alternative pathway at the inner diene site, resulting in the reaction being highly unfavourable.

==<i>Thermochemistry</i>==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 9</b> shows the activation energies and Gibbs free energies of the different reaction pathways.'''

!
! style="text-align: center; font-weight: bold;" | Activation Energy / <math>kJmol^{-1}</math>
! style="font-weight: bold;" | Gibbs Free Energy / <math>kJmol^{-1}</math>
|-
| style="text-align: center; font-weight: bold;" | DA ENDO
| style="text-align: center;" | +84.4
| style="text-align: center;" | -96.4
|-
| style="text-align: center; font-weight: bold;" | DA EXO
| style="text-align: center;" | +88.4
| style="text-align: center;" | -97.0
|-
| style="text-align: center; font-weight: bold;" | Cheletropic
| style="text-align: center;" | +106.7
| style="text-align: center;" | -153.4
|-
| style="text-align: center; font-weight: bold;" | Alternative DA ENDO
| style="text-align: center;" | +114.7
| style="text-align: center;" | +18.9
|-
| style="text-align: center; font-weight: bold;" | Alternative DA EXO
| style="text-align: center;" | +122.5
| style="text-align: center;" | +23.4
|}

(This is really a change in free energy. Best to just call it a reaction energy [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:42, 16 March 2018 (UTC))

[[File:PS4615_3_energy_diagram_FULL.png|thumb|center|1000px|alt=|<b>Figure 11</b>. The energy diagram illustrating the relative activation energies and Gibbs free energies of the Diels-Alder and Cheletropic reaction.]]

From <b>figure 11</b>, it can be seen that out of all the reaction pathways (excluding the alternative Diels-Alder), the cheletropic pathway has the greatest activation energy, making it the most kinetically stable compared to the other 2 pathways. One of the possible explanation for this is the fact that the reaction forms a new 5-membered ring, compared to 6-membered rings for the other pathways. The ring strain in the 5-membered ring raises the energy of the transition state, raising its activation energy. Even though it is the most kinetically inert compared to the other three, the cheletropic path is the most thermodynamically favourable, as it is the most exothermic pathway (most negative Gibbs free energy of reaction). This is because of the stabilisation of the product by the 2 strong S=O bonds (bond enthalpy of 518 kJ/mol each <ref>Luo, Yu-Ran. Comprehensive handbook of chemical bond energies. Boca Raton, Fla.: CRC Press, 2007.
</ref>) compared to only one S=O and one S-O (S-O contributes 348 kJ/mol <ref>Cottrell, T. L. The strengths of chemical bonds. New York: Academic Press, 1961.
</ref>) in the Diels-Alder products. The two S=O bonds has a much greater effect than the ring strain in the 5-membered ring, making it the most exothermic reaction of the three.

Contrarily, the ENDO Diels-Alder pathway has the lowest activation energy, making it the fastest kinetically compared to the other two paths. This is due to the stabilisation of the transition state by secondary orbital interactions (similar to Exercise 2 case). This involves the interaction between the p orbital of the oxygen in sulphur dioxide and the delocalised π orbitals of xylylene. This is not possible for the EXO case as it does not have the correct geometry for the interaction, making its activation energy higher (but still lower than cheletropic path) than the ENDO transition state. Due to steric repulsions between the oxygen in the S=O and the rest of the molecule, the ENDO product energy is slightly above the EXO product. This makes the EXO path more thermodynamically favourable than the ENDO pathway, as it is slightly more exothermic. If the reaction is carried out under equilibrating conditions, the cheletropic product will be the major product of the reaction between sulphur dioxide and xylylene, as it is the most thermonamically favourable pathway.

The energy diagram (<b>figure 11</b>) shows that the alternative Diels-Alder reaction at the inner site is both thermodynamically and kinetically unfavourable. Firstly, the activation energy of the reaction is greater than any of the pathways described before. The reactions (EXO and ENDO) are endothermic, which means that they require energy to convert from reactants to product overall. The ENDO product here is both the kinetic and thermodynamic product compared to the EXO case. The transition states for this alternative pathway is higher in energy than the preferred path because it lacks the aromatic ring formed at the 6-membered ring. This also explains the why the reaction is endothermic, as the products does not have the aromatic 6-membered ring in it like the normal Diels-Alder and cheletropic products.

=Extension: Electrocyclic reaction=

[[File:Ext_reaction_scheme.png|thumb|center|600px|alt=|<b>Figure 12</b>. The reaction scheme of the electrocyclic reaction of cyclobutene.]]

<b>Corresponding Log Files</b>

[[Media:PS4615_EXT_CYCLOBUTENE_MIN_PM6.LOG|PS4615_EXT_CYCLOBUTENE_MIN_PM6.LOG]]

[[Media:PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG|PS4615_EXT_CYCLOBUTENE_MIN_B3LYP.LOG]]

[[Media:PS4615_EXT_TS_BERNY_PM6.LOG|PS4615_EXT_TS_BERNY_PM6.LOG]]

[[Media:PS4615_EXT_TS_BERNY_B3LYP.LOG|PS4615_EXT_TS_BERNY_B3LYP.LOG]]

[[Media:PS4615_EXT_TS_IRC_PM6.LOG|PS4615_EXT_TS_IRC_PM6.LOG]]

[[Media:PS4615_EXT_PRODUCT_B3LYP.LOG|PS4615_EXT_PRODUCT_B3LYP.LOG]]

In this extension, the thermal electrocyclic ring opening of the molecule shown in the reaction scheme above was studied. Since electrocyclic reactions is a class of a pericyclic reaction, the stereochemistry of the product can be determined using the Woodward-Hoffman rules. From this, it was determined that the reaction undergoes conrotatory electrocyclic ring opening, which agrees with the calculations carried out using B3LYP (see the animation in <b>table 10</b> and the vibrations of the transition state at <b>figure 13</b>). The activation energy of the reaction was found to be <math> +122.4 kJmol^{-1} </math>, with the Gibbs free energy of the reaction at <math>-64.1 kJmol^{-1}</math>. This shows that the reaction has a significantly high activation energy, making it kinetically inert. One possible explanation to this is the raise in the TS energy due to steric interactions between the bulky methyl ester groups during the transition from the reactant to product (see animations). Since the reaction is significantly exothermic, the reaction is considered thermodynamically favourable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

!<b>Figure 13</b> shows the vibration of the transition state.
|-
|

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size><align>centre</align>
<uploadedFileContents>PS4615_EXT_TS_BERNY_B3LYP.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 29; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>EXT_TS_VIBRATION</name>
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<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>EXT_TS_VIBRATION</target>
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|
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 10</b> shows the IRC of the reaction, where the movie shows that the reaction is conrotatory.'''

!The reaction's IRC

|-

|[[File:PS4615_EXT_IRC.png|400px]]|

|-

!IRC movie. Click on the link for movie.

|-

|[[https://wiki.ch.ic.ac.uk/wiki/images/d/d1/PS4615_EXT_IRC_movie.gif]]|

|}

It is clear from the animations and the transition state vibrations that the reaction is a conrotatory electrocyclic ring opening. Aside from using the Woodward-Hoffmann rules, this can be determined and illustrated by looking the the HOMO of the reactants and products (see <b>table 11</b>). From the HOMO of the product, it can be seen that the only way that the reaction can proceed (working backwards) is through antarafacial interactions of the MOs at the terminal carbons, as this is the only way to achieve constructive interaction between the orbitals. In terms of the symmetry (when considering just the diene fragment), the HOMO is asymmetric. By following through with the reaction to the reactants, it can be seen that the terminal carbons rotate in the same direction to form the cyclobutene. This is illustrated in the in <b>figure 14</b>.

[[File:PS4615_EXT_orbitals_interaction_NEW.png|thumb|center|600px|alt=|<b>Figure 14</b>. This illustrates the Frontier orbital (HOMO) approach to determining the stereochemistry of the reaction.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''<b>Table 11</b>. The relevant molecular orbitals of the reaction.'''

!Cyclobutene HOMO

!Transition state HOMO

!Product HOMO

|-

|<jmol>
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|-

!Cyclobutene LUMO

!Transition state LUMO

!Product LUMO

|-

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|-
|}

=Conclusion=

In this experiment, a semi-empirical method PM6 and a hybrid method B3LYP were used to calculate the geometries and vibrations of 4 different transition states of 4 different pericyclic reactions successfully. Method three was used for all of the calculations, as it is the most accurate method out of the three. Starting with the first exercise, the C-C bond lengths involved in the reaction were analysed as the reaction progresses from the reactants, to the transition states and finally the product. It was also found that the bond formation is synchronous, which is not the case for the reactions in exercise 3. The activation energies and Gibbs free energies of the ENDO and EXO Diels-Alder reactions were calculated in exercise 2 up to the B3LYP level of accuracy. The relevant MOs were visualised to qualitatively show the effect of secondary orbital interactions and steric repulsions on the thermochemistry of the reactions. From the energies of the relavant MOs, it was proven that the Diels-Alder reaction in exercise 2 is an inverse electron-demand reaction. As for exercise 3, the different reaction paths were investigated for the reaction between sulphur dioxide and xylylene. It was found that the most thermodynamically favourable pathway is the Cheletropic path, whereas the ENDO Diels-Alder reaction path is the most kinetically driven. Lastly, calculations up to B3LYP level of accuracy for a thermal electrocyclic ring opening of cyclobutene was carried out. The IRC animation and the transition state vibrations showed that the reaction is conrotatory, which is in agreement with the Woodward-Hoffmann rules.

=Bibliography=

Rep:Mod:mg5715TS

2018-03-16T14:29:45Z

Tam10: /* Excercise 3 Diels-Alder vs Cheletropic */

==Introduction==

===Potential energy surface===
[[File:MG5715_TS_INTRO_DIATOMIC.PNG|thumb|500px|x500px|center|Fig.1 The potential energy curve of a diatomic molecule<ref>L., D. J. (1957). Model of a potential energy surface. J. Chem. Educ., 34(5), 215.</ref>]]
The potential energy surface of a diatomic molecule is anharmonic oscillation (as shown in Fig.1). The lowest point in this energy potential is a stationary point, which means it has a zero first derivative:
<center><math>\frac{dE(R)}{dR}=0</math></center>
<small><center>Equation 1. First derivative of 1-D potential energy</center></small>

R stands for the bond length and the physical meaning of the first derivative of potential energy is the force acting on the atoms and the second derivative is the force constant (k). The bond will vibrate; so the vibration wavenumber could be calculated by Equation 2.
<center><math>\tilde{v}=\frac{1}{2c\pi}\sqrt{\frac{k}{\mu}}</math></center>
<small><center>Equation 2. Vibrational wavenumber of a diatomic molecule</center></small>
where <math>\mu</math> is the reduced mass and it could be calculated by Equation 3.
<center><math>\mu=\frac{M_AM_B}{M_A+M_B}</math></center>
<small><center>Equation 3. Reduced mass of a diatomic molecule</center></small>

[[File:MG5715_TS_INTRO_TRIATOMIC.PNG|thumb|500px|x500px|center|Fig.3 Potential energy surface of triatomic molecule<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). http://doi.org/10.1016/0166-1280(90)85035-L</ref>]]
For a triatomic molecule (e.g.H<sub>2</sub>O), the potential energy surface has two coordinates including bond length R and bond angle <math>\theta</math> and the potential energy surface is shown in Fig.3. For a non-linear molecule including N atoms, it will have '''3N-6''' independent geometric variables. For each atom, it will have three variables (bond length, bond angle and torsional angles).The three global rotations and three global translations should be subtracted, so it has 3N-6 degrees of freedom. If it is a linear molecule, there only have two rotation axes, so it has '''3N-5''' independent geometric variables.
A stationary point of the potential energy surface, which has 3N-6 degrees of freedom, could be defined by equation 4.

<center><math>\frac{dE(\mathbf{R})}{dR_i}=0 i=1,2,3,...3N-6</math></center>
<small><center>Equation 4. General equation of a stationary point with 3N-6 variables</center></small>
where '''R''' is the set of all nuclear coordiantes.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). http://doi.org/10.1016/0166-1280(90)85035-L</ref>

[[File:MG5715_TS_INTRO_PES.PNG|thumb|500px|x500px|center|Fig.4 The 1-D potential energy surface of a reaction<ref>L., D. J. (1957). Model of a potential energy surface. J. Chem. Educ., 34(5), 215.</ref>]]
Fig.4 is a 1-D potential energy surface of a reaction. Products and reactants are the minimum points on the lowest energy pathway. For transition state, it is the maximum point on the lowest energy pathway. All of reactants, products and transition state are the stationary points, which means that they satisfy this equation:
(<math>\frac{dE(\mathbf{R})}{dR}=0</math>). The second derivative of potential energy surface, the force constant, is used to distinguish the products and reactants with the transition state. Reactants and products are {{fontcolor1|blue|'''minima'''}}, so the second derivative is positive.(<math>\frac{d^2E(\mathbf{R})}{dR^2}>0</math>) Transition state is the {{fontcolor1|blue|'''saddle point'''}} of the potential energy surface, which means its second derivative is negative.(<math>\frac{d^2E(\mathbf{R})}{dR^2}<0</math>) The force constant of transition state is negative; so, the vibration wavenumber will be imaginary at transition state according to Equation 2.

===Approximations===
The time-independent Schrödinger equation is:
<Center><math>\hat{H}\Psi_A=E\Psi_A </math></center>
<center><small>Equation 5. Time-independent Schrödinger equation</small></center>
where <math>\hat{H}</math> is an operator called Hamiltonian, <math>\Psi_A</math> is the wavefunction of electron A, and E stands for the energy.
Schrödinger equation could be rewritten by Dirac notation (<math>\hat{H}|\Psi =E|\Psi</math>).Premultiply the complex conjugation of the wavefunction and integrate over all variables and then rearrange the equation, an euqation of E will be gained. (<math>E=\frac{<\Psi^*|\hat{H}|\Psi>} {<\Psi^*|\Psi>}</math>) where the denominator is the overlap integer. If the wavefunction is normalised, the overlap integer should be 1; so <math>E=<\Psi^*|\hat{H}|\Psi></math>.

The Hamiltonian operator for a molecule could be separated into kinetic and potential energies of individual particles (<math>\hat{E}=\hat{T}_n+\hat{T}_e+\hat{V}_{ee}+\hat{V}_{en}+\hat{V}_{nn}</math>).T stands for the kinetic energy and V is the potential energy.The {{fontcolor1|blue|'''Born-Oppenheimer approximation'''}} is the first key approximation for Schrödinger equation. Because the motion of electrons is much faster than that of nuclei, the kinetic energy of the nucleus could be ignored and the potential energy of nuclei's interaction will be constant. Hence, the Hamiltonian operator could be rewritten to <math>\hat{E}_{BO}=+\hat{T}_e+\hat{V}_{ee}+\hat{V}_{en}+constant</math>

In quantum chemistry, another very important approximation is that the wavefunction of a molecule is the {{fontcolor1|blue|'''linear combination of atomic orbitals (LCAO)'''}} as shown in Equation 6.
<center><math>\Psi(r)=\sum_{n}^N c_n \phi_n(r)</math></center>
<center><small>Equation 6. linear combination of atomic orbitals</small></center>
where <math>\phi_n(r)</math> is the basis set (atomic orbital). Therefore the hamiltonian could be rewriten as Equation 7.
<center><math>E=<\Psi^*|\hat{H}|\Psi>=\sum_{n}^N \sum_{m}^N c_m <\phi_m(r)|\phi_n(r)> c_n</math></center>
<center><small>Equation 7. linear combination of atomic orbitals</small></center>

The more basis sets are used, the more accurate the molcular orbital is, but increasing the basis sets will increase the cost of computational effort.

===Computational Methods===
Although Gauss View contains lots of different calculation method, only two of them are used in this lab: (1) Semi-empirical method PM6 and (2) Density Functional Theory(DFT) method B3LYP.

The Semi-empirical method is based on the experimental data, which will save time for calculating. The density functional theory is the calculation based on theory and does not include any experimental data. Therefore, this process is slower than semi-empirical method.

===Methods to find Transition State===
* '''Method 1'''
(1) predict and draw a guess transition state structure

(2) optimise the guess transition state structure to TS(Berny) and set ''Calculate force constants'' to '''once''' and the output is the optimised transition state (Only have '''one''' imaginary frequency)

This method is quite easy and it is the fastest method.However, this method is not very reliable and it only works for small systems because it will fail easily if the predicted transition state is not close to the real transition state.

* '''Method 2'''
(1) predict and draw a guess transition state structure

(2) freeze the distance between atoms where the bond will be formed in the reaction

(3) optimise the frozen-bond structure to a minimum

(4) repeat method 1(2)

This method is similar to method 1 but this one is more reliable than method 1 because it freezes the atoms to prevent them from moving. This makes sure the system close to the transition state before calculation. However, this also will fail easily.

* '''Method 3'''
(1) draw the reactant(s) or product(s) and choose the one which has fewer molecules.

(2) optimise the reactant(s) or product(s) to a minimum

(3) break or form the bond and freeze the distance between atoms

(4) repeat method 2 (2)-(4)

This method is much more reliable than the previous two methods and it does not need to predict the possible transition state. However, this method is more complicated and it requires more steps.

==Excercise 1: Reaction of Butadiene with Ethylene==
[[file:MG5715_TS_EX1_REACTION SCHEME.JPG|thumb|550px|center|Fig.5 The reaction scheme of cycloaddition of butadiene and ethylene]]
The reaction of butadiene with ethylene is a traditional '''[4+2] cycloaddition''', which also known as '''Diels-Alder reaction'''.In Diels-Alder reaction, a conjugated diene (butadiene) will react with a dienophile (ethylene) to form a cyclohexene and the reaction scheme is shown in Fig 5. Although the s-''trans'' conformation is more energetically favourable, the conformation of diene should be s-''cis'' because of the interaction between the frontier molecular orbitals(FMO). Moreover, the energy barrier between s-''trans'' and s-''cis'' is not extremely high. In this exercise, all reactants, products and transition state were optimised by {{fontcolor1|blue|'''semi-empirical method PM6 '''}} in Gauss View and {{fontcolor1|blue|'''Method 2'''}} is used to locate the transition state.
===MO analysis===

[[file:MG5715_TS_EX1_MO_1.JPG|thumb|550px|center|Fig.6 The molecular orbital of cycloaddition of butadiene with ethylene]]

The MO diagram is shown in Fig.6 and this graph is drawn according to the energy calculated by PM6. The energy of product ({{fontcolor1|black|'''black'''}} line) should be lower than that of the reactants, and the energy of transition state ({{fontcolor1|#fe7af9|'''pink'''}} line) is higher than that of reactants. The HOMO and LUMO are shown in Table 1.

{| class="wikitable" style="margin: auto;"
|
! center; style="background: #0D4F8B; color: white; text-align: center;"| Butadiene
! center; style="background: #0D4F8B; color: white; text-align: center;" | Ethylene
! center; style="background: #0D4F8B; color: white; text-align: center;" colspan="2"| MO of Transition State
|-
| center;| LUMO

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|-
| center;| HOMO
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|+ Table 1. The HOMO and LUMO diagram of reactants, product and transition state
|}

For a [p+q]-cycloaddtion reaction, it could be driven either thermally or photochemically. For photochemical reaction, the electrons on HOMO will be excited to LUMO and become two SOMOs.Therefore, the photochemical cycloaddition is a little bit different with the thermal cycloaddition. A general rule called '''''Woodward Hoffmann Rule''''' is used to determine whether the cycloaddition is allowed or forbidden.

*Woodward-Hoffmann Rule for cycloaddition reactions
For a [p+q]-cylcoaddtion reaction, only two components are involved, where one contains p π-electrons and the other one has q π-electrons. s stands for suprafacial and a means antarafacial

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white; text-align: center;"| p+q
! center; style="background: #0D4F8B; color: white; text-align: center;" | Thermally allowed
! center; style="background: #0D4F8B; color: white; text-align: center;" | Photochemically allowed

|-
! center; | 4n
! center| p<sub>s</sub>+q<sub>a</sub> or p<sub>a</sub>+q<sub>s</sub>
! center| p<sub>s</sub>+q<sub>s</sub> or p<sub>a</sub>+q<sub>a</sub>

|-
! center;| 4n+2
! center| p<sub>s</sub>+q<sub>s</sub> or p<sub>a</sub>+q<sub>a</sub>
! center| p<sub>s</sub>+q<sub>a</sub> or p<sub>a</sub>+q<sub>s</sub>
|+ Table 2. Woodward-Hoffman Rule <ref>Semis, K. L., & Rules, B. W. (1965). Woodward-Hoff mann Rules : Electrocyclic Reactions.</ref>
|}

In this reaction, butadiene has 4 π-electrons and ethylene contains 2 π-electrons. The sum of p and q is 6 and they are all suprafacial. Hence, this [4+2] cycloaddition is {{fontcolor1|blue|'''thermally allowed'''}}.

*overlap integral
<center><math>S=\int\psi\psi^*\,d\tau</math></center>
<center><small>Equation 8. Calculation of overlap integral</small></center>

The overlap integral is calculated by equation 8 and it is telling how well two orbitals are overlapped. The value of overlap integral is between 0 and 1. 0 means that the two orbitals do not have any overlap and 1 means that they perfectly overlap with each other. Table 3 is used to determine whether the wavefunction is symmetric or antisymmetric.

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white; text-align: center;"| Symmetric
! center; style="background: #0D4F8B; color: white; text-align: center;" | Antisymmetric
|-
! center;|ψ(r<sub>1</sub>,r<sub>2</sub>)={{fontcolor1|red|'''+'''}}ψ(r<sub>2</sub>,r<sub>1</sub>)
! center;|ψ(r<sub>1</sub>,r<sub>2</sub>)={{fontcolor1|red|'''-'''}}ψ(r<sub>2</sub>,r<sub>1</sub>)
|+Table 3. Symmetric and Antisymetric wavefunction
|}

For two wavefunctions, the overlap integral will be 0 if the product of two wavefunctions is antisymmetric. If the product of two wavefunctions is symmetric, the overlap integral will be 1. Only when '''both of the wavefunctions are antisymmetric''' or '''both are antisymmetric''', the overlap integral will be 1. As shown in MO diagram, the antisymmetric orbital will overlap with the antisymmetric orbital.

===Analysis of bond lengths===
{| class="wikitable" style="margin: auto;"
|center; | [[file:MG5715_TS_E1_IRC_DISTANCE.jpg|thumb|none|500px|x500px|center|Fig.7 Disatance VS reaction coordination]]
|center; | [[file:MG5715_TS_E1_LABEL.PNG|thumb|none|500px|x500px|center|Fig.8 Labelled molecule]]
|+ Table 4. IRC bond distance analysis
|}

In Fig.7, it shows that the distances between C atoms change with reaction coordination. and Fig.8 shows the labelled molecule. Initially, the distance between C<sub>14</sub> and C<sub>1</sub> and distance between C<sub>7</sub> and C<sub>11</sub> are around 3.4 Å, which indicates there does not have any bond between those two atoms. The Van der Waal radius of C atom is 1.77Å <ref>Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials Translated from Neorganicheskie Materialy Original Russian Text, 37(9), 871–885. http://doi.org/10.1023/A:1011625728803</ref> 3.4 Å is smaller than twice of Van der Waals radius of C; therefore, C<sub>14</sub> is interacting with C<sub>1</sub> and a bond will be formed between them.

{| class="wikitable" style="margin: auto;"
|
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>3</sup>)-C(sp<sup>3</sup>)
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>3</sup>)-C(sp<sup>2</sup>)
! center; style="background: #0D4F8B; color: white;"| C(sp<sup>2</sup>)-C(sp<sup>2</sup>)
|-
! center;| Bond length/Å
! center| 1.542
! center| 1.488
! center| 1.459
|+ Table 4. Bond length of C-C bond<ref>Bernstein, H. J. (1961). BOND DISTANCES IN HYDROCARBONS * t. Retrieved from http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649</ref>
|}

Table 4. shows the literature value of C-C bond length with different hybridisation and comparing those with the Fig 7. It suggests C<sub>1</sub>, C<sub>7</sub>,C<sub>11</sub> and C<sub>14</sub> change from sp<sup>2</sup> to sp<sup>3</sup>; C<sub>4</sub> and C<sub>6</sub> remain sp<sup>2</sup>. Besides that, this table also confirms the product is hexene. The distance between C<sub>4</sub> and C<sub>6</sub> is 1.338 Å, which is similar to the bond lenght of C(sp<sup>2</sup>)-C(sp<sup>2</sup>). The rest of bond lengths are around 1.5 Å; so the rest of bonds are C(sp<sup>3</sup>)-C(sp<sup>3</sup>).

===Vibration===
{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Transition State vibration
! center; style="background: #0D4F8B; color: white;" | Inrinsic Reaction Coordinate(IRC)

|-
| center;| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 23; vibration 1;rotate x -20; </script>
<uploadedFileContents>MG5715_TS_E1_TS_VIB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| [[file:MG5715_TS_E1_IRC.gif‎]]

|-
| center;| [[file:MG5715_TS_E1_VF.PNG|thumb|none|500px|x500px|center|Fig 9. Vibration Frequencies of Transition State]]
| [[file:MG5715_TS_E1_IRC_PATH.PNG|thumb|none|500px|x500px|center|Fig 10. summary of IRC plot ]]

|}

As shown in Fig.9, there is only one imaginary frequency (at -948.8 cm<sup>-1</sup>); so it justifies the transition state is right. However, it is not enough for determining the transition state. It is critical to do the IRC calculation. RMS Gradient should be zero in reactants, products and also transition state because they are local minima. However, for transition state, it is saddle point; hence, the second derivative should be negative.

According to the gif shown above, it shows that bonds are formed '''synchronously'''.

===LOG File===
Transition state:[[File:MG5715_TS_E1_TS_MO.LOG]]

Butadiene:[[File:MG5715_TS_E1_BUTADIENE_MO.LOG]]

Ethylene:[[File:MG5715_TS_E1_ETHLYENE_MO.LOG]]

==Excercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

[[File:MG5715_TS_E2_REACTION.jpg|thumb|550px|center|Fig.11 The reaction scheme of Cyclohexadiene and 1,3-Dioxole]]

The reaction of cyclohexadiene and 1,3-Dioxole is also a Diels-Alder reaction, but this reaction will give two products (endo and exo) because of two possible transition states. The reaction scheme is shown in Fig.11 In this exercise, the transition state is opitimised by {{fontcolor1|blue|'''PM6'''}} firstly and then optimised again by {{fontcolor1|blue|'''B3LYP'''}}. Moreover, the transition state is determined by {{fontcolor1|blue|'''method 3'''}} in this exercise.

=== MO analysis of exercise 2===

[[File:MG5715_TS_E2_MO.jpg|thumb|550px|center|Fig.12 MO diagram of Cyclohexadiene and 1,3-Dioxole]]

The MO diagram of this reaction is displayed in Fig.12The energies of product's MO is shown in '''black''' lines and the {{fontcolor1|#fe7af9|'''pink'''}} lines represent the energies of transition states' MO, and all of them are drawn based on the relative energies calculated by '''B3LYP'''. Furthermore, the HOMO and LUMO of reactants are shown in Table 5. and the MOs of transition states are displayed in Table 6.

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white; text-align: center;"| HOMO
! style="background: #0D4F8B; color: white; text-align: center;" | LUMO

|-
| Clycohexadiene

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| 1,3-dioxole
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_REACTANTS_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|+ Table 5. LUMO and HOMO of reactants
|}

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white; text-align: center;"| ENDO TS
! style="background: #0D4F8B; color: white; text-align: center;" | EXO TS

|-
| LUMO+1
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| HOMO-1
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|+ Table 6. MO of Transition states
|}

====Secondary Orbital Interactions ====
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Endo-TS
! style="background: #0D4F8B; color: white;" | Exo-TS
|-
| Jmol of computed HOMO

|<jmol>
<jmolApplet>
<color>white</color>
<size>225</size>
<script> frame 48; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>MG5715_TS_E2_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>225</size>
<script> frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>MG5715_TS_E2_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| LCAO diagram of HOMO

| [[File:MG5715_TS_E2_ENDO_TS.jpg|thumb|550px|center]]

| [[File:MG5715_TS_E2_EXO_TS.jpg|thumb|550px|center]]
|+ Table 7. HOMO of Endo-TS and Exo- TS
|}

The computed HOMO and LACO diagram of HOMO are shown in Table 7. Endo-product is more stable than Exo-product due to lack of steric clash with the methyl group in cyclohexadiene. Furthermore, the Endo-TS is lower in energy because of '''Secondary Orbital Interaction'''. The lone pair of oxygen could donate the electron density to the LUMO of cyclohexadiene; hence, the Endo-TS will be stabilised. Both the Endo-TS and Endo-product are lower in energy; so this reaction is endo-selective.

==== Inverse VS Normal Demand Diels-Alder Reaction ====

[[File:MG5715_TS_E2_DA.jpg|thumb|550px|center|Fig.13 two tyes of Diels-Alder reaction]]

For a Diels-Alder reaction, the reactivity is controlled by relative energies of '''Frontier Molecular Orbitals (FMOs)'''. There are two different types as shown in Fig.13:(1) Normal demand and (2) Inverse demand. Usually, the reaction of an all carbon diene with a hetero-dienophile will give a ''normal electron demand'' because the heteroatom in dienophile may withdraw the electron density from dienophile and lower the energy of MOs. The best way to justify whether the reaction is normal demand or inverse demand is to sequence the energy of reactants as shown in Table 8. If the HOMO of dienophile is lower than that of diene, it is normal demand, vice versa. The HOMO of cyclohexadiene is the lowest; hence, this reaction is {{fontcolor1|blue|'''inverse demand'''}} Diels-Alder reaction. The reason is that the two oxygen atom in 1,3-dioxole donate the electron density toward the π-bonding and raise the energy of MOs.

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo-reaction
! style="background: #0D4F8B; color: white;" | Exo-reaction

|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_ENDO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>

|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>MG5715_TS_E2_EXO_SINGLEPOINT.LOG</uploadedFileContents>
</jmolApplet></jmol>
|+ Table 8. Single point energy of reactants
|}

=== Activation Barrier and Energy changed ===
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Energy calculated by B3LYP/kJmol<sup>-1</sup>
|-
! center| Cylcohexadiene
! center| 306.9
! center| -612593

|-
! center| 1,3-dioxole
! center| -137.3
! center| -701189

|-
! center| Endo-product
! center| 99.2
! center| -1313849

|-
! center| Endo-TS
! center| 362.2
! center| -1313622

|-
! center| Exo-product
! center| 99.7
! center| -1313845

|-
! center| Exo-TS
! center| 364.7
! center| -1313614
|+ Table 9. Energies of reactants, products and transition states
|}

According to the energies of reactants, products and transition states (shown in Table 9), the reaction energy and activation energy could be calculated by the following equation:
<pre>
Activation Energy = Transition state energy - Sum of energies of reactants
Reaction Energy = product energy - Sum of energies of reactants
</pre>

{| class="wikitable" style="margin: auto;"
! rowspan="2"|
! style="background: #0D4F8B; color: white;" colspan="2"| Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" colspan="2"| Reaction Energy/kJmol<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
|-
! center| Endo-reaction
! center| +192.6
! center| +159.8
! center| -70.3
! center| -67.4
|-
! center| Exo-reaction
! center| +195.1
! center| +169.7
! center| -69.9
! center| -63.8
|+ Table 10. Reaction energy and activation energy for both Endo and Exo product.
|}

All the energy calculated is shown in Table 10. Both the activation energy and reaction energy for Endo-product are lower than those for Exo-product. A thermodynamically favourable product is more stable, which means it has more negative reaction energy. The kinetically favourable product has lower reaction barrier (activation energy). Hence, the endo-product of this exercise is both '''thermodynamically and kinetically favourable'''.

===LOG File===
1,3-Dioxole:[[File:MG5715_TS_E2_REACTANTS_2.LOG]]

Cyclohexadiene:[[File:MG5715_TS_E2_REACTANTS_1.LOG]]

Exo-Transition State:[[File:MG5715_TS_E2_EXO.LOG]]

Endo-Transition State:[[File:MG5715_TS_E2_ENDO.LOG]]

==Excercise 3 Diels-Alder vs Cheletropic==

[[File:MG5715_TS_E3_REACTION.jpg|thumb|550px|center|Fig.14 Reaction Scheme of o-Xylylene with SO<sub>2</sub>]]

The reaction of o-xylylene with SO<sub>2</sub> could be either Diels-Alder or cheletropic reaction. For Diels-Alder reaction, o-Xylylene acts as diene and SO<sub>2</sub> acts as dienophile to form a six-membered ring and there are two possible products (endo-product and exo-product). As discussed in exercise 2, the Diels-Alder is endo-selective. For the cheletropic reaction, a five-membered ring will be formed and two new bonds are formed with the same atom. The reaction scheme of those reactions is displayed in Fig.14. In this exercise, the reactants, products and transition states were optimised by {{fontcolor1|blue|'''PM6'''}} and {{fontcolor1|blue|'''B3LYP'''}} and {{fontcolor1|blue|'''Method 3'''}} was used to find the transition state. The reaction energy and activation energy were calculated to find out the favourable reaction.

(Endo is only kinetically preferred out of the DA reactions [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== IRC Analysis===
{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | IRC
|-
| Cheletropic reaction
| [[File:MG5715_TS_E3_Cheletropic_IRC.gif]]
|-
| Endo Diels-Alder reaction
| [[File:MG5715_TS_E2_ENDO_irc.gif]]
|-
| Exo Diels-Alder reaction
| [[File:MG5715_TS_E3_EXO_irc.gif]]
|+ Table.11 The IRC of three possible reactions
|}

There are two different mechanisms for Diels-Alder reaction:(1)synchronous and symmetrical (concerted) mechanism and (2) multistage (non-concerted) and asynchronous mechanism.

* synchronous and symmetrical (concerted) mechanism
A very typical example of this mechanism is Exercise 1. The two new bonds are formed simultaneously and the two new bonds have the same bond length in the transition state.

* multistage (non-concerted) and asynchronous mechanism
The two bonds could not be formed at the same time because the bond length of them are different at transition state. Therefore, usually, a di-radical will be formed.

For Diels-Alder reaction, the distance between O and C in o-Xylylene is different from the distance between S and C in o-Xylylene at transition state because of distinct Van der Waal radii.
Therefore, the bond does not form synchronously, which could be observed in the IRC in Table 11. However, for cheletropic reaction, the two now bonds are both formed between S atom and C in o-Xylylene; so the two bond are formed synchronously as shown in IRC.

(Be careful: it looks like you're saying the DA reactions are multistage, which involves an intermediate (all positive eigenvalues in Hessian/positive frequencies) [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== Activation Energy and Reaction Energy===
[[File:MG5715_TS_E3_ENERGY.jpg|thumb|550px|center|Fig.15 Energy diagram of o-Xylylene with SO<sub>2</sub>]]

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Energy calculated by B3LYP/kJmol<sup>-1</sup>
|-
! center| O-Xylylene
! center| 469.5
! center| -812604

|-
! center| SO<sub>2</sub>
! center| -311.4
! center| -1440362

|-
! center| Endo-product
! center| 57.0
! center| -2253040

|-
! center| Endo-TS
! center| 237.8
! center| -2252919.7

|-
! center| Exo-product
! center| 56.3
! center| -2253041

|-
! center| Exo-TS
! center| 241.7
! center| -2252919.8

|-
! center| Cheletropic product
! center| -0.005251
! center| -2253024

|-
! center| Cheletropic TS
! center| 260.1
! center| -2252902
|+ Table 12. Energies of reactants, products and transition states
|}

{| class="wikitable" style="margin: auto;"
! rowspan="2"|
! style="background: #0D4F8B; color: white;" colspan="2"| Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" colspan="2"| Reaction Energy/kJmol<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
! style="background: #0D4F8B; color: white;"| PM6
! style="background: #0D4F8B; color: white;"| B3LYP
|-
! center| Endo-reaction
! center| +79.7
! center| +46.2
! center| -101.1
! center| -73.9
|-
! center| Exo-reaction
! center| +83.7
! center| +46.1
! center| -101.8
! center| -73.2
|-
| Cheletropic
! center| +102.0
! center| +63.0
! center| -158.1
! center| -58.8
|+ Table 13. Reaction energy and activation energy for both Endo and Exo product.
|}

The energies of reactants, products and transition states are shown in Table 12 and the calculated reaction energy and activation energy are displayed in Table 13. The energy diagram (Fig.15) is drawn according to the energy calculated by PM6. The product of the cheletropic reaction is the most stable because of aromaticity. However, the activation energy of cheletropic product is quite high. Therefore, at low temperature, a sultine (kinetic product) will be formed but this reaction is reversible. At high temperature, a sulfolene will be formed and this reaction is irreversible.

(Well done doing the B3LYP calculations, but it must have taken a long time. The results are distinctly different to the PM6 calculations, so you could have commented on that [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 14:29, 16 March 2018 (UTC))

=== Extension===
[[File:MG5715_TS_E3_EXTENSION_SCHEME.jpg|thumb|550px|center|Fig.16 Reaction Scheme of o-Xylylene with SO<sub>2</sub>]]
There are two dienes in o-Xylylene and therefore, it has another possible Diels-Alder reaction as shown in Fig.16. The energy calculated is displayed in Table 14 and they are calculated by PM6.

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Energy calculated by PM6/kJmol<sup>-1</sup>
|-
! center| O-Xylylene
! center| 469.5

|-
! center| SO<sub>2</sub>
! center| -311.4

|-
! center| Endo-product
! center| 172.3

|-
! center| Endo-TS
! center| 268.0

|-
! center| Exo-product
! center| 176.7

|-
! center| Exo-TS
! center| 275.8
|+ Table 14. Energy of reactants, products, and transition states
|}

{| class="wikitable" style="margin: auto;"
|
! style="background: #0D4F8B; color: white;" | Activation Energy/kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Reaction Energy/kJmol<sup>-1</sup>
|-
! center| Endo-reaction
! center| +109.9
! center| +14.2

|-
! center| Exo-reaction
! center| +117.7
! center| +18.6

|+ Table 15. Reaction energy and activation energy for both Endo and Exo product.
|}

Compare the energy in Table.15 with the data in Table.13, this reaction is quite unlikely to happen because the activation barrier is higher and the reaction energy is endothermic.

===LOG File===
o-Xylylene:[[File:MG5715_REACTANT_PM6.LOG]]

SO<sub>2</sub>:[[File:MG5715_SO2_PM6.LOG]]

Exo-Transition state:[[File:MG5715_EXO_TS_PM6.LOG]]

Endo-Transition state:[[File:MG5715_ENDO_TS_PM6.LOG]]

Cheletropic Transition state:[[File:MG5715_CHE_TS_PM6.LOG]]

==Conclusion==
In conclusion, Gauss View is a quite efficient way to locate the transition state and to calculate the energy of a reaction. Hence, it could suggest which product is thermodynamically favourable and which one is kinetically favourable. Besides that, it could mimic the reaction pathway by IRC, which can tell us whether the bonds are formed synchronously or not. One of the best way to confirm the transition state is to check the vibration frequency of transition state. For a transition state, it will always have only one imaginary frequency. According to this experiment, it suggests Diels-Alder reaction is endo-selective because of secondary orbital interaction and if the two bonds are formed with same atoms, they will form synchronously.

==Reference==

Rep:MOD:JDN15Y3lab

2018-03-16T13:43:02Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate. DFT calculations define the energy of a system as a sum of 6 components, E<sub>DFT</sub> = E<sub>NN</sub> + E<sub>T</sub> + E<sub>V</sub> + E<sub>Coul</sub> + E<sub>Exchange</sub> + E<sub>Corr</sub>.

E<sub>NN</sub> = nuclear-nuclear repulsion, E<sub>V</sub> = nuclear-electron attraction, E<sub>Coul</sub> = electron-electron Coloumb repulsion.

These terms above are the same used in the Hartree-Fock theory. The energies below are different from the terms used in the Hartree-Fock theory as E<sub>Corr</sub> is not accounted for in the theory.

E<sub>T</sub> = kinetic energy of the electrons, E<sub>Exchange</sub> = electron-electron exchange energies, E<sub>Corr</sub> = correlated movement of electrons of different spin.

B3LYP (Becke-3-LFP) is a hybrid method, which mixing exchange energies calculated in an exact manner with those obtained from DFT methods to improve performance.

== Exercise 1: Reaction between Butadiene and Ethene ==

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy. <br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

[[File:JDN15EXOClash.png| centre |300px]]

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}
By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

(The carbon atoms are all sp2-hybridised in xylylene. The structure forms a resonance with the diradical form (aromatic but still unstable) [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15RP2.png|centre|600px]]

(Use straight lines for reaction profiles [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

Based on the data from the table, we can calculate that the Cheletropic product has the lowest energy and hence is thermodynamically favoured. As sulfur is larger than C, the resulting twist in the 6 membered ring in the Diels-Alder products have a ring strain due to inefficient sp<sup>3</sup> hybridisation, resulting in a highly distorted structure. This is in comparison to the Cheletropic product, which is able to adopt a planar configuration that maximises the distance between the O and the neighbouring H atoms. However, the Cheletropic reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

From the transition state HOMO, we can observe that both the endo and exo TS have stabilising secondary orbital interactions, therefore reducing the reaction barrier in these reactions. This also explains why the energy of the exo and endo TS are relatively close in energy. We can also see that the Cheletropic TS has no stabilising secondary interactions and is highly antisymmetric with many nodes, resulting a higher energy TS.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!rowspan="2" style="text-align: center;"|
! colspan="2" style="text-align: center;"| Diels-Alder Reaction
!rowspan="2" style="text-align: center;"| Cheletropic Reaction
|-
!style="text-align: center;"| ENDO
!style="text-align: center;"| EXO
|-
|style="text-align: center;"|Transition State
HOMO
| [[File:JDN15EXOHOMO.png]]
| [[File:JDN15ENDOHOMO.png]]
| [[File:JDN15CHEHOMO.png]]
|}

(It's pretty hard to see what's going on in these MO pictures. Perhaps use transparent surfaces? [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:43, 16 March 2018 (UTC))

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)
!File Logs

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.105054
|style="text-align: center;" | 0.067300
|style="text-align: center;" | 119.8
|style="text-align: center;" | 20.7
|style="text-align: center;" | [[File:JDN15_EXO2_Product.LOG]]
[[File:JDN15_EXO_TS2.LOG]]
|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" | 0.102070
|style="text-align: center;" | 0.065612
|style="text-align: center;" | 112.0
|style="text-align: center;" | 16.3
|style="text-align: center;" | [[File:JDN15_ENDO2_Product.LOG]]
[[File:JDN15_ENDO2_TS.LOG]]
|}

Comparing the values from the table, we can see that both exo and endo for this Diels-Alder reaction has a much higher reaction barrier than the previous reactions (discussed earlier). Hence the secondary Diels-Alder reactions are the least kinetically favourable. We can also see that the reaction energies of the secondary Diels-Alder reactions are positive, indicating that the reaction is highly thermodynamically unfavourable as ΔG>0 and hence the reaction is not spontaneous.

==Conclusion==
Gaussian is a useful method to carry out molecular geometry optimisations and calculations. By investigating the free energies of the transition states and products, we can determine the reaction energies and reaction barriers of the reaction. We can then determine which reactions are kinetically or thermodynamically favoured. This computational method is a powerful tool that can be used for preliminary research before testing out the reactions experimentally. It also provides a visual representation that allows better understanding on the interactions between the MOs of the molecules before, during and after the reaction.

Rep:Mod:pk1615Yr3

2018-03-16T13:37:21Z

Tam10: /* Further work */

=Transition states and reactivity=

==Introduction==
This experiment involves using computational quantum chemistry methods to analyse molecular structures, their molecular orbitals (MO's) and energetics. Providing information about reaction pathways, activation energies and transition state (TS) intermediates. The transition state structures that are investigated are based on the shape of the potential energy surface; these are found through computational molecular-orbital based methods by solving the Schrödinger equation. The computational methods used to optimise and run frequency calculations on molecular structures are the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP.
<br>
===Computational methods used===
The semi-empirical PM6 method is based on the Hartree–Fock (HF) formalism, in which the wavefunction of a system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The PM6 method differs with the HF method as it makes many approximations and obtains some parameters from empirical data. This method is used for molecules where the full HF method of optimisation without any approximations is too expensive. The fact that the PM6 method incorporates empirical data as approximations allows for optimisation to be fast as less calculations need to be made. However, these approximations mean that results are less accurate. On the other hand, the B3LYP method is a DFT-hybrid method which is based on electron density in antithesis to the PM6 which is based on wavefunctions. The B3LYP method, which incorporates both the HF and DFT methods, uses less approximations making it a more accurate but more computationally expensive optimisation method compared to the PM6 method.
<br>
===The Potential Energy Surface of a system===
The Potential Energy Surface (PES) describes the energy of a system in terms of parameters such as the positions of atoms in a structure. For a molecule with N<sub>atoms</sub> there are 3N<sub>atoms</sub>-6 independent geometric variables that are determined; including bond lengths, bond angles and torsional angles. Using computational methods the points of a potential energy curve can be determined and analysis of its first and second derivatives yields important information about the systems reaction energetics. The first derivatives give the gradient and the second derivatives give the curvature of the (PES). Points with zero gradient are minima which correspond to products, or can be saddle points, energy maxima, that represent transition state species. The transition state is an intermediate structure between reactants and products in the reaction pathway; it is a maximum in the potential energy curve that requires maximum energy to be overcome to result in products.
<br>

The PES curve's first derivative can be related to the force acting on atoms which acts in the direction that will lower potential energy, giving it a negative value. At bond length distances above the equilibrium bond length the potential energy curve gradient is positive and the force acting upon it to reach the minimum equilibrium length point on the curve is negative. At bond length distances below the equilibrium bond length the potential energy curve gradient is negative and the force acting on it to increase the bond length is positive<ref name="intro" />. Since the TS is at the maxima the force acts on it in the direction to minimise bond length to reach products indicating it has a negative force constant. A TS can therefore be identified by an imaginary frequency in its first vibrational mode since calculating the frequency of a harmonic oscillator with a negative force constant yields an imaginary frequency. This frequency calculation was a method to confirm if a TS structure was created after optimisation.
<br>

The reactions that will be studied using these computational methods are pericyclic reactions which occur through a cyclic TS in a concerted fashion. More specifically Diels-Alder cycloadditions will be looked into where a [4+2] cycloaddition occurs to form a 6-membered ring system.

==Exercise 1==

[[File:Overall reaction pk1615.PNG|thumb|400px|centre|Scheme 1:Diels-Alder reaction of butadiene and ethene]]

The transition state of the Diels-Alder reaction between butadiene and ethene, shown above in scheme 1, will be studied. This reaction involves a [4+2] cycloaddition between the two reactant molecules resulting in a ring product. The PM6 optimisation method was used in this exercise to optimise the reaction molecules.
<br>

===Molecular orbital analysis===

Optimising the reactants, transition state and product molecules revealed the energies and shape of the molecular orbitals for each structure. This then helped to identify the reactant HOMO and LUMO MO's that reacted to form the transition state, leading to the construction of the molecular orbital diagram for the transition state, figure 2.
{|style="margin: 0 auto;"
| [[File:Mos of butadiene ethene word pk1615.PNG|thumb|upright|344x344px|Figure 1:Molecular orbital energy levels of butadiene and ethene.]]
| [[File:Mo diagram butadiene pk1615.PNG|thumb|upright|500x500px|Figure 2:Molecular orbital diagram of the Diels-Alder transition state.]]
|}
<br>

{| class="wikitable"
! Ethene MO's
! Butadiene MO's
! Transition state Mo's
|-
| Ethene-φ1 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ2 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene-φ2 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ3 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The Jmols of the MO's of the reactants and TS have been displayed above. It is observed that for a molecular orbital to react successfully and produce a product they need to be of the same symmetry. In the MO diagram it can be seen that symmetric reacts with symmetric and anti-symmetric reacts with anti-symmetric orbitals to product a TS HOMO or LUMO of the same symmetry.If they are of different symmetry the reaction is disallowed. This is seen where the butadiene HOMO which is asymmetric reacts with the ethene LUMO, also asymmetric, to product TS HOMO 1 and LUMO 2 which are both asymmetric.

The overlap integral for a symmetric-antisymmetric interaction is zero, whereas for a symmetric-symmetric or antisymmetric-antisymmetric interaction a non-zero value is obtained. The transition state MO diagram reveals that the transition state orbitals produced arise from s-s or a-a interactions, these inteaction contain non-zero overlap integrals, yielding true MO's.

===Carbon-Carbon bond length analysis===

{| class="wikitable"
|+ Table 1-Carbon-Carbon bond lengths of the reactants, TS and products.
! Carbon bonds
! Ethene bond lengths (Å)
[[File:Ethene pk1615.PNG]]
! Butadiene bond lengths (Å)
[[File:Butadiene pk1615.PNG]]
! Transition state bond lengths (Å)
[[File:Ts pk1615.PNG]]
! Cyclohexene bond lengths (Å)
[[File:Product pk1615.PNG]]
! Bond length change
|-
| C<sub>1</sub>-C<sub>2</sub>
| 1.327
| -
| 1.380
| 1.538
|Increase
|-
| C<sub>2</sub>-C<sub>3</sub>
| -
| -
| 2.115
| 1.536
|Decrease
|-
| C<sub>3</sub>-C<sub>4</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>4</sub>-C<sub>5</sub>
| -
| 1.471
| 1.411
| 1.333
|Decrease
|-
| C<sub>5</sub>-C<sub>6</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>6</sub>-C<sub>1</sub>
| -
| -
| 2.114
| 1.536
|Decrease
|}

The typical length for a C-C sp<sup>3</sup> bond is 1.54 Å, whereas the length of a C-C sp<sup>2</sup> bond is 1.34 Å <ref name="C length" />. In table 1 it can be seen that single and double bond values are approximately the same length as the typical values expected, confirming the structures obtained through optimisation. For example the bond between C<sub>1</sub>-C<sub>2</sub> is seen to increase as the bond becomes sp<sup>3</sup> hybridised from sp<sup>2</sup>.
<br>
The Van der Waals radius of a carbon atom is 1.7 Å <ref name="C radius" />. In the Diels-Alder transition state is can be seen that the bonds that form between C<sub>6</sub>-C<sub>1</sub> and C<sub>2</sub>-C<sub>3</sub>, 2.1 Å, are shorter than two carbon Van der Waals radii values, 3.4 Å. This confirms that in the TS the molecules, that were far apart, gradually come closer; when they are found within less than two carbon Van der Waals radii they are able to approach the formation of a single bond that is found in the products.
<br>

===Transition state vibration===
The vibration that corresponds to the reaction path at the transition state is identified as the one with a negative frequency, known as the imaginary frequency stated above. The Diels-Alder transition state at this vibration is displayed below. It can be seen that at this transition state vibration the bonds between the two reactants form in a synchronous manner, this is seen by the movement of the displacement vectors that move towards each other at the same time. This synchronous bond formation is further confirmed by the analysis of the IRC that shows the reactions proceeds through a concerted mechanism. This is the typical mechanism pathway found for Diels-Alder cycloadditions.

<jmol>
<jmolApplet>
<title>Transition state vibration</title>
<color>white</color>
<size>300</size>
<script>frame 17; vibration 1;rotate x -20; </script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The IRC for the Diels-Alder transition state can be found [[Media:CH IRC PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene TS can be found [[Media:CH OPT TS PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene product can be found [[Media:CH OPT MIN PRODUCTS pk1615.LOG|here]]

==Exercise 2==
[[File:Exercise 2 overall reactionpk1615.PNG|thumb|400px|centre|Scheme 2:Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole]]
In this exercise the [4+2] cycloaddition reaction between cyclohexadiene and 1,3-dioxole is investigated. This Diels-Alder reaction yields two products, the exo and endo products, due to the different symmetries of the transition state.
<br>
===Molecular orbital analysis===
Using the B3LYP optimisation method the TS for both the exo and endo molecules was determined. This yielded the occupied, HOMO, and unoccupied, LUMO, orbitals and their energies for each TS. The HOMO and LUMO orbitals for both symmetries are displayed below. These were then used to construct an MO diagram for this Diels-Alder reaction, figure 3, which was based on the MO diagram of the butadiene and ethene TS as these reacting molecules are symmetrically similar.

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>EXO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>EXO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>ENDO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
[[File:Exercise 2 mo edited pk1615.PNG|thumb|400px|centre|Figure 3:Molecular orbital diagram of Cyclohexadiene and 1,3-Dioxole TS (the exo TS has been draw, however, the same orbitals apply for the endo TS)]]

According to symmetry the cyclohexadiene and 1,3-dioxole MO's can be considered as the butadiene and ethene MO's from figure 2 respectively. The energy levels of the reactant and TS orbitals has been determined from their B3LYP/6-31G(d) optimised .chk file MO's, and have been positioned accordingly. It is observed that the energy level of these MO's is slightly shifted compared to the butadiene ethene MO's. The cyclohexadiene HOMO is lower in energy than the 1,3-dioxole HOMO, whereas, in figure 2, the butadiene HOMO is higher in energy compared to the ethene HOMO. It is to be noted that both the exo and endo TS have different geometries and their MO's differ slightly in energy, however,they both contain the same molecular orbital combinations and their MO's are found in similar energetic regions compared to reactant MO's, therefore, one molecular orbital diagram has been drawn for both.
<br>
The .log files for the B3LYP/6-31G(d) optimised molecules can be found here:[[Media:CYCLOHEXANE OPT FREQ MIN B pk1615.LOG|Cyclohexadiene]], [[Media:CYCLOPENTADIENE OPT FREQ MIN B pk1615.LOG|1,3-dioxole]], [[Media:EXO TS OPT FREQ B pk1615.LOG |Exo TS]], [[Media:ENDO_TS_OPT_FREQ_TS_B pk1615.LOG|Endo TS]], [[Media:EXO PRODUCT OPT FREQ MIN B. pk1615LOG|Exo product]], [[Media:ENDO PRODUCT OPT FREQ MIN B pk1615.LOG|Endo product]].

===Normal and Inverse demand Diels-Alder reaction analysis===
In a normal demand Diels-Alder reaction the HOMO of the electron rich diene reacts with the LUMO, π<sup>*</sup> bond, of the electron deficient dienophile ( the substituted alkene). In a normal demand reaction the HOMO of the diene reacts with the LUMO of the dienophile to form the HOMO and LUMO of the TS, this is seen in the reaction between butadiene (diene) and ethene (dienophile), figure 2, which produces HOMO 2 and LUMO 1.
<br>
In an inverse demand reaction, an electron deficient diene's LUMO now reacts with an electron rich dienophile's HOMO. This occurs due to a switch in energies of the diene's and dienophile's orbitals which occurs when an electron withdrawing group is attached to the diene, lowering its HOMO, and/or an electron donating group is attached to the dienophile, raising its π orbital's energy making it's HOMO higher in energy. This leads to the dienophile HOMO being high enough in energy to react with the diene's LUMO. This case is seen in the reaction between cyclohexadiene and 1,3-dioxole, figure 3, in which the dienophile, 1,3-dioxole, has electron donating oxygen atoms attached to it, raising its HOMO and allowing the TS HOMO 2 and LUMO 1 to be reached in an inverse demand reaction.
[[File:Inverse demand pk1615 .PNG|thumb|400px|centre|Figure 4:Diels-Alder normal and inverse reaction molecular orbital analysis]]

===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the B3LYP/6-31G(d) optimised .log files
{| class="wikitable"
|+ Table 2-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| Cyclohexadiene
| -233.324374
| -612593.1906
|-
| 1,3-dioxole
| -267.068642
| -701188.773
|-
| Reactants combined
| -500.393016
| -1313781.964
|-
| Endo TS
| -500.332146
| -1313622.149
|-
| Exo TS
| -500.329167
| -1313614.328
|-
| Endo product
| -500.418692
| -1313849.376
|-
| Exo product
| -500.417319
| -1313845.771
|}

{| class="wikitable"
|+ Table 3-Endo and Exo reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 159.8142
| -67.41234
|-
| Exo
| 167.63557
| -63.80753
|}

Table 2 gives energy values of reactants, TS's and products for both the exo and endo geometries. These energy values were used to obtain calculations of the reaction barriers, also known as the activation energies, and the reaction energies for the endo and exo reaction pathways, table 3. The reaction barrier is the maximum energy in the reaction pathway which needs to be overcome for a reaction to proceed to its product. The reaction barrier energy is calculated as the TS minus the reactants and is the energy value needed to reach the maximum in the potential energy surface of the system. Furthermore, the reaction energy is calculated as the reactant minus the products and is the energy obtained when the minimum of the potential energy surface is reached. The results of the energy barriers and energies shown that the endo product is both the kinetically and thermodynamically stable product. This is explained through secondary orbital interactions that occur in the endo product between the ring π bond and the oxygen p-orbitals displayed in figure 5.
<br>
[[File:Endo stabilisation pk1615.PNG|thumb|400px|centre|Figure 5:Endo product secondary orbital stabilisation interaction]]
<br>
These secondary orbital interactions stabilise the product, making the endo product the lowest energy product, the thermodynamic one. Additionally, through stabilising the product these secondary orbital interactions lower the energy barrier of the endo reaction making it the more kinetically stable one as well. The kinetic product has the lower energy barrier i.e less energy is needed to overcome its activation energy. Moreover, steric reasons that may affect the exo product, making it both thermodynamically and kinetically less stable, are the repulsive interactions that could occur between the bridgehead carbons of the ring and the 1,3-dioxole oxygens that are closer in the exo geometry. This could lead to destabilisation of the exo product molecule.

==Exercise 3==
[[File:Diels alder cheletropic pk1615.PNG|thumb|400px|centre|Scheme 3:Diels-Alder/Cheletropic reaction of o-Xylylene and SO<sub>2</sub>]]
This exercise involves studying the Diels-Alder and Cheletropic reactions between o-Xylylene- and SO<sub>2</sub>, dispayed in scheme 3.
<br>
The IRC for the three reaction pathways can be found here: [[Media:XYLENE ENDO IRC pk1615.LOG|Diels-Alder endo]], [[Media:XYLENE EXO IRC PM6 pk1615.LOG|Diels-Alder exo]], [[Media:ISO-INDENE IRC PM6 pk1615.LOG|Cheletropic]].
<br>
The PM6 optimised .log files for the reaction molecules can be found here: [[Media:XYLYLENE REACTANT OPT MIN PM6 pk1615.LOG|o-Xylylene]], [[Media:SO2 OPT MIN PM6 pk1615.LOG|SO<sub>2</sub>]], [[Media:XYLENE OPT TS PM6 ENDO pk1615.LOG|Endo TS]], [[Media:XYLENE OPT TS PM6 exo pk1615.LOG|Exo TS]], [[Media:ISO-INDENE OPT TS PM6 pk1615.LOG|Cheletropic TS]], [[Media:XYLENE OPT MIN PM6 ENDO pk1615.LOG|Endo product]], [[Media:XYLENE OPT MIN PM6 pk1615 exo.LOG|Exo product]], [[Media:ISO-INDENE OPT MIN PM6 pk1615.LOG|Cheletropic product]].
===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the PM6 optimised .log files.
{| class="wikitable"
|+ Table 4-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| ortho-Xylylene
| 0.177678
| 466.493625
|-
| SO<sub>2</sub>
| -0.119269
| -313.1407834
|-
| Reactants
| 0.058409
| 153.352841
|-
| DA Endo TS
| 0.090560
| 237.765298
|-
| DA Exo TS
| 0.092077
| 241.748182
|-
| Cheletropic TS
| 0.099061
| 260.084675
|-
| DA Endo product
| 0.021705
| 56.9864818
|-
| DA Exo product
| 0.021454
| 56.3274813
|-
| Cheletropic Product
| 0.000005
| 0.013127501
|}

{| class="wikitable"
|+ Table 5-Reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 84.4124569
| -96.3663593
|-
| Exo
| 88.3953407
| -97.0253599
|-
| Cheletropic
| 106.731834
| -153.339714
|}
<br>
The most favourable route in this reaction is the endo route. As seen in table 5 the endo TS has the lowest reaction barrier energy, therefore, it is easier to overcome this reaction barrier to reach the TS and get a product. This lower energy barrier value is due to the endo TS and product having the secondary orbital interactions stated above; now between the oxygen p orbital and the pi orbitals of the conjugated benzene ring. These secondary orbital interactions stabilise the molecule, lowering its reaction energy barrier. It is to be noted that the cheletropic product is the more thermodynamically stable one but has a very high energy barrier which is unfavourable to reach as a lot of energy is needed to overcome it; this is an undesirable route. The endo product is the kinetically stable one and is the route that is preferred. A reaction profile diagram for the three pathways has been constructed in figure 6, enabling their energetics to be compared.

(You should show this secondary orbital overlap too [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 16 March 2018 (UTC))

<br>
[[File:Exercise 3 reaction coordinate 3.PNG|thumb|400px|centre|Figure 6:Reaction profile diagram]]
<br>
Observing the IRC paths for the three reaction TS's, it can be seen that the xylylene 6-membered ring bonds change in length as the reaction proceeds from reactants to products through the TS. The xylylene ring obtains aromaticity as the bond length changes, this could be considered a driving force for the reaction and proves the molecule's instability as it readily rearranges as the reaction proceeds to the product.

===An alternative reaction route===
An alternative reaction route can occur in the Diels-Alder reaction between o-Xylylene and SO<sub>2</sub>, where the SO<sub>2</sub> molecule reacts with the diene inside the six-membered ring of the xylylene molecule. This approach is displayed in scheme 4.
[[File:Alternative route pk1615.PNG|thumb|400px|centre|Scheme 4:Diels-Alder alternative reaction of o-Xylylene and SO<sub>2</sub>]]
{| class="wikitable"
|+ Table 6-Reaction barriers and energies.
! Reaction
! Energy barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 114.631969
| -18.906229
|-
| Exo
| 122.469083
| -23.353824
|}

(The reaction energies are not negative by my calculations [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 16 March 2018 (UTC))

<br>
This endo and exo route are neither thermodynamically or kinetically stable since they have low reaction energy values (are not stable) and have high energy barriers. These high energy barriers require large amounts of energy to be overcome which is undesirable and would lead to products that are not very thermodynamically stable.
<br>
The IRC for the the alternative reaction pathways can be found here: [[Media:ENDO TS IRC pk1615.LOG|Alternative Diels-Alder endo]], [[Media:EXO TS IRC pk1615.LOG|Alternative Diels-Alder exo]].

==Further work==
An electrocyclic reaction is a pericyclic reaction that involves a rearrangement of a pi to a sigma bond to form a ring product, such as the one displayed in scheme 5.
[[File:Electrocyclic pk1615.PNG|thumb|400px|centre|Scheme 5: Electrocyclic reaction.]]
<br>
[[File:Further work disrotation pk1615.PNG|thumb|400px|centre|Figure 7: Electrocyclic reaction orbital alignment.]]
<br>
This reaction is photochemically allowed to occur in a 4π disrotatory mechanism according to the Woodward-Hoffmann rules. The molecular orbital interactions that yield the ring product are shown in figure 7. It can be seen that the orbitals move in a disrotatory fashion. The TS of the molecule was optimised to the PM6 level and the MO's where identified in order to confirm their movement.

(It's true that it would undergo disrotation under photochemical conditions, but you are running these calculations on the ground state ie thermal. Your IRC actually goes via conrotation (HOMO) if you observe it [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:37, 16 March 2018 (UTC))

<br>
{|style="margin: 0 auto;"
| [[File:Further work reactant MO pk1615.PNG|thumb|upright|344x344px|Figure 8: Reactant MO (1).]]
| [[File:Further work TS MO pk1615.PNG|thumb|upright|344x344px|Figure 9: TS MO (3).]]
|}
<br>
Even though the PM6 level of optimisation is not the most accurate for viewing the correct symmetry of the MO's; it is concluded through the MO's that this electrocyclic reaction proceeds with disrotatory motion, as the orbitals allign as expected in the TS LUMO of the molecule leading to the formation of the sigma bond. A higher level of optimisation would be more suitable to determine the direction of orbital movement.
<br>
The IRC for the TS can be found [[Media:TS IRC pk1615.LOG|here]].
<br>
The PM6 optimised .log files can be found here: [[Media:REACTANTS OPT MIN PM6 pk1615.LOG|Reactant]], [[Media:PRODUCT OPT TS PM6 pk1615.LOG|TS]], [[Media:PRODUCT OPT MIN PM6 pk1615.LOG|Product]].

==Conclusion==
Over the years computational chemistry has been and is still being widely developed. It provides the opportunity to optimise structures; revealing information about their bond lengths, bond angles, MO's and their energetics. These optimised structures can then be used for comparison to synthetically formed structures in the lab. Optimisation methods such as the PM6 and B3LYP methods have proven to yield accurate results for molecules and TS's that can be used to further analyse and compare the thermochemistry of reactions. A huge advantage of quantum computational chemistry is that it allows for the prediction and analysis of a TS that cannot be isolated as an individual structure in the physical world, as in the case of the pericyclic reactions that have been investigated in this experiment.

==References==
<references>
<ref name="intro">Computational Quantum Chemistry. Chapter 1, 2013, Pages 1-62.</ref>
<ref name="C length">B.P. Stoicheff. "The variation of carbon-carbon bond lengths with environment as determined by spectroscopic studies of simple polyatomic molecules". Tetrahedron, Vol 17, Issues 3–4, 1962, Pages 135-145.</ref>
<ref name="C radius">A Bondi. "Van der Waals Volumes and Radii". J. Phys. Chem., 68 (3), 1964, Pages 441–451.</ref>
</references>

Rep:Mod:pk1615Yr3

2018-03-16T13:35:23Z

Tam10: /* Exercise 3 */

=Transition states and reactivity=

==Introduction==
This experiment involves using computational quantum chemistry methods to analyse molecular structures, their molecular orbitals (MO's) and energetics. Providing information about reaction pathways, activation energies and transition state (TS) intermediates. The transition state structures that are investigated are based on the shape of the potential energy surface; these are found through computational molecular-orbital based methods by solving the Schrödinger equation. The computational methods used to optimise and run frequency calculations on molecular structures are the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP.
<br>
===Computational methods used===
The semi-empirical PM6 method is based on the Hartree–Fock (HF) formalism, in which the wavefunction of a system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The PM6 method differs with the HF method as it makes many approximations and obtains some parameters from empirical data. This method is used for molecules where the full HF method of optimisation without any approximations is too expensive. The fact that the PM6 method incorporates empirical data as approximations allows for optimisation to be fast as less calculations need to be made. However, these approximations mean that results are less accurate. On the other hand, the B3LYP method is a DFT-hybrid method which is based on electron density in antithesis to the PM6 which is based on wavefunctions. The B3LYP method, which incorporates both the HF and DFT methods, uses less approximations making it a more accurate but more computationally expensive optimisation method compared to the PM6 method.
<br>
===The Potential Energy Surface of a system===
The Potential Energy Surface (PES) describes the energy of a system in terms of parameters such as the positions of atoms in a structure. For a molecule with N<sub>atoms</sub> there are 3N<sub>atoms</sub>-6 independent geometric variables that are determined; including bond lengths, bond angles and torsional angles. Using computational methods the points of a potential energy curve can be determined and analysis of its first and second derivatives yields important information about the systems reaction energetics. The first derivatives give the gradient and the second derivatives give the curvature of the (PES). Points with zero gradient are minima which correspond to products, or can be saddle points, energy maxima, that represent transition state species. The transition state is an intermediate structure between reactants and products in the reaction pathway; it is a maximum in the potential energy curve that requires maximum energy to be overcome to result in products.
<br>

The PES curve's first derivative can be related to the force acting on atoms which acts in the direction that will lower potential energy, giving it a negative value. At bond length distances above the equilibrium bond length the potential energy curve gradient is positive and the force acting upon it to reach the minimum equilibrium length point on the curve is negative. At bond length distances below the equilibrium bond length the potential energy curve gradient is negative and the force acting on it to increase the bond length is positive<ref name="intro" />. Since the TS is at the maxima the force acts on it in the direction to minimise bond length to reach products indicating it has a negative force constant. A TS can therefore be identified by an imaginary frequency in its first vibrational mode since calculating the frequency of a harmonic oscillator with a negative force constant yields an imaginary frequency. This frequency calculation was a method to confirm if a TS structure was created after optimisation.
<br>

The reactions that will be studied using these computational methods are pericyclic reactions which occur through a cyclic TS in a concerted fashion. More specifically Diels-Alder cycloadditions will be looked into where a [4+2] cycloaddition occurs to form a 6-membered ring system.

==Exercise 1==

[[File:Overall reaction pk1615.PNG|thumb|400px|centre|Scheme 1:Diels-Alder reaction of butadiene and ethene]]

The transition state of the Diels-Alder reaction between butadiene and ethene, shown above in scheme 1, will be studied. This reaction involves a [4+2] cycloaddition between the two reactant molecules resulting in a ring product. The PM6 optimisation method was used in this exercise to optimise the reaction molecules.
<br>

===Molecular orbital analysis===

Optimising the reactants, transition state and product molecules revealed the energies and shape of the molecular orbitals for each structure. This then helped to identify the reactant HOMO and LUMO MO's that reacted to form the transition state, leading to the construction of the molecular orbital diagram for the transition state, figure 2.
{|style="margin: 0 auto;"
| [[File:Mos of butadiene ethene word pk1615.PNG|thumb|upright|344x344px|Figure 1:Molecular orbital energy levels of butadiene and ethene.]]
| [[File:Mo diagram butadiene pk1615.PNG|thumb|upright|500x500px|Figure 2:Molecular orbital diagram of the Diels-Alder transition state.]]
|}
<br>

{| class="wikitable"
! Ethene MO's
! Butadiene MO's
! Transition state Mo's
|-
| Ethene-φ1 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ2 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene-φ2 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ3 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The Jmols of the MO's of the reactants and TS have been displayed above. It is observed that for a molecular orbital to react successfully and produce a product they need to be of the same symmetry. In the MO diagram it can be seen that symmetric reacts with symmetric and anti-symmetric reacts with anti-symmetric orbitals to product a TS HOMO or LUMO of the same symmetry.If they are of different symmetry the reaction is disallowed. This is seen where the butadiene HOMO which is asymmetric reacts with the ethene LUMO, also asymmetric, to product TS HOMO 1 and LUMO 2 which are both asymmetric.

The overlap integral for a symmetric-antisymmetric interaction is zero, whereas for a symmetric-symmetric or antisymmetric-antisymmetric interaction a non-zero value is obtained. The transition state MO diagram reveals that the transition state orbitals produced arise from s-s or a-a interactions, these inteaction contain non-zero overlap integrals, yielding true MO's.

===Carbon-Carbon bond length analysis===

{| class="wikitable"
|+ Table 1-Carbon-Carbon bond lengths of the reactants, TS and products.
! Carbon bonds
! Ethene bond lengths (Å)
[[File:Ethene pk1615.PNG]]
! Butadiene bond lengths (Å)
[[File:Butadiene pk1615.PNG]]
! Transition state bond lengths (Å)
[[File:Ts pk1615.PNG]]
! Cyclohexene bond lengths (Å)
[[File:Product pk1615.PNG]]
! Bond length change
|-
| C<sub>1</sub>-C<sub>2</sub>
| 1.327
| -
| 1.380
| 1.538
|Increase
|-
| C<sub>2</sub>-C<sub>3</sub>
| -
| -
| 2.115
| 1.536
|Decrease
|-
| C<sub>3</sub>-C<sub>4</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>4</sub>-C<sub>5</sub>
| -
| 1.471
| 1.411
| 1.333
|Decrease
|-
| C<sub>5</sub>-C<sub>6</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>6</sub>-C<sub>1</sub>
| -
| -
| 2.114
| 1.536
|Decrease
|}

The typical length for a C-C sp<sup>3</sup> bond is 1.54 Å, whereas the length of a C-C sp<sup>2</sup> bond is 1.34 Å <ref name="C length" />. In table 1 it can be seen that single and double bond values are approximately the same length as the typical values expected, confirming the structures obtained through optimisation. For example the bond between C<sub>1</sub>-C<sub>2</sub> is seen to increase as the bond becomes sp<sup>3</sup> hybridised from sp<sup>2</sup>.
<br>
The Van der Waals radius of a carbon atom is 1.7 Å <ref name="C radius" />. In the Diels-Alder transition state is can be seen that the bonds that form between C<sub>6</sub>-C<sub>1</sub> and C<sub>2</sub>-C<sub>3</sub>, 2.1 Å, are shorter than two carbon Van der Waals radii values, 3.4 Å. This confirms that in the TS the molecules, that were far apart, gradually come closer; when they are found within less than two carbon Van der Waals radii they are able to approach the formation of a single bond that is found in the products.
<br>

===Transition state vibration===
The vibration that corresponds to the reaction path at the transition state is identified as the one with a negative frequency, known as the imaginary frequency stated above. The Diels-Alder transition state at this vibration is displayed below. It can be seen that at this transition state vibration the bonds between the two reactants form in a synchronous manner, this is seen by the movement of the displacement vectors that move towards each other at the same time. This synchronous bond formation is further confirmed by the analysis of the IRC that shows the reactions proceeds through a concerted mechanism. This is the typical mechanism pathway found for Diels-Alder cycloadditions.

<jmol>
<jmolApplet>
<title>Transition state vibration</title>
<color>white</color>
<size>300</size>
<script>frame 17; vibration 1;rotate x -20; </script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The IRC for the Diels-Alder transition state can be found [[Media:CH IRC PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene TS can be found [[Media:CH OPT TS PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene product can be found [[Media:CH OPT MIN PRODUCTS pk1615.LOG|here]]

==Exercise 2==
[[File:Exercise 2 overall reactionpk1615.PNG|thumb|400px|centre|Scheme 2:Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole]]
In this exercise the [4+2] cycloaddition reaction between cyclohexadiene and 1,3-dioxole is investigated. This Diels-Alder reaction yields two products, the exo and endo products, due to the different symmetries of the transition state.
<br>
===Molecular orbital analysis===
Using the B3LYP optimisation method the TS for both the exo and endo molecules was determined. This yielded the occupied, HOMO, and unoccupied, LUMO, orbitals and their energies for each TS. The HOMO and LUMO orbitals for both symmetries are displayed below. These were then used to construct an MO diagram for this Diels-Alder reaction, figure 3, which was based on the MO diagram of the butadiene and ethene TS as these reacting molecules are symmetrically similar.

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>EXO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>EXO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>ENDO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
[[File:Exercise 2 mo edited pk1615.PNG|thumb|400px|centre|Figure 3:Molecular orbital diagram of Cyclohexadiene and 1,3-Dioxole TS (the exo TS has been draw, however, the same orbitals apply for the endo TS)]]

According to symmetry the cyclohexadiene and 1,3-dioxole MO's can be considered as the butadiene and ethene MO's from figure 2 respectively. The energy levels of the reactant and TS orbitals has been determined from their B3LYP/6-31G(d) optimised .chk file MO's, and have been positioned accordingly. It is observed that the energy level of these MO's is slightly shifted compared to the butadiene ethene MO's. The cyclohexadiene HOMO is lower in energy than the 1,3-dioxole HOMO, whereas, in figure 2, the butadiene HOMO is higher in energy compared to the ethene HOMO. It is to be noted that both the exo and endo TS have different geometries and their MO's differ slightly in energy, however,they both contain the same molecular orbital combinations and their MO's are found in similar energetic regions compared to reactant MO's, therefore, one molecular orbital diagram has been drawn for both.
<br>
The .log files for the B3LYP/6-31G(d) optimised molecules can be found here:[[Media:CYCLOHEXANE OPT FREQ MIN B pk1615.LOG|Cyclohexadiene]], [[Media:CYCLOPENTADIENE OPT FREQ MIN B pk1615.LOG|1,3-dioxole]], [[Media:EXO TS OPT FREQ B pk1615.LOG |Exo TS]], [[Media:ENDO_TS_OPT_FREQ_TS_B pk1615.LOG|Endo TS]], [[Media:EXO PRODUCT OPT FREQ MIN B. pk1615LOG|Exo product]], [[Media:ENDO PRODUCT OPT FREQ MIN B pk1615.LOG|Endo product]].

===Normal and Inverse demand Diels-Alder reaction analysis===
In a normal demand Diels-Alder reaction the HOMO of the electron rich diene reacts with the LUMO, π<sup>*</sup> bond, of the electron deficient dienophile ( the substituted alkene). In a normal demand reaction the HOMO of the diene reacts with the LUMO of the dienophile to form the HOMO and LUMO of the TS, this is seen in the reaction between butadiene (diene) and ethene (dienophile), figure 2, which produces HOMO 2 and LUMO 1.
<br>
In an inverse demand reaction, an electron deficient diene's LUMO now reacts with an electron rich dienophile's HOMO. This occurs due to a switch in energies of the diene's and dienophile's orbitals which occurs when an electron withdrawing group is attached to the diene, lowering its HOMO, and/or an electron donating group is attached to the dienophile, raising its π orbital's energy making it's HOMO higher in energy. This leads to the dienophile HOMO being high enough in energy to react with the diene's LUMO. This case is seen in the reaction between cyclohexadiene and 1,3-dioxole, figure 3, in which the dienophile, 1,3-dioxole, has electron donating oxygen atoms attached to it, raising its HOMO and allowing the TS HOMO 2 and LUMO 1 to be reached in an inverse demand reaction.
[[File:Inverse demand pk1615 .PNG|thumb|400px|centre|Figure 4:Diels-Alder normal and inverse reaction molecular orbital analysis]]

===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the B3LYP/6-31G(d) optimised .log files
{| class="wikitable"
|+ Table 2-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| Cyclohexadiene
| -233.324374
| -612593.1906
|-
| 1,3-dioxole
| -267.068642
| -701188.773
|-
| Reactants combined
| -500.393016
| -1313781.964
|-
| Endo TS
| -500.332146
| -1313622.149
|-
| Exo TS
| -500.329167
| -1313614.328
|-
| Endo product
| -500.418692
| -1313849.376
|-
| Exo product
| -500.417319
| -1313845.771
|}

{| class="wikitable"
|+ Table 3-Endo and Exo reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 159.8142
| -67.41234
|-
| Exo
| 167.63557
| -63.80753
|}

Table 2 gives energy values of reactants, TS's and products for both the exo and endo geometries. These energy values were used to obtain calculations of the reaction barriers, also known as the activation energies, and the reaction energies for the endo and exo reaction pathways, table 3. The reaction barrier is the maximum energy in the reaction pathway which needs to be overcome for a reaction to proceed to its product. The reaction barrier energy is calculated as the TS minus the reactants and is the energy value needed to reach the maximum in the potential energy surface of the system. Furthermore, the reaction energy is calculated as the reactant minus the products and is the energy obtained when the minimum of the potential energy surface is reached. The results of the energy barriers and energies shown that the endo product is both the kinetically and thermodynamically stable product. This is explained through secondary orbital interactions that occur in the endo product between the ring π bond and the oxygen p-orbitals displayed in figure 5.
<br>
[[File:Endo stabilisation pk1615.PNG|thumb|400px|centre|Figure 5:Endo product secondary orbital stabilisation interaction]]
<br>
These secondary orbital interactions stabilise the product, making the endo product the lowest energy product, the thermodynamic one. Additionally, through stabilising the product these secondary orbital interactions lower the energy barrier of the endo reaction making it the more kinetically stable one as well. The kinetic product has the lower energy barrier i.e less energy is needed to overcome its activation energy. Moreover, steric reasons that may affect the exo product, making it both thermodynamically and kinetically less stable, are the repulsive interactions that could occur between the bridgehead carbons of the ring and the 1,3-dioxole oxygens that are closer in the exo geometry. This could lead to destabilisation of the exo product molecule.

==Exercise 3==
[[File:Diels alder cheletropic pk1615.PNG|thumb|400px|centre|Scheme 3:Diels-Alder/Cheletropic reaction of o-Xylylene and SO<sub>2</sub>]]
This exercise involves studying the Diels-Alder and Cheletropic reactions between o-Xylylene- and SO<sub>2</sub>, dispayed in scheme 3.
<br>
The IRC for the three reaction pathways can be found here: [[Media:XYLENE ENDO IRC pk1615.LOG|Diels-Alder endo]], [[Media:XYLENE EXO IRC PM6 pk1615.LOG|Diels-Alder exo]], [[Media:ISO-INDENE IRC PM6 pk1615.LOG|Cheletropic]].
<br>
The PM6 optimised .log files for the reaction molecules can be found here: [[Media:XYLYLENE REACTANT OPT MIN PM6 pk1615.LOG|o-Xylylene]], [[Media:SO2 OPT MIN PM6 pk1615.LOG|SO<sub>2</sub>]], [[Media:XYLENE OPT TS PM6 ENDO pk1615.LOG|Endo TS]], [[Media:XYLENE OPT TS PM6 exo pk1615.LOG|Exo TS]], [[Media:ISO-INDENE OPT TS PM6 pk1615.LOG|Cheletropic TS]], [[Media:XYLENE OPT MIN PM6 ENDO pk1615.LOG|Endo product]], [[Media:XYLENE OPT MIN PM6 pk1615 exo.LOG|Exo product]], [[Media:ISO-INDENE OPT MIN PM6 pk1615.LOG|Cheletropic product]].
===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the PM6 optimised .log files.
{| class="wikitable"
|+ Table 4-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| ortho-Xylylene
| 0.177678
| 466.493625
|-
| SO<sub>2</sub>
| -0.119269
| -313.1407834
|-
| Reactants
| 0.058409
| 153.352841
|-
| DA Endo TS
| 0.090560
| 237.765298
|-
| DA Exo TS
| 0.092077
| 241.748182
|-
| Cheletropic TS
| 0.099061
| 260.084675
|-
| DA Endo product
| 0.021705
| 56.9864818
|-
| DA Exo product
| 0.021454
| 56.3274813
|-
| Cheletropic Product
| 0.000005
| 0.013127501
|}

{| class="wikitable"
|+ Table 5-Reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 84.4124569
| -96.3663593
|-
| Exo
| 88.3953407
| -97.0253599
|-
| Cheletropic
| 106.731834
| -153.339714
|}
<br>
The most favourable route in this reaction is the endo route. As seen in table 5 the endo TS has the lowest reaction barrier energy, therefore, it is easier to overcome this reaction barrier to reach the TS and get a product. This lower energy barrier value is due to the endo TS and product having the secondary orbital interactions stated above; now between the oxygen p orbital and the pi orbitals of the conjugated benzene ring. These secondary orbital interactions stabilise the molecule, lowering its reaction energy barrier. It is to be noted that the cheletropic product is the more thermodynamically stable one but has a very high energy barrier which is unfavourable to reach as a lot of energy is needed to overcome it; this is an undesirable route. The endo product is the kinetically stable one and is the route that is preferred. A reaction profile diagram for the three pathways has been constructed in figure 6, enabling their energetics to be compared.

(You should show this secondary orbital overlap too [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 16 March 2018 (UTC))

<br>
[[File:Exercise 3 reaction coordinate 3.PNG|thumb|400px|centre|Figure 6:Reaction profile diagram]]
<br>
Observing the IRC paths for the three reaction TS's, it can be seen that the xylylene 6-membered ring bonds change in length as the reaction proceeds from reactants to products through the TS. The xylylene ring obtains aromaticity as the bond length changes, this could be considered a driving force for the reaction and proves the molecule's instability as it readily rearranges as the reaction proceeds to the product.

===An alternative reaction route===
An alternative reaction route can occur in the Diels-Alder reaction between o-Xylylene and SO<sub>2</sub>, where the SO<sub>2</sub> molecule reacts with the diene inside the six-membered ring of the xylylene molecule. This approach is displayed in scheme 4.
[[File:Alternative route pk1615.PNG|thumb|400px|centre|Scheme 4:Diels-Alder alternative reaction of o-Xylylene and SO<sub>2</sub>]]
{| class="wikitable"
|+ Table 6-Reaction barriers and energies.
! Reaction
! Energy barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 114.631969
| -18.906229
|-
| Exo
| 122.469083
| -23.353824
|}

(The reaction energies are not negative by my calculations [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 16 March 2018 (UTC))

<br>
This endo and exo route are neither thermodynamically or kinetically stable since they have low reaction energy values (are not stable) and have high energy barriers. These high energy barriers require large amounts of energy to be overcome which is undesirable and would lead to products that are not very thermodynamically stable.
<br>
The IRC for the the alternative reaction pathways can be found here: [[Media:ENDO TS IRC pk1615.LOG|Alternative Diels-Alder endo]], [[Media:EXO TS IRC pk1615.LOG|Alternative Diels-Alder exo]].

==Further work==
An electrocyclic reaction is a pericyclic reaction that involves a rearrangement of a pi to a sigma bond to form a ring product, such as the one displayed in scheme 5.
[[File:Electrocyclic pk1615.PNG|thumb|400px|centre|Scheme 5: Electrocyclic reaction.]]
<br>
[[File:Further work disrotation pk1615.PNG|thumb|400px|centre|Figure 7: Electrocyclic reaction orbital alignment.]]
<br>
This reaction is photochemically allowed to occur in a 4π disrotatory mechanism according to the Woodward-Hoffmann rules. The molecular orbital interactions that yield the ring product are shown in figure 7. It can be seen that the orbitals move in a disrotatory fashion. The TS of the molecule was optimised to the PM6 level and the MO's where identified in order to confirm their movement.
<br>
{|style="margin: 0 auto;"
| [[File:Further work reactant MO pk1615.PNG|thumb|upright|344x344px|Figure 8: Reactant MO (1).]]
| [[File:Further work TS MO pk1615.PNG|thumb|upright|344x344px|Figure 9: TS MO (3).]]
|}
<br>
Even though the PM6 level of optimisation is not the most accurate for viewing the correct symmetry of the MO's; it is concluded through the MO's that this electrocyclic reaction proceeds with disrotatory motion, as the orbitals allign as expected in the TS LUMO of the molecule leading to the formation of the sigma bond. A higher level of optimisation would be more suitable to determine the direction of orbital movement.
<br>
The IRC for the TS can be found [[Media:TS IRC pk1615.LOG|here]].
<br>
The PM6 optimised .log files can be found here: [[Media:REACTANTS OPT MIN PM6 pk1615.LOG|Reactant]], [[Media:PRODUCT OPT TS PM6 pk1615.LOG|TS]], [[Media:PRODUCT OPT MIN PM6 pk1615.LOG|Product]].

==Conclusion==
Over the years computational chemistry has been and is still being widely developed. It provides the opportunity to optimise structures; revealing information about their bond lengths, bond angles, MO's and their energetics. These optimised structures can then be used for comparison to synthetically formed structures in the lab. Optimisation methods such as the PM6 and B3LYP methods have proven to yield accurate results for molecules and TS's that can be used to further analyse and compare the thermochemistry of reactions. A huge advantage of quantum computational chemistry is that it allows for the prediction and analysis of a TS that cannot be isolated as an individual structure in the physical world, as in the case of the pericyclic reactions that have been investigated in this experiment.

==References==
<references>
<ref name="intro">Computational Quantum Chemistry. Chapter 1, 2013, Pages 1-62.</ref>
<ref name="C length">B.P. Stoicheff. "The variation of carbon-carbon bond lengths with environment as determined by spectroscopic studies of simple polyatomic molecules". Tetrahedron, Vol 17, Issues 3–4, 1962, Pages 135-145.</ref>
<ref name="C radius">A Bondi. "Van der Waals Volumes and Radii". J. Phys. Chem., 68 (3), 1964, Pages 441–451.</ref>
</references>

Rep:Mod:cjc415 TS

2018-03-16T13:28:09Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

==Introduction==
This wiki explores a variety of pericyclic reactions, namely Diels-Alders and Cheletropic reactions and their transitions states.

===Potential energy surfaces (PES)===
A potential energy surface gives the energy of a molecule as a function of its geometry. It serves as a tool to help in the analysis of reaction dynamics and molecular geometry. The PES has a total of 3N-6 degrees of freedom.

At the stationary points, the gradient is equal to zero. These energy minima correspond to the physically stable species, such as reactants and products while transition states correspond to saddle points. When the second derivative is calculated, the energy minima and transition states can be differentiated. If a positive value is obtained, it suggests that an energy minima is obtained. Conversely, a negative value corresponds to a transition state.

This is also reflected in Gaussview. A transition state would produce one negative frequency while minima points will not reflect negative values, hence no imaginary frequencies are present.

===What is a transition state?===
A transition state (TS) is usually defined as a structure along the reaction coordinate which corresponds to the highest potential energy along this coordinate. In terms of mathematics, the TS of a chemical reaction represents a Saddle Point on the Potential Energy Surface (PES).

A transition state of a reactive pathway is the one with lowest energy compared to other paths perpendicular to it. It is also the highest energy point of that reactive pathway.

===Diels Alders reaction===
Otherwise known as a [4+2] cycloaddition, the Diels-Alder reaction involves a conjugated diene and an alkene, known as the dienophile. The reaction is concerted and occurs via a single, cyclic transition state.

Usually, the diene is electron-rich while the dienophile is electron poor. The HOMO of the diene would interact with the LUMO of the dienophile. However, there is also a possibility of an inverse electron demand Diels-Alder reaction, whereby it is the LUMO of the diene interacting with the HOMO of the dienophile. This can occur if electron withdrawing substituents are added to the diene and electron donating substituents are added to the dienophile. There are other types of Diels-Alder reactions, such as Hetero-Diels-Alder, which involves at least one heteroatom and lewis acid activation Diels-Alder reactions, which involves the use of lewis acids such as zinc chloride to act as catalysts of normal-demand Diels-Alder reactions by coordinating to the dienophile.

When selectivity issues arise, in the case of example 2, where the dienophile is substituted, this would give rise to the possibility of either the endo or exo product. The kinetic endo product is favoured in irreversible reactions due to the stabilisation of the endo transition state by dipolar, orbital and van der waals interactions. The exo product is considered the thermodynamic product due better sterics.

===Cheletropic reactions===
Cheletropic reactions are pericyclic reactions involving a transition state with a cyclic array of atoms and interacting orbitals. It would involve a reorganisation of sigma and pi bonds in the cyclic array. A key feature of these reactions are that in one of the reagents, both new bonds are being made on the same atom. In the case of example 3, both new bonds are made on the sulfur atom.

===Studying Transition States using Gaussview===
When more than one product can be formed, it is important to study the transition state. In the formation of kinetic products, the pathway which involves the lower activation energy and hence more stable transition state, is favoured. Should thermodynamic products be favoured, the more stable thermodynamic product is favoured.

Gaussview is being used to study these transition states. By optimising the structures in their transition states, the MOs and their respective energies can be analysed and extracted.

In this lab, semi-empirical PM6 and Density Function Theory (DFT) methods are being used to optimise the structures. PM6 is a faster but less accurate method. It replaces the two electron integrals, exchange and Coulomb integrals, which are challenging to determine.

DFT optimisations defines the energy of the system as a summation of 6 individual components, namely: nuclear-nuclear repulsion, nuclear-electron attraction, electron-electron coloumb repulsion, kinetic energy of electrons, electron-electron exchange energies and correlated movement of electrons of different spins.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Overall reaction scheme===
[[Image:CJC Ex1 Rxn scheme.jpg |300px]]

It is to be noted that the trans-butadiene form is the lowest global energy minimum. However, it is the cis conformation that is reacting with ethene.

===Molecular orbitals===
The three tables below show the jmols of the optimised reactants (butadiene and ethene) as well as MO 16, 17, 18 and 19 of the transition state.

{| class="wikitable"
|-
| colspan="3"|'''Butadiene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 BUTADIENE MINIMISED UPDATED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
It is to be noted that the trans-butadiene form is the lowest global energy minimum. However, it is the cis conformation that is reacting with ethene.

{| class="wikitable"
|-
| colspan="3"|'''Ethene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 ETHENE MINIMISED.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="5"|'''Transition state'''
|-
! Optimised TS
! MO 16
! MO 17 (HOMO)
! MO 18 (LUMO)
! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 108; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The MO diagram for the transition state is shown below, with S representing 'Symmetric' and AS representing 'Asymmetric'.

It is assumed based on prior knowledge that only orbitals of the same symmetry combine.

It is to be noted that the MO for a TS is very much different compared to a reactant-product MO diagram. For a transition state MO, the resulting orbitals which the electrons occupy are destabilised and at a higher energy level with respect to the original orbitals in the reactants.

[[Image:CJC415 Ex1 MO.jpg |500px]]

The antisymmetric HOMO of butadiene (MO 11) reacts with the antisymmetric LUMO of ethene (MO 7) to give two antisymmetric MOs (MO 16 and 19).
Similarly, the symmetric LUMO of butadiene (MO 12) reacts with the symmetric HOMO of ethene (MO 6) to give two symmetric MOs (MO 17 and 18).

When symmetric and asymmetric orbitals overlap, the orbital overlap integral is zero, hence causing them to be unable to overlap, even if they are of similar energies. On the other hand, when two symmetric orbitals or two asymmetric orbitals overlap, the orbital overlap integral is non zero, allowing interaction to occur.

To determine the energy levels of the respective MOs in the TS with respect to the original MOs in butadiene and ethene, the energy levels of the MOs were compared. It was found that MO 16 and 17 were very similar in energy, at -0.32536 and -0.32531 respectively.

===Bond lengths===
{| class="wikitable"
|-
! Butadiene
! Ethene
! Cyclohexene
! Transition state
|-
|[[Image:CJC415 Ex1 Butadiene.bmp |80px]]
|[[Image:CJC415 Ex1 Ethene.bmp |50px]]
|[[Image:CJC415 Ex1 Cyclohexene.jpg |150px]]
|[[Image:CJC415 Ex1 TS.bmp |150px]]
|}

Going from reactants to TS and to products, the shortening of the C5-C6 bond, going from single to double bond was observed. Distances between C1-C2 and C3-C4 were also reduced as bonds were formed. Conversely, lengthening of C1-C6 and C4-C5 bonds were observed, going from double to single bonds.

The typical sp3 and sp2 C-C bond lengths are 1.54 Å and 1.34 Å respectively and the Van der Waals radius of the C atom is 1.70 Å. It can be noted that the partly formed C-C bonds (C1-C2 and C3-C4), which were at lengths 2.11Å in the TS, are longer than the typical sp3 bond, but also shorter than twice the radius of the carbon atom. This would suggest that the orbitals are sufficiently close to interact but the formation of a full C-C bond has yet to be completed.

===Reaction pathway===
From the jmol file shown below, formation of bonds between diene and dienophile took place simultaneously, hence bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 109; vibration 1</script>
<uploadedFileContents>CJC415 Ex1 CORRECT PRODUCT MINIMISEDTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Molecular orbitals===
The jmols of the optimised reactants and products are shown in the tables below. They were optimized using the B3LYP 6-31G(d) level.

{| class="wikitable"
|-
| colspan="3"|'''Cyclohexadiene'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 CORRECT CYCLOHEXADIENE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="3"|'''1,3 dioxole'''
|-
! Optimised molecule
! HOMO
! LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 DIOXOLE B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="2"|'''Optimised products'''
|-
! Exo product
! Endo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 EXO PRODUCT MINIMISED B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex2 ENDO PRODUCT MINIMISED B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

At the transition state, the interactions between the 4 MOs (shown above) produced the following 4 MOs for the endo and exo products accordingly.

{| class="wikitable"
|-
| colspan="5"|'''Transition State MOs - Exo product'''
|-
! Optimised molecule
! MO 40
! MO 41 (HOMO)
! MO 42 (LUMO)
! MO 43
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 54; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|-
| colspan="5"|'''Transition State MOs - Endo product'''
|-
! Optimised molecule
! MO 40
! MO 41 (HOMO)
! MO 42 (LUMO)
! MO 43
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CJC415 Ex2 ENDO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Based on the energy levels obtained from the log files of the optimised structures, the MO diagram shown below was drawn. For a normal Diels-Alder reaction, where the diene is electron rich and the dienophile is electron poor, the diene has a higher HOMO than the dienophile. However, from the MO diagram in this example, dioxole, which acts as the dienophile, has a higher energy HOMO than cyclohexadiene. This would imply that it is an inverse demand Diels-Alder reaction.

The dienophile is electron rich due to the presence of two oxygen atoms adjacent to the C=C bond, donating electron density to the double bond, hence resulting in a higher energy HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:CJC415 Ex2 Exo MO.jpg|frameless|658x658px]]
|[[File:CJC415 Ex2 Endo MO.jpg|frameless|678x678px]]
|}

===Calculating Energies===
The energies extracted from the log files of the molecules are from optimisations using the B3LYP/6-31G(d) method at 298K.

{| class="wikitable"
|-
! Structure
! Energy (hartree/particle)
|-
|Cyclohexadiene
| -233.324375
|-
|1,3 dioxole
| -267.068132
|-
|Endo product
| -500.418692
|-
|Endo TS
| -500.332149
|-
|Exo product
| -500.417323
|-
|Exo TS
| -500.329166
|}

To calculate the activation and reaction energies for the products formed, the following calculations were made:

1) Activation energy = Energy of TS - sum of energy of reactants

2) Reaction energy = Energy of product - sum of energy of reactants

The conversion between hartree and KJ/mol is: 1 hartree = 2625.4976 KJ/mol

Combined energies of reactants = -1.313779 x 10<sup>6</sup> KJ/mol

The reaction barriers and reaction energies of the products formed are shown below.

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo
| 166.3
| -65.5
|-
|Endo
| 158.1
| -69.1
|}

===Kinetic and thermodynamic products===

From the calculated reaction energies, it can observed that the endo product is both the kinetic and thermodynamic product. It has a smaller reaction barrier and hence a lower activation energy, making it the kinetic product. Moreover, it also has a lower reaction energy and is more stable than the exo product, hence making it the thermodynamic product.

This is different from the large majority of Diels-Alders reactions, whereby the exo product is more thermodynamically favoured as it has lower steric interactions. The endo product is then the kinetic product due to the presence of stabilising secondary orbital interactions.

The reason for this is as follows. As seen from the 3D chemdraw diagram of the product below, the endo product experiences additional secondary non bonding interactions. It is also slightly less hindered compared to the exo product which experiences a greater steric clash between the two hydrogens (circled in red) which are pointing towards each other in space. The endo product experiences less steric clashes as seen from the fact that the hydrogens are further apart.

[[File:CJC415 Ex2 Steric clashes.jpg|frameless|658x658px]]

Moreover, from the jmols above, the endo TS experiences stabilising secondary orbital interactions between the p orbitals of oxygen in 1,3-dioxole and the p orbitals of carbon in cyclohexadiene. These interactions are not present in the exo product. Hence the TS of the endo product would be lower in energy.

==Exercise 3: Diels-Alder vs Cheletropic==
Unlike the previous two examples, which are purely Diels-Alder reactions, this final example involves a competing cheletropic reaction in addition to the Diels-Alder reaction pathways.

It is common for cheletropic reactions to involve SO<sub>2</sub>. Such a competing reaction arises due to the competing thermodynamic and kinetic products. Experimental work has found that Diels-Alder product is the kinetic product of SO<sub>2</sub> with conjugated dienes. However, this product is thermally unstable and undergoes a retro-Diels-Alder reaction. A thermodynamic product then forms, producing a stable five membered ring. Hence, the dominance of cheletropic products arises not from reactivity but from product instability. <ref>[http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852]</ref>

The optimised structures of the reactants, transition states and products that have been optimized at PM6 level of the 3 different reaction routes are shown below:

{| class="wikitable"
|-
| colspan="8"|'''Optimised structures at 298K'''
|-
! Xylylene
! SO2
! Endo TS
! Exo TS
! Cheletropic TS
! Endo Product
! Exo Product
! Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 XYLYLENE REACTANT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 SO2 REACTANT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 ENDO TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 EXO TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 CHELETROPIC TS MINIMUM.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 ENDO PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 EXO PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>CJC415 Ex3 CHELETROPIC PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(It seems that you've read in the wrong file for the Endo TS (it has frozen bonds). It's also missing 2 hydrogens. For all your JMols you must make sure you select the correct frame [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

===IRC paths===
The IRC paths for these 3 reactions as well as the log file links are shown below.
{| class="wikitable"
|-
|Endo DA reaction
| [[Image:CJC415 Ex3 Endo IRC movie.gif]]
| [[File:CJC415 Ex3 ENDO PRODUCT.LOG]]
[[File:CJC415 Ex3 ENDO TS.LOG]]
|-
|Exo DA reaction
| [[Image:CJC415 Ex3 Exo IRC movie.gif]]
| [[File:CJC415 Ex3 EXO PRODUCT.LOG]]
[[File:CJC415 Ex3 EXO TS.LOG]]
|-
|Cheletropic reaction
| [[Image:CJC415 Ex3 Cheletropic IRC movie.gif]]
| [[File:CJC415 Ex3 CHELETROPIC PRODUCT.LOG]]
[[File:CJC415 Ex3 CHELETROPIC TS.LOG]]
|}

===Energy calculations===

The optimized energies of the structures in hartrees obtained from their log files are tabulated below.
{| class="wikitable"
|-
! Structure
! Energy at RT (hartree/particle)
|-
|Xylylene
| 0.178764
|-
|SO2
| -0.118614
|-
|Exo DA TS
| 0.092077
|-
|Exo DA Product
| 0.021451
|-
|Endo DA TS
| 0.090559
|-
|Endo DA Product
| 0.021697
|-
|Cheletropic TS
| 0.099062
|-
|Cheletropic Product
| 0.000005
|}

(Your xylylene energy is a bit high [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

Similar as the previous calculations:

1) Activation energy = Energy of TS - sum of energy of reactants

2) Reaction energy = Energy of product - sum of energy of reactants

The conversion between hartree and KJ/mol is: 1 hartree = 2625.4976 KJ/mol

Combined energies of reactants = 157.9236 KJ/mol

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo DA
| 83.8
| -101.6
|-
|Endo DA
| 79.8
| -100.9
|-
|Cheletropic
| 102.2
| -157.9
|}

Using the values calculated from above, the following reaction coordinate was drawn.

[[Image:CJC415 Ex3 Reaction coordinate.jpg |frameless|800x800px]]

(Please use straight lines for reaction profiles. But the data is clear [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

From the reaction profile and calculations above, it can be seen that the activation energy of both endo and exo reactions are similar in energy, at +79.8KJ/mol and +83.8KJ/mol respectively. It is much lower than the cheletropic reaction which has an activation of +102.2KJ/mol. This is because both the transition states of the endo and exo pathways experience stabilising secondary interactions while the cheletropic TS, which also has numerous nodes, does not.

(Numerous nodes in the HOMO? It would be good to show this [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:28, 16 March 2018 (UTC))

It can be easily seen that the thermodynamic product is the cheletropic product due to the fact that the product is of the lowest energy. However, the amount of activation energy required is the largest. Hence, this pathway is likely to be reactive only under thermodynamic conditions, such as at high temperature and under equilibrating conditions.

Favouring the cheletropic product which is the most stable could be because the product is able to adopt a planar geometry, allowing the distance between the oxygen and neighbouring hydrogen atoms to be maximised.

Based on the activation energy values, it can be deduced that the endo Diels-Alders product is the kinetic product as that reaction pathway has the lowest energy barrier. This is because the endo product has secondary stabilising interactions between the oxygen on sulfur dioxide and the pi system of xylylene. Hence, this route would be favoured when the reaction is irreversible, under low temperatures and non equilibrating conditions.

===Extension: Reaction at second cis-butadiene fragment of xylylene===

One of the key reasons why the cheletropic and Diels-Alders reactions occur (shown above) is due to the reactivity of xylylene. Though it has a conjugated pi system and is planar, it is not aromatic. This is because the π electrons are not in a cyclic arrangement and since xylylene contains 8 π electrons, it does not fulfill Hückel's rule which states that a cyclic, planar molecule with 4n+2 π electrons are required for the molecule to be aromatic. Hence, xylylene is anti-aromatic. The formation of a stable aromatic benzene ring in the above 3 reactions would drive product formation, since the products are more stable than the reactants.

Apart from the outer cis-butadiene, there is another inner cis-butadiene fragment present that can participate in a Diels-Alders reaction. However, this site is not favoured due to the presence of steric hinderance and the formation of a strained bicyclic ring in the product as shown in the reaction scheme below.

[[Image:CJC415 Ex3 Extension rxn scheme.jpg |frameless|800x800px]]

It is important to note that in the cheletropic and Diels-Alders reactions involving the outer cis-butadiene, a stable benzene ring is formed in the product. However, this stabilising aromaticity is not found when the inner cis-butadiene reacts, causing it to be unfavoured.

{| class="wikitable"
|-
!
! Log file
! Energy (hartress)
|-
|Exo TS
| [[File:CJC415 Extension EXO TS.LOG]]
| 0.105054
|-
|Exo Product
| [[File:CJC415 Extension EXO PRODUCT.LOG]]
| 0.067301
|-
|Endo TS
| [[File:CJC415 Extension ENDO TS.LOG]]
| 0.102070
|-
|Endo Product
| [[File:CJC415 Extension ENDO PRODUCT.LOG]]
| 0.065607
|}

Similar to the previous section, the combined energies of reactants = 157.9236 KJ/mol. Hence, using the same formulas to calculate the activation and reaction energies, the following values were obtained:

{| class="wikitable"
|-
!
! Activation energies (KJ/mol)
! Reaction energies (KJ/mol)
|-
|Exo DA
| 117.9
| 18.8
|-
|Endo DA
| 110.1
| 14.3
|}

==Conclusion==
Different pericyclic reactions were studied in this lab using Gaussian to optimize the products, reactants and transition states as well as study their optimized geometry. This has allowed us to rationalize and explain the reasoning behind why certain products were favoured over others as well as calculate the activation and reaction energies of these pathways. Doing so has allowed us to draw out the MOs to see the orbital interactions as well as predict product formation, something extremely useful that can be done before experiments are being carried out.

==References==

Rep:Kh1015TSEx3RD

2018-03-16T12:59:45Z

Tam10:

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===
Figure 4.3 under Methodology section shows the reaction scheme for Exercise 3.

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

(Nice to see someone investigating the rates of reaction. There are a few more considerations - including which approximations you are using - when attempting to calculate rates. One of them is the shape of the PES, such as the "wideness" of the barrier. However, the thing that happens to break this the most is there is another barrier: the conversion of the endo and exo products, which is lower than all the other barriers! This means that, under kinetic conditions, the endo isn't the major product [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:59, 16 March 2018 (UTC))

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

(Some suggestions: 1) If you normalise to the common point (reactants) then you can read off the activation and reaction energies more easily. 2) The numeric values of the x axis have no real meaning so these axis labels can be removed. 3) Placing the values of the activation and reaction energies on the chart itself will further improve legibility (especially where the endo- and exo- products overlap [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:59, 16 March 2018 (UTC))

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomers), it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring would end up with a stable 6 π electrons system (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash (Red being not favourable and Blue being favourable) in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This was due to the approach of two orthogonal lone pairs of S atom towards the 5,6-dimethylenecyclohexa-1,3-diene in the chelotropic TS (Orange colour) that was not present in the Diels-Alder reactions. This contributes to the observation that the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, was much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

(Nice analysis. It's pretty difficult to get much information about primary interactions with NCI. Perhaps it would be more valuable to get information about the products with NCI [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:59, 16 March 2018 (UTC))

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Mod:aps315TS

2018-03-16T11:14:22Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

== Introduction ==

In a simplistic view, a transition state is classified as the highest energy point along a reaction coordinate. As a result, it is characterized as a stationary point and can be confirmed by determining the first derivative of the reaction coordinate as zero. However, this approximation is not an accurate representation of a chemical system undergoing a reaction. This constricted approximation does not account for the possibility of displacement from a system's equilibrium. A chemical system can in fact be displaced in 3N-6 degrees of freedom and a Potential Energy Surface (PES) is a more accurate description of a chemical system undergoing a reaction. A PES is a plot of potential energy against two combinations of these possible degrees of freedom. On a PES a transition state is now characterized as a saddle point and can be confirmed as having a first derivative equal to zero and a second derivative that is negative.

This report shall discuss the determination of transition states for three pericyclic reactions. These transition states will be located and characterized using GuassView by optimizing the reagents towards a minimum then subsequently optimizing the transition state using PM6 and B3LYP methods. The PM6 method is semi-empirical; it is effectively a less involved or reduced form of the Hartree-Fock method and is employed for swiftness. The B3LYP method was carried out using a 6-31G(d) basis set, it is a hybrid function utilizing he Hartree-Fock as well as the DFT method and is employed for a more accurate transition state determination.

In addition, Intrinsic Reaction Coordinate (IRC) calculations were utilized to examine the profile of the minimum energy pathway. An IRC follows the minimum energy pathway along the PES from the transition state towards the reactants and/or the products dependent upon how the calculation was ran. IRC calculations were employed to analyse the reaction profile, changes in bond length and to visualize the reaction.

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a Diels-Alder reaction, a [4+2] cycloaddition, producing cyclohexene as the product. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup> In order for the reaction to occur butadiene must adopt the s-cis conformation. This reaction obeys normal electron demand with the diene (butadiene) being more electron rich than the dienophile (ethylene). A reaction scheme is presented below (Scheme 1).
[[File:Diels-Alder(2)_aps315.jpg|350px|thumb|centre|'' '''Scheme 1.''' Reaction of Butadiene with Ethylene.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between butadiene and ethylene was constructed using relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 1). Butadiene's non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

The MOs 16 and 19 produced by Guassian for the transition state are presented below and are correlated to the appropriate interactions in the MO diagram (Figure 1). These demonstrate orbital interactions between the HOMO of butadiene and the LUMO of ethylene, with both having asymmetric symmetry. As a result, it can be inferred that in order for orbital interaction to be favorable and result in overall stabilization of the molecule, the symmetries must be the same (e.g asymmetric and asymmetric) and they must have non-zero orbital overlap integrals. This arises due to the requirement for an overall symmetric function and non-zero overlap integrals corresponding to orbital spacial overlap.<sup>2</sup> A symmetric-symmetric and asymmetric-asymmetric interaction will have a non-zero overlap while opposing symmetries (asymmetric-symmetric/ symmetric-asymmetric) will have zero overlap integral and an overall asymmetric function.

[[File:Diels-Alder aps315(4).jpg|350px|thumb|centre|'' '''Diagram 1.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

<b> Figure 1. </b>

<b> Ethylene </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>Ethylene HOMO</title>
<color>white</color>
<uploadedFileContents>ETHENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>Ethylene LUMO</title>
<color>white</color>
<uploadedFileContents>ETHENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

<b> Butadiene </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<uploadedFileContents>BUTENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<uploadedFileContents>BUTENE_OPT(1)_APS315.LOG</uploadedFileContents>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

<b> Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 16 (HOMO-1)</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 16; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS HOMO</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 17; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS LUMO</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 18; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>

|
<jmol>
<jmolApplet>
<title>TS 19 (LUMO+1)</title>
<color>white</color>
<uploadedFileContents>EX1_TS_APS315.LOG</uploadedFileContents>
<script> frame 32; mo 19; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>

|}

=== Carbon Bond Lengths ===
The Diels-Alder reaction involves the formation of two C-C sigma bonds and the breaking of three C-C pi bonds. The C-C bond lengths calculated by Guassian for the reagents, transition state and product are presented below (Table 1). C-C bonds 1,2 and 6 correspond to the bonds of butadiene and bond 4 corresponds to the bond of ethylene (Diagram 2).

Typical bond lengths for C-C sp<sup>2</sup> single and double bond as well as sp<sup>3</sup> single bond are 1.460, 1.316 and 1.507 Å respectively. The values obtained vary by approximately 0.01 Å compared with typical values, however, when compared with literature values for cyclohexene, the values compare well with slight deviation.<sup>3</sup> The double bond calculated is 0.012 Å longer than that in literature, this deviation most likely arises due to the method applied, PM6, providing less accurate values. The use of B3LYP/6-31G(d) would most likely provide a substantially closer value.

The typical van der Waals radius of a carbon atom is 1.70 Å whilst the length of the partly formed C-C bonds in the transition state are 2.113 and 2.116 Å. The van der Waals radius is defined as half the distance of closest approach between two non-bonded atoms, therefore the total distance is 3.40 Å. The values obtained are substantially shorter than this radius by 1.287 and 1.284 Å, aligning with the partial formation of C-C bonds in the transition state.

As the reaction progresses bonds 3 and 5 shorten as the C-C bonds are formed. Simultaneously, bonds 2,4 and 6 all elongate whilst bond 1 shortens, represented below in Graph 1.

[[File:Bond_Numbers_aps315.jpg|250px|thumb|centre|'' '''Figure 2.''' C-C Bond Numbers.'']]

{| class="wikitable" border="1"| centre
|+ '' '''Table 1.''' C-C Bond Lengths during Diels-Alder Reaction''
! Bond !! Reagents Bond Length / Å !! Transition State Bond Length / Å !! Product Bond Length / Å
|-
| '''Bond 1''' || 1.468 || 1.411 || 1.338
|-
| '''Bond 2''' || 1.335 || 1.380 || 1.500
|-
| '''Bond 3''' || - || 2.113 || 1.540
|-
| '''Bond 4''' || 1.327 || 1.382 || 1.541
|-
| '''Bond 5''' || - || 2.116 || 1.540
|-
| '''Bond 6''' || 1.335 || 1.380 || 1.500
|}

[[File:BondLengths_aps315.JPG|550px|thumb|centre|'' '''Graph 1.''' C-C Bond Length Changes with Reaction Coordinate.'']]

=== Bond Vibration ===
The vibration that corresponds to the formation of the transition state is presented below (Image 2). The formation of the new sigma bonds can be seen to occur simultaneously, this demonstrates the synchronous, concerted nature of the Diels-Alder mechanism.

[[File:TS_Vibrations_aps315.gif | centre ]]

=== Relevant Files ===

Butadiene - [[:File:BUTENE_OPT(1)_APS315.LOG]]

Ethylene - [[:File:ETHENE_OPT(1)_APS315.LOG]]

Transition State - [[:File:EX1_TS_APS315.LOG]]

Cyclohexene - [[:File:PRODUCT_aps315.LOG]]

Transition State IRC - [[:File:TS_IRC_aps315.LOG]]

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

The reaction between cyclohexadiene and 1,3-dioxole is a Diels-Alder reaction, a [4+2] cycloaddition, producing two possible products dependent upon the orientation of molecule approach (Scheme 2). An exo product is formed when the substituents of the 1,3-dioxole are facing away from the cyclohexadiene π system. Alternatively, the endo product is formed when the substituents of the 1,3-dioxole are facing towards the cyclohexadiene π system. In general, the endo product is frequently the thermodynamically preferred due to secondary orbital effects that involve stabilizing overlap in the endo transition state. This pericyclic reaction proceeds via a concerted mechanism, with a single transition state.<sup>1</sup>
[[File:Ex2_Scheme(2)_aps315.jpg|450px|thumb|centre|'' '''Scheme 2.''' Reaction of Cyclohexadiene and 1,3-Dioxole.'']]

=== Molecular Orbitals ===
An MO diagram for the formation of the transition state between cyclohexadiene and 1,3-dioxole was constructed using average relative energies calculated in Gaussian for the transition state. This is presented below (Diagram 2). Non-bonding molecular orbitals are not involved in the formation of the transition state and so have not been included to make the diagram clearer.

Due to the electron-donating nature of the oxygen atoms present in 1,3-dioxole, the dienophile becomes more electron rich, raising the energies of its HOMO and LUMO. This results in a [4+2] cycloaddition that obeys inverse electron demand.<sup>1</sup> When comparing the exo and endo transition states, both still obey inverse electron demand and follow the MO diagram displayed below, however, the relative energies of the molecular orbitals is shifted. The endo transition state can be seen to have a lower energy HOMO by 0.00492 Hartrees/particle and a higher energy LUMO by 0.00237 Hartrees/particle. This shift in energies arises due to stabilization of the endo HOMO by secondary orbital effects; overlap between the π system of cyclohexadiene and 1,3-dioxole. The exo transition state is only stabilized through primary interactions, whereas the endo transition state is stabilized through both primary and secondary interactions. This is presented below (Figure 2).

The associated MOs are presented below for both the Exo and Endo transition states (Figure 3).

[[File:Ex2_MO_aps315.jpg|350px|thumb|centre|'' '''Diagram 2.''' MO Diagram for the formation of Diels-Alder Transition State.'']]

[[File:Ex2_Secondary_aps315.jpg|350px|thumb|centre|'' '''Figure 2.''' Primary and Secondary Orbital Interactions in Transition State.'']]

<b> Figure 3. </b>

<b> Endo Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 40 (HOMO-1)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
<script> frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS MO 41 (HOMO)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
<script> frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 42 (LUMO)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
<script> frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS MO 43 (LUMO+1)</title>
<color>white</color>
<uploadedFileContents>ENDO_TS(7)_aps315.LOG</uploadedFileContents>
<script> frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

<b> Exo Transition State </b>

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 40 (HOMO-1)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS MO 41 (HOMO)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|
<jmol>
<jmolApplet>
<title>TS MO 42 (LUMO)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title>TS MO 43 (LUMO+1)</title>
<color>white</color>
<uploadedFileContents>EXO_TS(3)_aps315.LOG</uploadedFileContents>
<script> frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat; ""</script>
</jmolApplet>
</jmol>
|}

=== Thermochemistry ===
The energy barriers and the reaction energies at room temperature are presented below (Table 2)(Figure 4). The energy barrier is the activation energy required for a reaction to occur, a product with a lower activation energy is kinetically preferred as it will more readily overcome the energy requirement for the reaction and thus form faster. The endo product can be seen to have a lower activation energy and thus can be determined to be the kinetically preferred product. This arises due to the endo transition state being lower in energy as it is stabilized by secondary orbital effects (Figure 2).

The reaction energy is characterized as the difference in energy between the reactants and products. The product with the more negative reaction energy is thermodynamically preferred as it is the more stable. The endo product can be seen to have a more negative reaction energy and thus can be determined to be the thermodynamically preferred product. This most likely arises due to steric clash that can be observed in the exo product between the carbon bridge and five-membered ring which is not observed for the endo product.

{| class="wikitable" border="1"| centre
|+ '' '''Table 2.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.057016 || 149.695519 || -0.030848 || -80.99143017
|-
| '''Exo''' || 0.060002 || 157.535263 || -0.028146 || -73.89732863
|}

[[File:Ex2_ReactionProf2_aps315.jpg|350px|thumb|centre|'' '''Figure 4.''' Reaction Profile for the Formation of Exo and Endo Products'']]

=== Relevant Files ===

Cyclohexadiene(BL3YP) - [[:File:CYCLOHEXADIENE(2)_aps315.LOG]]

1,3-Dioxole(B3LYP) - [[:File:DIOXOLE(2)_APS315.LOG]]

Endo Product(B3LYP) - [[:File:ENDOPROD_APS315.LOG]]

Exo Product(BL3YP) - [[:File:EXOPROD(2)_APS315.LOG]]

Exo TS (BL3YP) - [[:File:EXO_TS(3)_aps315.LOG]]

Endo TS (BL3YP) - [[:File:ENDO_TS(7)_aps315.LOG]]

== Exercise 3: Diels-Alder vs Cheletropic ==
The reaction between xylylene and sulfur dioxide can proceed via two possible reaction mechanisms; a Diels-Alder reaction, a [4+2] cycloaddition, or a cheletropic reaction (Scheme 2). The Diels-Alder reaction can again proceed via endo or exo mechanisms dependent upon the orientation of approach of sulfur dioxide. The cheletropic reaction generates a five-membered heterocyclic ring product. Due to the significantly different mechanisms, as expected, the reaction profiles of these reactions vary greatly.

[[File:Ex3_ReactionScheme_aps315.jpg|450px|thumb|centre|'' '''Scheme 3.''' Reaction of Xylylene and Sulfur Dioxide.'']]

=== IRC ===

The IRC calculations performed for these three alternative mechanisms have been visualised and are presented below. The endo and exo Diels-Alder reactions can be seen to be asynchronous whereas the cheletropic reaction can be seen to be synchronous. Xylylene's lack of stability is displayed through the IRCs for the reactions; the bond lengths of the six-membered ring undergo variations throughout the IRC and equalize upon the formation of the product.

''' Endo Diels-Alder '''
[[File:EndoIRC_aps315.gif | centre ]]

''' Exo Diels-Alder '''
[[File:ExoIRC_aps315(1).gif | centre ]]

''' Cheletropic '''
[[File:CheleIRC_aps315.gif | centre ]]

=== Thermochemistry ===

The energy barriers and the reaction energies at room temperature are presented below (Table 3)(Figure 5). The data collected suggests that the endo Diels-Alder product is kinetically preferred with the mechanism having the lowest activation energy. This result arises due to reasons discussed for the previous example; secondary orbital interactions stabilise the endo product's transition state. However, the endo product can be seen to be at a higher energy than that of the exo product; this arises due to the destabilizing steric clash between the oxygen atom and the six-membered heterocyclic ring. The reaction energies of the three mechanisms are all substantially large, this arises due to the stability of the aromatic ring formed that provides a strong driving force to the products. The cheletropic product has a substantially higher activation energy than the Diels-Alder, however has the lowest energy product and thus is the thermodynamically preferred product. This result can be explained by examining bond energies; C-S 272 kj/mol, C-O 358 kj/mol and S=O 522 kj/mol. The S=O is markedly more stable than the alternative C-O and S-O bonds formed during the Diels-Alder reaction, making the cheletropic product more stable.

{| class="wikitable" border="1"| centre
|+ '' '''Table 3.'''Activation and Reaction Energies''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.031064 || 81.55853821 || -0.037798 || -99.23865656
|-
| '''Exo''' || 0.032581 || 85.541422 || -0.038043 || -99.88190411
|-
| '''Cheletropic''' || 0.039566 || 103.880541 || -0.059492 || -156.1962579
|}

(You're using far too many decimal places - 10 micro J/mol in the reactants! [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

[[File:Ex3_ReactionProf3_aps315.jpg|450px|thumb|centre|'' '''Figure 5.''' Reaction Profile of Xylylene and Sulfur Dioxide.'']]

(Label the energy axis. If you put values on the profile it will make it easier to read the data [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:14, 16 March 2018 (UTC))

Xylylene has an additional site where a Diels-Alder reaction can occur. This reaction is 'endocyclic', occuring with the diene present in the six-membered ring, the 'exocyclic' reaction was previously analysed. The energy barriers and the reaction energies at room temperature for these reactions are presented below (Table 4)(Figure 6). As can be seen, the product energies for both the endo and exo reaction are higher than the energies of the reagents. In addition, the activation energies are substantially higher than for the 'exocyclic' reaction. These results arise due to the lack of aromatic stability provided by the 'endocyclic' products.

{| class="wikitable" border="1"| centre
|+ '' '''Table 4.'''Activation and Reaction Energies for 'Endocyclic' Reaction''
! Product !! Activation Energy / Hartrees/particle !! Activation Energy / kJ/mol !! Reaction Energy / Hartrees/particle !! Reaction Energy / kJ/mol
|-
| '''Endo''' || 0.042574 || 111.778046 || 0.006113 || 16.0496827
|-
| '''Exo''' || 0.045558 || 119.612538 || 0.00781 || 20.505157
|}

[[File:Ex3(1)_ReactionProf_aps315.jpg|450px|thumb|centre|'' '''Figure 6.''' Reaction Profile of 'Endocyclic' Xylylene and Sulfur Dioxide.'']]

=== Relevant Files ===

''' 'Exocyclic' Diels-Alder '''

Xylylene - [[:File:XYLYLENE_APS315.LOG]]

Sulfur Dioxide - [[:File:SO2_APS315.LOG]]

Endo TS - [[:File:EX3_ENDO_TS(8)_APS315.LOG]]

Endo IRC - [[:File:EX3_ENDO_IRC(1)_APS315.LOG]]

Endo Product - [[:File:EX3_ENDOPROD_APS315.LOG]]

Exo TS - [[:File:EX3_Exo_TS(1)_APS315.LOG]]

Exo IRC - [[:File:EX3_EXO_IRC_APS315.LOG]]

Exo Product - [[:File:EX3_EXOPPROD(1)_APS315.LOG]]

''' Cheletropic '''

Cheletropic TS - [[:File:EX3_CHELE_TS(2)_APS315.LOG]]

Cheletropic IRC - [[:File:EX3_CHELE_IRC(1)_APS315.LOG]]

Cheletropic Product - [[:File:EX3_CHELE_PROD_APS315.LOG]]

''' 'Endocyclic' Diels-Alder '''

Endo TS - [[:File:EX3(1)_ENDO_TS_APS315.LOG]]

Endo Product - [[:File:EX3(1)_ENDOPRODUCT_APS315.LOG]]

Exo TS - [[:File:EXO(1)_Exo_TS(1)_APS315.LOG]]

Exo Product - [[:File:EX3(1)_EXOPRODUCT_APS315.LOG]]

== Conclusion ==

The data produced by GuassView correlates well with pre-existing theory. For instance, the effects of the endo rule, aromatic stability and steric clash could all be employed to explain and align with the results obtained. The computational methods employed proved highly effective with limited knowledge of the reactions required. Only a fundamental understanding of chemistry is required to conduct and analyse these methods.

The approach of modelling provides unparalleled access to understanding chemical reactions and pathways and allows for chemistry to be conducted theoretically with well estimated outcomes that align with experimental values.

== References ==
1. J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', ''Oxford University Press'', '''2''', 2012.

2. P. Atkins, J. Rourke, T. Overton and F. Armstrong, '' Shriver & Atkins Inorganic Chemistry'', ''Oxford University Press'', '''5''', 2010.

3. A. Orpen and D. Watson, ''J. Chem. Soc. Dalt. Trans.'', 1987.

Mod:GFP Mutation Project

2018-03-15T14:48:41Z

Tam10: /* Possible Projects */

==Introduction==

In 2017, Banerjee et al. performed exhaustive single point mutations on seven residues surrounding the chromophore of Green Fluorescent Protein<ref name="Banerjee"> Banerjee S., Schenkelberg C.D., Jordan T.B., Reimertz J.M., Crone E.E., Crone D.E., Bystroff C., ''Biochemistry'', 7 Feb 2017, '''56(5)''', 736-747, {{DOI|10.1021/acs.biochem.6b00800}}.</ref>. In the unfolded state, proteins with the chromophore do not fluoresce. The rigid structure of the environment in the folded prevents non-radiative decay via a rotation around the free double bond in the chromophore that would otherwise occur in the unfolded state.<ref name="Zhang" /> This would suggest that mutations that disrupt the environment or allow greater freedom for the chromophore would disrupt fluorescence. Despite this, GFP was found to be surprisingly tolerant of these mutations, even in highly conserved residues.

Four mutants were found by Banerjee to be totally dark, but even these displayed some degree of fluorescence when stored, suggesting a slow chromophore maturation (CM) rate. Low relative fluorescence (RF) in mutants that wasn't due to a slower CM rate were often due to an increased mobility of the chromophore. This would reduce the barrier to non-radiative decay.

In this study we aim to correlate computational results with Banerjee's experimental work, with particular focus on mutants that change the emission and excitation wavelength.

==Existing Data==

===Interactive Model===

The model below shows the seven residues tested by Banerjee in red, and the two residues previously tested in blue. The ESPT pathway is shown with dashed green lines.

<jmol>
<jmolApplet>
<color>white</color>
<size>800</size>
<name>GFP</name>
<script>

colorCartoon=1;

zoom 200;

delete chain=B;
select all;

cartoon only;
color cartoons structure;
color cartoons translucent 4;

select {69};
select add {94};
select add {145};
select add {148};
select add {165};
select add {181};
select add {183};
select add {96};
select add {203};
select add {222};

wireframe 0.1;

select {65};
select add {66};
select add {67};

centre selected;

select add atomno=[3662, 1632, 1633, 1771, 1769, 1770, 1768, 1767];

cartoon off;
wireframe 0.2;
spacefill 0.4;

connect (atomno=494) (atomno=3662) hbond green create;
connect (atomno=1633) (atomno=3662) hbond green create;
connect (atomno=1633) (atomno=1771) hbond green create;
connect (atomno=482) (atomno=1770) hbond green create;

set echo _69 {69}; echo Q69;
set echo _94 {94}; echo Q94;
set echo _145 {145}; echo F145;
set echo _148 {148}; echo H148;
set echo _165 {165}; echo F165;
set echo _181 {181}; echo H181;
set echo _183 {183}; echo Q183;
set echo _96 {96}; echo R96; color echo blue;
set echo _203 {203}; echo T203; color echo blue;
set echo _222 {222}; echo E222; color echo blue;

</script>
<uploadedFileContents>Tam10_1GFL.pdb</uploadedFileContents>
</jmolApplet>
<jmolbutton>
<script>
if (colorCartoon == 0) {
select all;
colorCartoon = 1;
color cartoons translucent 4;
} else {
select all;
colorCartoon = 0;
color cartoons translucent 8;
}

</script>
<text>Toggle Ribbons</text>
<target>GFP</target>
</jmolbutton>
</jmol>

===Residues===

====S65-G67-Y66====

'''Chromophore'''

The chromophore is formed by the autocatalytic cyclisation and oxidation of residues 65-67, in a process known as chromophore maturation (CM).

This process requires a positively charged residue near the carbonylic oxygen of Y66, which stabilises the enolic tautomer during CM<ref name="Wood"> Wood, T. I., Barondeau, D. P., Hitomi, C., Kassmann, C. J., Tainer, J. A., and Getzoff, E. D. ''Biochemistry'', 2005, '''44''', 16211-16220, {{DOI|10.1021/bi051388j}}</ref>. This positive charge usually comes from R96.

The chromophore only fluoresces in its protein environment. Outside of this, a rotation about the doubly bond in Y66 forms the lowest energy route from the excited state, and is non-radiative<ref name="Zhang"> Zhang, Q., Chen, X., Cui, G., Fang, W.-H., and Thiel, W. ''Angewandte Chemie International Edition'', 2014, '''53''', 8649-8653, {{DOI|10.1002/anie.201405303}}</ref>.

====R96====

'''Arginine'''

<font color="blue">''Previously characterised''</font>

Highly conserved residue<ref name="Wood" />.

Two mutations on this residue, R96A and R96M, which would otherwise switch off fluorescence can be compensated with mutation Q183R, which is close enough to the Y66 carbonyl oxygen to replace R96's role.

====T203====

'''Threonine'''

<font color="blue">''Previously characterised''</font>

Stabilises the phenolate form of chromophore Y66<ref name="Tsien"> Tsien, R. Y. ''Annual Review Biochemistry'', 1998, '''67''', 509-544, {{DOI|10.1146/annurev.biochem.67.1.509}}</ref>.

====E222====

'''Glutamic Acid'''

<font color="blue">''Previously characterised''</font>

Highly conserved.

E222K displays wild-type fluorescence<ref name="Banerjee" />.

Serves as the control for Banerjee's work, and was in agreement with Nakano and co-workers' findings<ref name="Nakano"> Nakano, H., Okumura, R., Goto, C., and Yamane, T. ''Biotechnology and Bioprocess Engineering'', 2002, '''7''', 311-315, {{DOI|10.1007/BF02932841}}</ref>.

Could help catalyse CM. Proton sink for proposed ESPT. Despite this, a mutation with a positively charged side-chain is brightly fluorescent (E222K). E222R has reduced fluorescence. E222A, E222P and E222W have no fluorescence.

====Q69====

'''Glutamine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.01 (Q69L)
Dimmest RF: 0.56 (Q69Y)

Tolerant of all mutations. Hydrogen bonds with Q183 and has space to accept any side chain.

Q69 is part of the central helix that folds early. Despite this, no mutations eliminate nor increase fluorescence. Generally they cause a reduction in RF.

====Q94====

'''Glutamine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.25 (Q94P)
Dimmest RF: 0.46 (Q94G)
Dark: Q94D

Packs with R96. Q94D (dark) allows R96 to adopt a non-native rotamer, slowing or halting CM. Conformation changes during CM.

====F145====

'''Phenylalanine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.22 (F145M)
Dimmest RF: 0.18 (F145W)

Constrains rotation of chromophore. F145W does not impeded CM, but has a lower QY and glows yellow.

In strand 7 that folds last according to Banerjee. This side chain is tightly packed, and is in close contact with S205/T205 (T205 in precursor structures) and H169.

====H148====

'''Histidine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.18 (H148W)
Dimmest RF: 0.57 (H148Y)

Hydrogen bonds with chromophore phenolate, but tolerates all mutations. Conformation changes during CM.

In strand 7 that folds last according to Banerjee. Surface residue with space to accommodate mutations.

====F165====

'''Phenylalanine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.12 (F165W)
Dimmest RF: 0.51 (F164G)

Constrains rotation of chromophore. Tolerates all mutations, but Banerjee suggests packing may affect relative fluorescence.

Unusual rotamer (''p'' χ<sub>1</sub> = 60°) against V150 due to lack of space. Mutations here that have high relative energies at this rotamer are likely to pack in such a way to increase mobility around the chromophore, reducing QY. <font color="green">'''Check rotamers at mutation at this point'''</font>

====H181====

'''Histidine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.03 (H181M)
Dimmest RF: 0.36 (H181W)
Dark: H181D

Packs with R96. H181D (dark) allows R96 to adopt a non-native rotamer. Tightly packed, and H181W clashes with A179 making the chromophore more mobile.

====Q183====

'''Glutamine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.08 (Q183N)
Dimmest RF: 0.50 (Q183R)
Dark: Q183L
Dark: Q183P

Hydrogen bonds with Q69 and packs against R96. Q183L (dark) interferes with packing of side-chains. Q183P (dark) creates suboptimal backbone conformation.

===Dark Mutants===

These mutants expressed little or no fluorescence out of the 140 mutants. Of the four totally dark mutants, all acquired some degree of fluorescence after storage at 4ºC for 3 months.<ref name="Banerjee" />

====H181D====

'''Histidine to Aspartic Acid'''

'''RF = 0'''<ref name="Banerjee" />

"A larger negative ellipticity near 217 nm ... suggesting more β-sheet character in these mutants than in the wild-type protein"<ref name="Banerjee" />

Forms a stable salt bridge with R96, bending R96 away from the chromophore and reducing rate of CM.

====Q183P====

'''Glutamine to Proline'''

'''RF = 0'''<ref name="Banerjee" />

"A smaller positive ellipticity near 200 nm ... indicating a lower degree of hydrogen bonding"<ref name="Banerjee" />

"A larger negative ellipticity near 217 nm ... suggesting more β-sheet character in these mutants than in the wild-type protein"<ref name="Banerjee" />

====Q183L====

'''Glutamine to Leucine'''

'''RF = 0'''<ref name="Banerjee" />

"A larger negative ellipticity near 217 nm ... suggesting more β-sheet character in these mutants than in the wild-type protein"<ref name="Banerjee" />

====Q94D====

'''Glutamine to Aspartic Acid'''

'''RF = 0'''<ref name="Banerjee" />

CM is slowed or halted in this mutant, so it might not be possible to study it here.

The negative charge stabilises the protonated state of the chromophore. Excitation maximum is 385 nm.

Forms a stable salt bridge with R96, bending R96 away from the chromophore and reducing rate of CM.

====F145W====

'''Phenylalanine to Tryptophan'''

'''RF = 0.18'''<ref name="Banerjee" />

"A smaller positive ellipticity near 200 nm ... indicating a lower degree of hydrogen bonding"<ref name="Banerjee" />

"A larger negative ellipticity near 217 nm ... suggesting more β-sheet character in these mutants than in the wild-type protein"<ref name="Banerjee" />

This mutant fluorescences intensely yellow, but possibly has a low QY. F145 is already tightly packed, and increasing the size of the group to tryptophan adds to this steric clash with S205/T205 and H169. F145M on the other hand has relieved sterics and is brighter.

Emission is blue shifted by 2 nm - a phenomenon seen in red fluorescent proteins. The modelled protein's tryptophan forms a hydrogen bond with the chromophore's phenolate oxygen, allowing it to accommodate a larger negative charge, increasing the gap between the ground and excited states.

Banerjee suggests that an S205G or H169 -> shorter side chain mutation could potentially raise the QY. <font color="green">'''Mini Project?'''</font>

===Special Cases===

====F145M====

'''Phenylalanine to Methionine'''

'''RF = 1.22'''<ref name="Banerjee" />

In contrast to F145W, this mutant is brighter and has a 2 nm red shift in its excitation spectrum. Supposedly, more water will have access to the cavity which could help stabilise the excited state (increased Stoke shift?) <font color="green">'''Check will additional water in the cavity on mutation'''</font>

==Possible Projects==

===Changes in Emission and Absorption Profiles===

Banerjee's paper contains a huge amount of data. Their main finding is that there is little change in the emission and absorption profiles between most mutations. We should be able to show this lack of change with QM calculations provided there is not much structural change in these mutants.

====Computational Methods====

Using a small set of reference geometries, we will first compare the performance of several hybrid DFT functionals (TD/B3LYP, TD/CAM-B3LYP, TD/wB97XD, TD/APFD) in producing vertical excitation energies and emissions from the excited state.

Once a suitable method has been chosen, we will begin the process of screening many mutants including the exceptional mutants listed above.

===Non-Covalent Interactions===

We can check how sterics play a role in holding the chromophore rigid by performing an NCI calculation<ref name="Johnson"> Johnson E.R., Keinan S., Mori-Sánchez P., Contreras-García J., Cohen A.J., Yang W. ''JACS'', 15 Mar 2010, '''132''', 6498-6506, {{DOI|10.1021/ja100936w}}.</ref>. We will be able to compare strong and weak attractive and repulsive forces between different mutations, giving insight as to how packing is influenced. Other effects may become visible after NCI analysis.

====Computational Methods====

The JMol interface provides a graphical NCI analysis using the electronic densities produced from QM calculations in Gaussian (cube files).

==References==

<references/>

Mod:GFP Mutation Project

2018-03-15T14:26:50Z

Tam10: /* Special Cases */

==Introduction==

In 2017, Banerjee et al. performed exhaustive single point mutations on seven residues surrounding the chromophore of Green Fluorescent Protein<ref name="Banerjee"> Banerjee S., Schenkelberg C.D., Jordan T.B., Reimertz J.M., Crone E.E., Crone D.E., Bystroff C., ''Biochemistry'', 7 Feb 2017, '''56(5)''', 736-747, {{DOI|10.1021/acs.biochem.6b00800}}.</ref>. In the unfolded state, proteins with the chromophore do not fluoresce. The rigid structure of the environment in the folded prevents non-radiative decay via a rotation around the free double bond in the chromophore that would otherwise occur in the unfolded state.<ref name="Zhang" /> This would suggest that mutations that disrupt the environment or allow greater freedom for the chromophore would disrupt fluorescence. Despite this, GFP was found to be surprisingly tolerant of these mutations, even in highly conserved residues.

Four mutants were found by Banerjee to be totally dark, but even these displayed some degree of fluorescence when stored, suggesting a slow chromophore maturation (CM) rate. Low relative fluorescence (RF) in mutants that wasn't due to a slower CM rate were often due to an increased mobility of the chromophore. This would reduce the barrier to non-radiative decay.

In this study we aim to correlate computational results with Banerjee's experimental work, with particular focus on mutants that change the emission and excitation wavelength.

==Existing Data==

===Interactive Model===

The model below shows the seven residues tested by Banerjee in red, and the two residues previously tested in blue. The ESPT pathway is shown with dashed green lines.

<jmol>
<jmolApplet>
<color>white</color>
<size>800</size>
<name>GFP</name>
<script>

colorCartoon=1;

zoom 200;

delete chain=B;
select all;

cartoon only;
color cartoons structure;
color cartoons translucent 4;

select {69};
select add {94};
select add {145};
select add {148};
select add {165};
select add {181};
select add {183};
select add {96};
select add {203};
select add {222};

wireframe 0.1;

select {65};
select add {66};
select add {67};

centre selected;

select add atomno=[3662, 1632, 1633, 1771, 1769, 1770, 1768, 1767];

cartoon off;
wireframe 0.2;
spacefill 0.4;

connect (atomno=494) (atomno=3662) hbond green create;
connect (atomno=1633) (atomno=3662) hbond green create;
connect (atomno=1633) (atomno=1771) hbond green create;
connect (atomno=482) (atomno=1770) hbond green create;

set echo _69 {69}; echo Q69;
set echo _94 {94}; echo Q94;
set echo _145 {145}; echo F145;
set echo _148 {148}; echo H148;
set echo _165 {165}; echo F165;
set echo _181 {181}; echo H181;
set echo _183 {183}; echo Q183;
set echo _96 {96}; echo R96; color echo blue;
set echo _203 {203}; echo T203; color echo blue;
set echo _222 {222}; echo E222; color echo blue;

</script>
<uploadedFileContents>Tam10_1GFL.pdb</uploadedFileContents>
</jmolApplet>
<jmolbutton>
<script>
if (colorCartoon == 0) {
select all;
colorCartoon = 1;
color cartoons translucent 4;
} else {
select all;
colorCartoon = 0;
color cartoons translucent 8;
}

</script>
<text>Toggle Ribbons</text>
<target>GFP</target>
</jmolbutton>
</jmol>

===Residues===

====S65-G67-Y66====

'''Chromophore'''

The chromophore is formed by the autocatalytic cyclisation and oxidation of residues 65-67, in a process known as chromophore maturation (CM).

This process requires a positively charged residue near the carbonylic oxygen of Y66, which stabilises the enolic tautomer during CM<ref name="Wood"> Wood, T. I., Barondeau, D. P., Hitomi, C., Kassmann, C. J., Tainer, J. A., and Getzoff, E. D. ''Biochemistry'', 2005, '''44''', 16211-16220, {{DOI|10.1021/bi051388j}}</ref>. This positive charge usually comes from R96.

The chromophore only fluoresces in its protein environment. Outside of this, a rotation about the doubly bond in Y66 forms the lowest energy route from the excited state, and is non-radiative<ref name="Zhang"> Zhang, Q., Chen, X., Cui, G., Fang, W.-H., and Thiel, W. ''Angewandte Chemie International Edition'', 2014, '''53''', 8649-8653, {{DOI|10.1002/anie.201405303}}</ref>.

====R96====

'''Arginine'''

<font color="blue">''Previously characterised''</font>

Highly conserved residue<ref name="Wood" />.

Two mutations on this residue, R96A and R96M, which would otherwise switch off fluorescence can be compensated with mutation Q183R, which is close enough to the Y66 carbonyl oxygen to replace R96's role.

====T203====

'''Threonine'''

<font color="blue">''Previously characterised''</font>

Stabilises the phenolate form of chromophore Y66<ref name="Tsien"> Tsien, R. Y. ''Annual Review Biochemistry'', 1998, '''67''', 509-544, {{DOI|10.1146/annurev.biochem.67.1.509}}</ref>.

====E222====

'''Glutamic Acid'''

<font color="blue">''Previously characterised''</font>

Highly conserved.

E222K displays wild-type fluorescence<ref name="Banerjee" />.

Serves as the control for Banerjee's work, and was in agreement with Nakano and co-workers' findings<ref name="Nakano"> Nakano, H., Okumura, R., Goto, C., and Yamane, T. ''Biotechnology and Bioprocess Engineering'', 2002, '''7''', 311-315, {{DOI|10.1007/BF02932841}}</ref>.

Could help catalyse CM. Proton sink for proposed ESPT. Despite this, a mutation with a positively charged side-chain is brightly fluorescent (E222K). E222R has reduced fluorescence. E222A, E222P and E222W have no fluorescence.

====Q69====

'''Glutamine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.01 (Q69L)
Dimmest RF: 0.56 (Q69Y)

Tolerant of all mutations. Hydrogen bonds with Q183 and has space to accept any side chain.

Q69 is part of the central helix that folds early. Despite this, no mutations eliminate nor increase fluorescence. Generally they cause a reduction in RF.

====Q94====

'''Glutamine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.25 (Q94P)
Dimmest RF: 0.46 (Q94G)
Dark: Q94D

Packs with R96. Q94D (dark) allows R96 to adopt a non-native rotamer, slowing or halting CM. Conformation changes during CM.

====F145====

'''Phenylalanine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.22 (F145M)
Dimmest RF: 0.18 (F145W)

Constrains rotation of chromophore. F145W does not impeded CM, but has a lower QY and glows yellow.

In strand 7 that folds last according to Banerjee. This side chain is tightly packed, and is in close contact with S205/T205 (T205 in precursor structures) and H169.

====H148====

'''Histidine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.18 (H148W)
Dimmest RF: 0.57 (H148Y)

Hydrogen bonds with chromophore phenolate, but tolerates all mutations. Conformation changes during CM.

In strand 7 that folds last according to Banerjee. Surface residue with space to accommodate mutations.

====F165====

'''Phenylalanine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.12 (F165W)
Dimmest RF: 0.51 (F164G)

Constrains rotation of chromophore. Tolerates all mutations, but Banerjee suggests packing may affect relative fluorescence.

Unusual rotamer (''p'' χ<sub>1</sub> = 60°) against V150 due to lack of space. Mutations here that have high relative energies at this rotamer are likely to pack in such a way to increase mobility around the chromophore, reducing QY. <font color="green">'''Check rotamers at mutation at this point'''</font>

====H181====

'''Histidine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.03 (H181M)
Dimmest RF: 0.36 (H181W)
Dark: H181D

Packs with R96. H181D (dark) allows R96 to adopt a non-native rotamer. Tightly packed, and H181W clashes with A179 making the chromophore more mobile.

====Q183====

'''Glutamine'''

<font color="red">''Characterised by Banerjee et al''</font><ref name="Banerjee" />.

Brightest RF: 1.08 (Q183N)
Dimmest RF: 0.50 (Q183R)
Dark: Q183L
Dark: Q183P

Hydrogen bonds with Q69 and packs against R96. Q183L (dark) interferes with packing of side-chains. Q183P (dark) creates suboptimal backbone conformation.

===Dark Mutants===

These mutants expressed little or no fluorescence out of the 140 mutants. Of the four totally dark mutants, all acquired some degree of fluorescence after storage at 4ºC for 3 months.<ref name="Banerjee" />

====H181D====

'''Histidine to Aspartic Acid'''

'''RF = 0'''<ref name="Banerjee" />

"A larger negative ellipticity near 217 nm ... suggesting more β-sheet character in these mutants than in the wild-type protein"<ref name="Banerjee" />

Forms a stable salt bridge with R96, bending R96 away from the chromophore and reducing rate of CM.

====Q183P====

'''Glutamine to Proline'''

'''RF = 0'''<ref name="Banerjee" />

"A smaller positive ellipticity near 200 nm ... indicating a lower degree of hydrogen bonding"<ref name="Banerjee" />

"A larger negative ellipticity near 217 nm ... suggesting more β-sheet character in these mutants than in the wild-type protein"<ref name="Banerjee" />

====Q183L====

'''Glutamine to Leucine'''

'''RF = 0'''<ref name="Banerjee" />

"A larger negative ellipticity near 217 nm ... suggesting more β-sheet character in these mutants than in the wild-type protein"<ref name="Banerjee" />

====Q94D====

'''Glutamine to Aspartic Acid'''

'''RF = 0'''<ref name="Banerjee" />

CM is slowed or halted in this mutant, so it might not be possible to study it here.

The negative charge stabilises the protonated state of the chromophore. Excitation maximum is 385 nm.

Forms a stable salt bridge with R96, bending R96 away from the chromophore and reducing rate of CM.

====F145W====

'''Phenylalanine to Tryptophan'''

'''RF = 0.18'''<ref name="Banerjee" />

"A smaller positive ellipticity near 200 nm ... indicating a lower degree of hydrogen bonding"<ref name="Banerjee" />

"A larger negative ellipticity near 217 nm ... suggesting more β-sheet character in these mutants than in the wild-type protein"<ref name="Banerjee" />

This mutant fluorescences intensely yellow, but possibly has a low QY. F145 is already tightly packed, and increasing the size of the group to tryptophan adds to this steric clash with S205/T205 and H169. F145M on the other hand has relieved sterics and is brighter.

Emission is blue shifted by 2 nm - a phenomenon seen in red fluorescent proteins. The modelled protein's tryptophan forms a hydrogen bond with the chromophore's phenolate oxygen, allowing it to accommodate a larger negative charge, increasing the gap between the ground and excited states.

Banerjee suggests that an S205G or H169 -> shorter side chain mutation could potentially raise the QY. <font color="green">'''Mini Project?'''</font>

===Special Cases===

====F145M====

'''Phenylalanine to Methionine'''

'''RF = 1.22'''<ref name="Banerjee" />

In contrast to F145W, this mutant is brighter and has a 2 nm red shift in its excitation spectrum. Supposedly, more water will have access to the cavity which could help stabilise the excited state (increased Stoke shift?) <font color="green">'''Check will additional water in the cavity on mutation'''</font>

==Possible Projects==

===Changes in Emission and Absorption Profiles===

Banerjee's paper contains a huge amount of data. Their main finding is that there is little change in the emission and absorption profiles between most mutations. We should be able to show this lack of change with QM calculations provided there is not much structural change in these mutants.

===Non-Covalent Interactions===

We can check how sterics play a role in holding the chromophore rigid by performing an NCI calculation<ref name="Johnson"> Johnson E.R., Keinan S., Mori-Sánchez P., Contreras-García J., Cohen A.J., Yang W. ''JACS'', 15 Mar 2010, '''132''', 6498-6506, {{DOI|10.1021/ja100936w}}.</ref>. We will be able to compare strong and weak attractive and repulsive forces between different mutations, giving insight as to how packing is influenced.

==References==

<references/>

Mod:wiki checker

2018-03-14T14:41:02Z

Tam10: /* Code */

==Wiki Checking Code==

This code serves two purposes:
# Crosscheck text inside a wiki page against an existing database.
# Check ownership of images and scan for existing duplicates.

The code is parallelised and designed to be used on the HPC.

===Usage===

====Setting up a Job====

The following sections go through the structure of the modifiable part of the script

=====PBS Variables=====

These variables can be adjusted in the same way as any PBS job script.

=====Setting the Database Path=====

For the first run, a blank database file must be created. This can have any name (in this example, "stringdatabase") and can be created by executing:

<pre>touch stringdatabase</pre>

The path is then set in the wiki_checker script, under the <code>string_database_path</code> variable:

<pre>string_database_path = "/full/path/to/stringdatabase" </pre>

As PBS jobs are executed in a temporary path, the ''full'' path to the database must be used.

=====Logging=====

The output of the checker is sent to the file corresponding to the log_path. This is a write-only task, and therefore the file does not need to be manually created. For the same reason as above, the full path must be used.

=====Checking a List of Wikis=====

Each job will perform text or image checking, or both, on a list of wiki URLs given by the <code>wikilist</code> variable:

<pre>wikilist = [
"https://wiki.ch.ic.ac.uk/wiki/index.php?title=<wikipagename1>",
"https://wiki.ch.ic.ac.uk/wiki/index.php?title=<wikipagename2>"
]</pre>

Each URL should be enclosed by double quotation marks and separated by a comma (a new line can be used in addition for ease of reading).

=====Text Checking=====

Setting the <code>check_text</code> variable to <code>True</code> switches on text checking, where each wiki in the list is compared against the database. Setting to <code>False</code> switches off this functionality.

(Added 8th May 2017)

Strings that are similar (using the same threshold) as paragraphs in <code>exclude_paras</code> are ignored. It's useful to add all explicit questions from the exercise to this list - some students will write the questions into their wikis which would otherwise be flagged.

(Added 8th May 2017)

Strings that contain any of the strings in <code>exclude_strings</code> are ignored. For example, JMols can frequently appear as paragraphs. If you're not interested in testing similarity of JMol code, you can add "<nowiki><jmol></nowiki>" to prevent them appearing in the log.

=====Adding a URL to the Database=====

When <code>add_to_database</code> is set to <code>True</code>, paragraphs are added to the database. Setting to <code>False</code> switches off this functionality.

=====Similarity Threshold=====

Set the <code>tolerance</code> to check for a percentage match between new wiki paragraphs and the database paragraphs. A higher number corresponds to a strict match, and 0 will include all possible combinations of paragraphs, and is not recommended!

=====Ownership of Images=====

Setting <code>check_images</code> to <code>True</code> will perform analysis on all images in the page. It has two functions:

# It checks whether any images do not belong to the page owner. This is a naive algorithm, and looks for the most common username in all images to set the page owner. Under normal circumstances this should not fail, but in the extremely rare occasion where a user has copied every image from one person only it will not flag a warning.

# It checks for images that are exact pixel matches of existing images. A flag usually occurs when a user has uploaded the same file with a different name, but can occur when an image is copied from another page or the file is copied directly from another user. It can also rarely occur when exactly the same file is generated by two separate users by chance.

=====Checking Time of Latest Edits=====

(Added 6th May 2017)

Setting <code>latest_edits</code> to an integer greater than 0 will switch on printing of the times of that number of edits in history.

This utility can be used to check whether the wiki has been edited after a deadline.

====Submitting a Job====

The script is itself a PBS job script, and can be submitted directly with qsub:

<pre>qsub wiki_checker.py</pre>

===Analysing the Results===

Each wiki page that is checked produces an output of the following structure:

<pre><current date and time>
Target URL: <url>

<text analysis>

<image analysis>

Execution completed in <real walltime></pre>

====Text Analysis====

Any similarity flags have the following structure:

<pre>
Database Match: <URL>
String: <string1>
Match: <string2>
Similarity: <percentage>
</pre>

The <code><URL></code> indicates which database url triggered the match. <code>string1</code> and <code>string2</code> are the strings from the wiki under test and the database string respectively. The <code>percentage</code> indicates how similar the strings are.

====Image Analysis====

Images are flagged if there the image belongs to or has belonged to another user, or it is a pixel match of an existing image.

Ownership issues are shown as:

<pre>
Image: <image URL>
Owner: <username>
Users: ['<username1>', '<username2>'...]
</pre>

This is usually not a problem, and can occur when files are overwritten. If none of the users in the <code>Users</code> list correspond to the <code>Owner</code>, then it suggests the image URL has been used and the file was not created/uploaded. The image URL can be checked for further analysis.

Duplicates appear as:

<pre>
Image: <image URL>
Owner: <username>
Duplicates: ['<duplicate1 URL>', '<duplicate2 URL>'...]
</pre>

Again, this is usually not a problem and can occur when a user has renamed a file after uploading (creating a duplicate on the server). Occasionally it can occur when a user has downloaded another user's image and uploaded it with their own name.

====Latest Edition====

The times of the latest editions can be printed using the <code>latest_edits</code> to an integer greater than 0.

The output of <code>latest_edits=3</code> will look like:

<pre>
Latest Editions:
Time: <time0>, <date0> User: <user0>
Time: <time1>, <date1> User: <user1>
Time: <time2>, <date2> User: <user2>
</pre>

The username is printed in case an edit is made by a marker. It can also be used to check whether anyone else has edited a wiki page.

===Scaling and Parallelisation===

The code scales linearly with the number of items in the database. Over time, it will become slower (~6 mins CPU time for 8000 database strings * 44 wiki strings).

It is recommended therefore to make use of multiprocessing by installing the '''joblib''' module and setting <code>ncpus</code> in the #PBS node selection line. Bottlenecks in the code are parallelised, and linear scaling with number of cores can be seen when the database is heavily used.

When parallelisation isn't available, the code will default to multithreading for image analysis.

===Known Issues===

====Image checking hangs for 180 seconds====

Sometimes image analysis will take 180 seconds instead of the typical ~1 second. This is a server-side issue and can't be fixed.

===Installation===

====Notes====
The easiest way to distribute small pieces of code across wiki is pasting it in as text. The code below can be copied and pasted directly into an empty .py file on the server, such as "wiki_checker.py". Note that you must run the following local-session commands on vim to prevent a huge number of tabs being inserted:

<pre>
:set noautoindent
:set nosmartindent
</pre>

=====Code=====

<pre>
#! /usr/bin/env python

#############
# #
# JOB SETUP #
# #
#############

#This section can be modified as needed

#PBS -l select=1:ncpus=4:mem=16000MB
#PBS -l walltime=1:00:00
#PBS -j oe

__version__ = '1.0.5'

#String database should be empty for first run
#It will be populated during use and shouldn't be modified
string_database_path = ""#/path/to/string/database

#Output results to log
log_path = ""#path/to/log

#Below is a comma separated list of strings of new URLs to check
wikilist = [
#"https://wiki.ch.ic.ac.uk/wiki/index.php?title=<wikipagename1>",
#"https://wiki.ch.ic.ac.uk/wiki/index.php?title=<wikipagename2>"
]

#check_text to perform plagiarism checking
#Set add_to_database to False for test runs, otherwise duplicate strings will be added to the string database
#tolerance sets the threshold to consider a string suspicious. Default is 0.8
check_text = True
add_to_database = True
tolerance = 0.8

#check_images will perform owner and duplicate analysis on images
check_images = True

#This will print out the submission time of the latest editions
#The number is how far back in history to go (useful if someone has changed the page)
latest_edits = 3

#Add paragraphs here that you might expect to appear frequently, but aren't potential cases of plagiarism (eg questions from the exercise)
exclude_paras = [
]

#Add strings here that indicate a paragraph is not to be flagged (eg <jmol>)
#Adding <jmol> prevents everyone's JMOL code from being flagged repeatedly
exclude_strings = [
]

#######################
# #
# WIKI CHECKER SCRIPT #
# #
#######################

#This section should not be modified

from difflib import SequenceMatcher as sim
try:
from joblib import Parallel, delayed
except:
is_parallel = False
import threading
else:
is_parallel = True
from lxml import html
import time, urllib, os, requests

def wikiVsDB(wiki_url, string_database_path, log_path=None, add_to_database=True, ncpus=4, tolerance=0.8, exclude_strings=None, exclude_paras=None):
"""Compare a wiki URL with the string database
wiki_url: Wiki URL to compare
string_database_path: Path to string database containing previous entries
log_path: Path to log results. If none or empty, this defaults to stdout
add_to_database: If true, the wiki will be added to the database. Set to False for trial runs
ncpus: Numbed of processors to run on
tolerance: Level of match before a string is flagged
exclude_strings: If any of these strings are in the string to be tested, it is ignored.
exclude_paras: If any of these paragraphs are similar to the string to be tested, it is ignored.
"""

url_dict = urlToDict(wiki_url)
DB_dict = stringDBToDict(string_database_path)
url_list = [[k, v] for k, v in url_dict.items()]

if is_parallel:
Parallel(n_jobs = ncpus)(delayed(strVsDict)(string, url, DB_dict, log_path, tolerance, exclude_strings, exclude_paras) for string, url in url_list)
else:
for string, url in url_list:
strVsDict(string, url, DB_dict, log_path, tolerance, exclude_strings, exclude_paras)

if add_to_database:
addToDB(string_database_path, url_dict)

def strVsDict(string, url, string_url_dict, log_path, tolerance=0.8, exclude_strings=None, exclude_paras=None):
"""Compare a string to a database dict
string: String to compare
url: URL from where the string came from. For printing purposes
string_url_dict: Dictionary to compare with in the form {<string0>: <url0>, <string1>: <url1>}
tolerance: Level of match before a string is flagged
"""

a_str = string
a_url = url
tol = float(tolerance)

if not exclude_strings:
exclude_strings = []

if not exclude_paras:
exclude_paras = []

#For every string, perform tests. If they fail a test, the next string is considered
#Ordered tests for efficiency
for b_str, b_url in string_url_dict.items():

#Make sure string doesn't contain any strings we don't want in the database
if any([a_str in e_s for e_s in exclude_strings]):
continue

#Make sure the record isn't already in the database
if b_url == a_url:
continue

#Test if strings are similar
similarity = sim(None, a_str, b_str).ratio()
if float(similarity) < tol:
continue

#Make sure this string isn't similar to the paragraph exclusion list (eg a question from the exercise)
exclude_para_sims = [sim(None, a_str, e_str).ratio() for e_str in exclude_paras]
if any([float(e_sim) >= tol for e_sim in exclude_para_sims]):
continue

#If the string has made it this far, it is flagged and printed in the log
comp_strings = [
"Database Match: {}\n".format(b_url),
"String: {}\n".format(a_str),
"Match: {}\n".format(b_str),
"Similarity: {:.1%}\n\n".format(similarity)]
write(log_path, "".join(comp_strings))

def urlToDict(url, min_string_length=10):
"""Convert HTML from a URL to a dictionary of paragraphs"""

string_dict={}
wiki = urllib.urlopen(url)

paras = [p for p in wiki.readlines() if "<p>" in p]
for p in paras:
split_list = p.split(">")
join_list = []

for s in split_list:
join_list.append(s.split("<")[0])
joined = "".join(join_list)
if len(joined.split()) >= min_string_length:
string_dict[joined.strip("\n").replace("\t", " ")] = url

return string_dict

def stringDBToDict(string_database_path):
"""Parses the string database into a dictionary"""

string_dict = {}

with open(string_database_path, "r") as db:
for line in db.readlines():
split_line = line.split("\t")
if len(split_line) == 2:
string, url = line.split("\t")
string_dict[string.strip()] = url.strip()

return string_dict

def getTimeStr(m, s):
m = int(m)
s = int(s)
if m == 1:
m_string = " " + str(m) + " Minute"
elif m == 0:
m_string = ""
else:
m_string = " " + str(m) + " Minutes"

if s == 1:
s_string = " " + str(s) + " Second"
else:
s_string = " " + str(s) + " Seconds"

return "Execution completed in" + m_string + s_string

def addToDB(string_database_path, url_dict=None, url=None, min_string_length=10):

if url:
url_dict = urlToDict(url, min_string_length)

with open(string_database_path, "a") as db:
for string, url in url_dict.items():
db.write(string + "\t" + url + "\n")

def wikiImageInfo(url, log_path="", ncpus=4):

wikipage = requests.get(url)
wiki_html = html.fromstring(wikipage.content)
i_s = wiki_html.find_class("image")
images = ["https://wiki.ch.ic.ac.uk" + i.attrib['href'] for i in i_s if i.attrib.get('href')]

image_dict = {}
if is_parallel:
image_list = Parallel(n_jobs = ncpus)(delayed(checkImage)(image, image_dict, is_parallel) for image in images)
image_dict = {k: v for k, v in image_list}
else:
threads = [None] * len(images)
for i in range(len(threads)):
threads[i] = threading.Thread(target=checkImage, args=(images[i], image_dict, is_parallel))
threads[i].start()

for i in range(len(threads)):
threads[i].join()

users = [image_info["users"] for image_info in image_dict.values()]
users = [a for b in users for a in b]
if users:
user = max(set(users), key=users.count)

for image, info in image_dict.items():
if not all(user==u for u in info["users"]):
write(log_path, "Image: {}\n".format(image))
write(log_path, "Owner: {}\n".format(user))
write(log_path, "Users: {}\n\n".format(info["users"]))
if image_info["duplicates"]:
if not all(user==u for u in info["users"]):
write(log_path, "Image: {}\n".format(image))
write(log_path, "Owner: {}\n".format(user))
write(log_path, "Duplicates: {}\n\n".format(info["duplicates"]))

def checkImage(image_url, image_dict, is_parallel):
image_info = {}
imagepage = requests.get(image_url, timeout=None)
image_html = html.fromstring(imagepage.content)
c_s = image_html.find_class("mw-userlink")
users = [c.text for c in c_s]
image_info["users"]=users

a_s = image_html.find_class("mw-imagepage-duplicates")
d_s = [a.findall("li") for a in a_s]
d_s = [a for b in d_s for a in b]
image_info["duplicates"] = []
duplicates = [d[0].attrib['href'] for d in d_s if d[0].attrib.get('href')]
if duplicates:
for d in duplicates:
if d.startswith("/"):
image_info["duplicates"].append("https://wiki.ch.ic.ac.uk" + d)
else:
image_info["duplicates"].append(d)
if is_parallel:
return [image_url, image_info]
else:
image_dict[image_url] = image_info

def getLatest(wiki_url, log_path, history_number):
if not history_number:
return

url = wiki_url + "&action=history"
wikipage = requests.get(url)
wiki_html = html.fromstring(wikipage.content)
history = wiki_html.find_class("mw-changeslist-date")
history_users = wiki_html.find_class("mw-userlink")

latest = [h.text for h in history]
users = [u.text for u in history_users]

write(log_path, "Latest Editions:\n")
for n in range(min(len(latest), history_number)):
write(log_path, "Time: {:<25s} User: {}\n".format(latest[n], users[n]))
write(log_path, "\n")

def write(target, string):
if target:
with open(target, "a") as log:
log.write(string)
else:
print(string)

ncpus = int(os.environ["NCPUS"]) #Set this in the PBS resources above

for wiki_url in wikilist:
write(log_path, time.ctime() + "\n")
write(log_path, "Target URL: {}\n\n".format(wiki_url))
i_time = time.time()

if check_text:
wikiVsDB(
wiki_url,
string_database_path,
log_path,
add_to_database,
ncpus,
tolerance,
exclude_strings,
exclude_paras
)

if check_images:
wikiImageInfo(
wiki_url,
log_path,
ncpus
)

if latest_edits:
getLatest(
wiki_url,
log_path,
latest_edits
)

exec_time = time.time() - i_time
m, s = divmod(exec_time, 60)
write(log_path, getTimeStr(m, s) + "\n\n\n")

</pre>

Rep:Mod:ts ew515

2018-03-07T13:35:26Z

Tam10: /* Exercise 3: The Diels-Alder and Cheletropic Reactions of ortho-Xylylene with Sulfur Dioxide */

== Introduction ==
Presented here is a computational modelling of various pericyclic reactions using semi-empirical and Density Functional Theory (DFT) methods in the software Gaussian. Within each exercise, the program will be used to do such things as: describe/visualize relevant molecular orbitals and their symmetries, monitor the geometric development of a reaction, and calculate reaction and activation energies to differentiate between kinetic and thermodynamic pathways.

=== Gaussian ===
The computational methods in Gaussian rely on several assumptions to allow the N-body Schrodinger equation to be approximated. To begin with, the <u>Born-Oppenheimer approximation</u> notes the vast difference in kinetic energies between nuclei and electrons to provide its assumption that their motions can be separated from one another, i.e. the N-body wave-function can be separated into an electronic portion (dependent on nuclear position, ''not'' motion, and treated quantum mechanically) and a nuclear one (treated classically). Additionally, the total electronic wave-function is decomposed into single-electron wave-functions that are derived from atom-centered functions (the basis set) via a <u>linear combination of atomic orbitals</u> (LCAO). Finally, the energetic element of electron-electron repulsion is not calculated discretely between each and every electron in the system. Instead, the approximate single-electron wave-functions are treated independently and exposed to an averaged repulsive field of the other electrons in the system.

=== Methods/Levels of Theory ===
The simplest type of ''ab initio'' method (computing properties from first principles, i.e. the electronic Schrodinger equations) is the <u>Hartree-Fock (HF) method</u>, which approaches the N-body quantum system via the approximations described above. One of the essential differences between HF theory and following <u>ab initio</u> approaches is the mathematical approach to approximating electron-electron repulsions.

In a more computationally-intensive fashion than HF, <u>Density Functional Theory</u> includes an approximation of instantaneous electron-electron repulsions (or, as a whole, an approximation of correlated electron motion) by introducing an exchange-correlation potential in energy calculations instead of an averaged repulsive field. There are a variety of specific approaches to handling the computation of electron exchange and correlation energies. In this work, a "hybrid functional" known as B3LYP is used. Additionally, DFT computes energies directly from the electron density, instead of by an operation on the approximate wave-function.

Finally, <u>semi-empirical methods</u>, such as PM6, use a combination of both quantum mechanical calculation and parameterized empirical data to yield less accurate but faster modelling than given by the above theories.

=== The Potential Energy Surface ===
In the context of analyzing a reaction, Gaussian will not only use the above methods to geometrically optimize reactants and products, but also to identify the relevant transition states lying along their interconversion. The underlying component that unifies the procedure of identifying these states is the <u>potential energy surface</u> (PES). As an idea, the PES represents the molecular energy as a function of molecular geometry. If presented as a three-dimensional plot, the vertical axis would represent potential energy, while the horizontal axes would represent reduced coordinates that correspond to some or all of the fundamental geometric degrees of freedom in the system (i.e. the 3N-6 normal modes for a nonlinear molecule).

With this idea in mind, an energetic topology can be envisioned with minima, maxima, and saddle points depending on the relative configuration of atoms in the molecule or system. When carrying out minima/maxima/transition state optimizations, Gaussian will use the topology gradient (first derivative of energy with respect to geometric change, dE) and curvature (second derivative, d2E) to differentiate between these features. All three of these features are similar in that they are "flat points" with a gradient of 0 with respect to geometric change. Individually, minima have a positive curvature (increase in energy) in every direction and maxima have a negative curvature (decrease in energy) in every direction. As transition states are the highest energy point along the lowest energy pathway, it follows that transition states have positive curvatures in every direction except for ''one'' negative curvature along a particular'' ''geometric degree of freedom (the direction of the reaction that goes "down" to both reactants and products).

These curvatures are measured by Gaussian as vibrational frequencies. In simple terms, molecular vibrations occur along some geometric coordinate and the energy is either raised (a positive frequency, seen experimentally) or lowered (a negative frequency, imaginary). Thus, a frequency analysis is used to confirm an optimized minima by checking for no imaginary vibrations (a stable point with positive curvature), while an optimized TS is expected to show one imaginary vibration (a saddle point with a negative curvature along one geometric degree of freedom, ''the reaction pathway'').

== Exercise 1: The Diels-Alder Reaction of Butadiene with Ethylene ==
[[File:Ew515 E1 scheme.png|centre|409x409px|Scheme 1: The [4+2] cycloaddition (Diels-Alder reaction) of butadiene with ethylene|thumb]]Using the <u>semi-empirical PM6</u> method: 1) The butadiene and ethylene reactants were optimized independently, 2) a fixed-geometry pseudo-TS was minimized, 3) the pseudo-TS was unfrozen and optimized to a true transition state structure, 4) the optimized TS was used to run an <u>intrinsic reaction coordinate</u> (IRC) calculation to approximate the minimum energy pathway between reactants and products, and 5) the cyclohexene product was geometrically optimized.

=== Frontier Molecular Orbital (FMO) Analysis ===
[[File:Ew515 E1 MOs.bmp|thumb|677x677px|Figure 1: Frontier molecular orbital (FMO) diagram of the reactants and transition state. Each MO is represented as its linear combination of atomic orbitals, as well as its computed visualization, with numbering/energies in bold.]]
The Diels-Alder reaction of butadiene with ethylene is a concerted [4+2] cycloaddition. The reaction can be considered by the HOMO/LUMO interactions of the reactants (Fig. 1). Frontier molecular orbitals were annotated as symmetric or antisymmetric with respect to orbital phases at reactant termini.

Per the Woodward-Hoffman (WF) rules (N + A = odd, where N is the number of electron pairs and A is the number of antarafacial components), the [4+2] cycloaddition is thermally achievable via a suprafacial/suprafacial interaction of reactants (as seen in the simplified reaction scheme TS). This was confirmed by the MO analysis of the reactants and transition state.

The relevant molecular orbitals that comprise the FMO manifold are the HOMO/LUMO pairs of each reactant. As summarized by the WF rules, the '''antisymmetric''' butadiene HOMO is able to interact with the '''antisymmetric''' ethylene LUMO to yield a non-zero orbital overlap while the '''symmetric''' ethylene HOMO can do the same with the '''symmetric''' butadiene LUMO. In the case of pericyclic reactions with an even number of electron pairs, a hypothetical suprafacial/suprafacial interaction would yield unproductive symmetric/antisymmetric interactions (with an orbital overlap integral of zero). Instead a thermally-promoted reaction would be required to pass through a suprafacial/antarafacial interaction to achieve any productive orbital overlap.

MO energies and visualizations for the reactants were taken from the first frame of the intrinsic reaction coordinate calculation (see next section) of the system, instead of the independently optimized reactants, while transition state MOs were taken from the optimized transition state calculation.

{| class="wikitable"
! colspan="4" |Butadiene MOs
|-
| colspan="2" |<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 78; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E1 IRC.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

MO #17 (HOMO, antisymmetric)
| colspan="2" |<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 78; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E1 IRC.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
MO #18 (LUMO, symmetric)
|-
! colspan="4" |Ethene MOs
|-
| colspan="2" |<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 78; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E1 IRC.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
MO #16 (HOMO, symmetric)
| colspan="2" |<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 78; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E1 IRC.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
MO #19 (LUMO, antisymmetric)
|-
! colspan="4" |Transition State MOs
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E1 TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
MO #16 butadiene HOMO + ethene LUMO (in phase a/a overlap)
|><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E1 TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
MO #17 butadiene LUMO + ethene HOMO (in phase s/s overlap)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E1 TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
MO #18 butadiene LUMO + ethene HOMO (out of phase s/s overlap}
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E1 TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
MO #19 butadiene HOMO + ethene LUMO (out of phase a/a overlap)
|}

=== Intrinsic Reaction Coordinate Analysis & C-C Bond Length Development ===
[[File:Ew515 E1 TSimaginaryvibe.gif|thumb|Figure 2a: The imaginary vibration of the optimized transition state, illustrating the geometric degree of freedom that represents passing across the saddle point towards the reactants/products]]
A comparison between the imaginary vibration used to confirm an appropriate transition structure (Fig. 2a) and the entire animation of interconverting geometries along the IRC (Fig. 2b) illustrates the discussion about PES topology/curvatures from the previous section.

The IRC analysis of the reaction system, starting from the optimized transition state, was used to plot the development of carbon-carbon bond lengths as the reaction proceeds (Fig. 3). Relevant lengths are plotted in color, while standard sp3-sp3 (1.54 angstroms) and sp3-sp2 (1.50 angstroms) lengths, as well as carbon's Van der Waals radius (1.70 angstroms), are plotted as grey dotted lines.

Bond lengths change as would be expected:
* Pi bonds in the reactants form sigma bonds and increase in length, however, the resulting sp3-sp3 bond (C5-C6) is longer (1.54 angstroms, as standard) than the resulting sp3-sp2 bonds (C1-C2/C3-C4) which match the standard length of 1.50 angstroms
* The two new sigma bonds formed in the reaction (C4-C5/C1-C6) gradually decrease in length from arbitrarily higher values until settling on the standard sp3-sp3 length (1.54) with C5-C6
* Finally, the newly formed pi bond (an sp2-sp2 sigma bond in the reactants at 1.47 angstroms) decreases in length to 1.34 angstroms
[[File:Ew515 E1 IRC.gif|thumb|Figure 2b: Animation of the calculated intrinsic reaction coordinate, passing through the optimized transition state]]
[[File:Ew515 E1 C-c bonds crop.png|thumb|911x911px|Figure 3: A plot of carbon-carbon bonds as the reaction develops as calculated by the Intrinsic Reaction Coordinate (IRC) calculation. Colored lines are bond lengths in the system (see legend) and dotted lines are standard carbon-carbon bond lengths/Van der Waals radius. |none]]

== Exercise 2: The Diels-Alder Reaction of Cyclohexadiene with 1,3-Dioxole ==
[[File:Ew515 E2 scheme.png|centre|thumb|552x552px|Scheme 2: The [4+2] cycloaddition of cyclohexadiene with 1,3-dioxole to yield both endo and exo isomers as products]]
Using firstly the '''PM6''' method followed by a '''DFT (B3LYP)''' calculation: the cyclohexadiene and 1,3-dioxole reactants were optimized independently, 2) a fixed-geometry pseudo-TS was minimized for both endo and exo interactions, 3) both were unfrozen and optimized to a true transition state, 4) the transition structures were used to run an IRC calculation (only PM6), and 5) the endo/exo products of the IRC were optimized.

=== Frontier Molecular Orbital (FMO) Analysis ===
In a similar fashion to exercise 1, this [4+2] cycloaddition can also be considered via the HOMO/LUMO overlap of each reactant. Again, the optimized transition state showed a thermally-accessible suprafacial/suprafacial interaction in the cycloaddition. '''Antisymmetric/antisymmetric''' and '''symmetric/symmetric''' interactions between reactants yielded non-zero orbital overlaps (to give bonding/antibonding FMOs in the transition state) as before.
{| class="wikitable"
!Endo TS
!Exo TS
|-
|[[File:Ew515 E2 EndoMOs.bmp|left|thumb|733x733px|Figure 4: Frontier molecular orbital diagram of cyclohexadiene and 1,3-dioxole reactants, featuring the '''endo''' transition state. Each MO is represented as its linear combination of atomic orbitals, as well as its computed visualization, with numbering/energies in bold.]]
|[[File:Ew515 E2 exoMOs.bmp|none|thumb|733x733px|Figure 5: Frontier molecular orbital diagram of the cyclohexadiene and 1,3-dioxole reactants, featuring the '''exo''' transition state. Each MO is represented as its linear combination of atomic orbitals, as well as its computed visualization, with numbering/energies in bold.]]
|}
Interestingly, there is a reordering of reactant HOMOs. Instead of an electron-rich diene reacting with a relatively electron-poor dienophile (higher energy butadiene HOMO relative to ethene HOMO, Fig. 1), cyclohexadiene's reaction with 1,3-dioxole actually demonstrates an '''inverse demand Diels-Alder''' reaction, wherein the electron-rich dioxole (the dienophile) HOMO lies higher in energy than that of cyclohexadiene (the diene).

Between the endo and exo transition structures, there is a notable difference in the energies and orbital overlap of either HOMO (MO #41):
{| class="wikitable"
!Endo TS HOMO
!Exo TS HOMO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<script>frame 24; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E2 endoTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

MO #41, E = - 0.19051[[File:Ew515 E2 endo2ndary.bmp|centre|thumb|385x385px|Figure 6: A Gaussian visualization illustrating the primary orbital overlap (shown in green, between the termini of the reacting pi systems) as well as the secondary orbital interactions (shown in red, between electron density on the oxygen atoms of the dioxole and saturated carbons of the cyclohexadiene) that are unique to the endo transition state]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ew515 E2 exoTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

MO #41, E = - 0.18560[[File:Ew515 E2 exoTSno2ndary.bmp|centre|thumb|461x461px|Figure 7: A Gaussian visualization illustrating the primary orbital overlap (shown in green, between the termini of the reacting pi systems) as well as the lack of secondary orbital interactions.]]
|}
The termini of the reacting pi systems overlap to yield primary orbital interactions (present in both endo and exo transition states) that lead the system to undergoing a cycloaddition (as described previously in reference to the WH rules). Uniquely, the endo transition state offers an additional stabilizing feature over that of the exo TS: secondary orbital overlap -- an overlap of orbital density on the dioxole oxygen atoms with that on the unsaturated carbon atoms of the cyclohexadiene (Fig. 6, primary overlap in green/secondary overlap in red). The lack of any additional orbital interaction is distinctly seen in the HOMO of the exo transition state (Fig. 7).

=== Thermochemistry ===
{| class="wikitable"
! rowspan="2" |
! colspan="2" |Endo
! colspan="2" |Exo
|-
|Hartrees
|kJ/mol
|Hartrees
|kJ/mol
|-
|Activation Barrier
|0.059703
|156.750238
|0.062689
|164.589982
|-
|Reaction Energy
|<nowiki>-0.026838</nowiki>
|<nowiki>-70.46317437</nowiki>
|<nowiki>-0.025469</nowiki>
|<nowiki>-66.86886459</nowiki>
|}
The thermochemical data from the optimized reactants, transitions states, and products were used to tabulate activation barriers and overall reaction energies for both the endo and exo reactions above. The data show each pathway to have a moderate reaction barrier, while each is exothermic overall.

The endo TS has a lower activation barrier than the exo, meaning it is the kinetically preferred (faster formed) pathway as is expected in Diels-Alder reactions. This may be explained by he FMO analysis described previously in which both TS's were seen to satisfy the WF rules (allowing primary orbital overlap) but the endo TS had additional secondary orbital overlap in the HOMO to further stabilize it.

Interestingly, the data also show that the endo product is thermodynamically favored, with the endo reaction contributing around an extra -3.5 kJ/mol to the reaction energy compared to the exo pathway. This might not be in agreement with a first guess (i.e. any endo/exo rule of thumb), however it can be attributed to the relative steric interactions in the exo (Fig. 8) and endo (Fig. 9) products. In the exo product there are unfavorable interactions between the saturated ethylene bridge of the cyclohexene unit (pictured pointing up) with the methylene portion of the dioxole unit (pictured pointing right) that are not present in the endo product (in which the methylene unit of dioxole is ''endo'' to the saturated portion of the ring and better tolerated spatially).
[[File:Ew515 E2 exoProdSterics.bmp|left|thumb|289x289px|Figure 8: Image of the exo product, illustrating the relevant steric interactions between the ethylene bridge of the cyclohexene unit with the methylene bridge of the dioxole unit]]
[[File:Ew515 E2 endoProdSterics.bmp|none|thumb|339x339px|Figure 9: Image of the endo product, illustrating a lesser steric clash between the cyclohexene/dioxole units]]

<br/>
== Exercise 3: The Diels-Alder and Cheletropic Reactions of ortho-Xylylene with Sulfur Dioxide ==
[[File:Ew515 E3 scheme.png|centre|thumb|557x557px|Scheme 3: The Diels-Alder and cheletropic reaction pathways available to o-xylylene and sulfur dioxide]]
Uniquely, between the o-xylylene and SO2 reactants, there are two reactions available to them: a Diels-Alder cycloaddition(forming both endo, Fig. 10a, and exo, Fig. 10b, products), or a cheletropic cycloaddition (Fig. 10c).
{| class="wikitable"
![[File:Ew515 E3 DAendoIRC.gif|thumb|Figure 10a: Diels-Alder Endo|270x270px]]
![[File:Ew515 E3 DAexoIRC.gif|thumb|Figure 10b: Diels-Alder Exo|258x258px]]
![[File:Ew515 E3 chelIRC.gif|thumb|303x303px|Figure 10c: Cheletropic]]
|}
The thermochemical data from these reaction calculations were tabulated from the individually optimized reactants (i.e. at infinite separation), the optimized transition states, and respective products:
{| class="wikitable"
! rowspan="3" |
! colspan="4" |Diels-Alder
! colspan="2" rowspan="2" |Cheletropic
|-
! colspan="2" |Endo
! colspan="2" |Exo
|-
|Hartrees
|kJ/mol
|Hartrees
|kJ/mol
|Hartrees
|kJ/mol
|-
|Activation Barrier
|0.030927
|81.1988447
|0.032446
|85.1869795
|0.039428
|103.518222
|-
|Reaction Energy
|<nowiki>-0.037936</nowiki>
|<nowiki>-99.60097559</nowiki>
|<nowiki>-0.038178</nowiki>
|<nowiki>-100.2363466</nowiki>
|<nowiki>-0.059635</nowiki>
|<nowiki>-156.5717044</nowiki>
|}
Between the three of them, the cheletropic is hugely more thermodynamically favorable with an almost 50% increase in exothermicity. Interestingly, the cheletropic reaction also provided the largest reaction barrier, significantly above those of each Diels-Alder pathway.

Between the Diels-Alder products, the endo TS was relatively lower in energy (the kinetically favorable process) while the exo product was more favorable (the thermodynamically preferred pathway). All energy levels for each of these reactions are depicted in Fig. 12.
{| class="wikitable"
!Cheletropic
!Diels-Alder (Endo)
!Diels-Alder (Exo)
|-
![[File:Ew515 E3 chelprodsterics.bmp|frameless]]
![[File:Ew515 E3 endoprodsterics.bmp|frameless]]
![[File:Ew515 E3 exoprodsterics.bmp|frameless]]
|}
[[File:Ew515 E3 chelTop.gif|thumb|Figure 11: An axial view of the intrinsic reaction coordinate of the cheletropic reaction, focusing on the formation of the aromatic ring in the xylylene portion of the system]]
These energetic differences can be considered by the steric interactions present in the respective products. The cheletropic product adopts a planar and symmetric conformation with minimal interactions between the bulky oxygen atoms and adjacent hydrogens. Alternatively, the endo DA product shows a significantly more unfavorable orientation of the saturated ring hydrogens and external oxygen (situated axially) that is akin to a 1,3 diaxial type interaction. The exo product has its external oxygen atom situated equatorially preventing such a steric clash.

(There is also the retention of both S=O bonds in the cheletropic product. The sulfur is too large to form a planar 6-membered ring [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 13:35, 7 March 2018 (UTC))

One of the most obvious features driving the exothermicity of these reactions is the formation of an aromatic product. The reactive and unstable xylylene reactant is non-aromatic but disposed to rearrange quickly to recover aromaticity (Fig. 11). It is likely that the formation of aromaticity occurs early in the reaction coordinate.

[[File:Ew515 E3 energies.png|centre|thumb|802x802px|Figure 12: A sketch of relative energy levels for the independent reactants (at infinite separation), the transition states, and respective products]]
All Gaussian files can be found here: [[File:ew515_Exercise1_LOGFiles.zip]], [[File:ew515_Exercise2_LOGFiles.zip]], [[File:ew515_Exercise3_LOGFiles.zip]]

== References ==
1 ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', ed. nonymous , The Royal Society of Chemistry, 2013, p. 1-62.

2 A. Szabo and N. S. Ostlund, ''Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory'', Dover Publications, 1989.

Rep:Mod:ZZY15 TS

2018-03-07T12:18:04Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

=''' Transition States and reactivity '''=
== Introduction ==

A potential energy surface (PES) is a plot of the energy of a system against certain parameters such as the positions of the atoms. In computational chemistry, PES gives the energy as a function of its geometry. Born-Oppenheimer approximation is used to separate electronic and nuclear motion. The nuclei are considered to be stationary relative to electron motion. This helps simplify the Schrödinger equation. Without any other external fields, the potential energy of a molecule doesn’t change as it is translated or rotated in space. Hence the potential energy only depends on the internal coordinates of a molecule. In Cartesian terms, there are 3 internal coordinates for each atom: x, y and z. Thus, there will be 3N total coordinates for the molecule. Eliminate 3 translations and 3 rotations, the PES has 3N-6 degrees of freedom, where N is the number of atoms (N>2).

At T = 0K, the system will always want to be at the lowest possible potential energy. A minimum point on the PES has positive curvatures (i.e. the second derivative: <math>\dfrac{\partial ^2 U}{\partial q^2} > 0</math>) in all degrees of freedom. As the reaction proceeds, it goes from one minimum point on the PES, i.e. the reactant, to another minimum point, the product, through the lowest energy path. As the reaction goes along this path, it would pass through one degree of freedom for which the energy is a maximum. This is the saddle point of the PES, i.e. maximum point on the minimum energy pathway. This saddle point is defined as the transition state. It has negative curvature in only one degree of freedom and positive curvatures in all others. At the minima and saddle point, the slope of the PES is zero (i.e. the first derivative: <math>\dfrac{\partial U}{\partial q} = 0</math> ).

In the lab, we use computer simulation for determining molecular structure by geometry optimization in Gaussian. The energy of the system is determined by solving the Schrödinger equation. The first and second derivatives of the energy with respect to all degrees of freedom are calculated. This allows locating of stationary points. Moreover, the vibrational frequencies of the system can be predicted by the second derivatives, which can be all organized in the Hessian matric. The frequencies are related to the eigenvalues of the Hessian matrix in the harmonic approximation.<ref>P. Atkins and J. De Paula, Atkins' Physical Chemistry, University Press, Oxford, 10th edn., 2014.,pp 908-909</ref>

[[File:EQUATION_ZZY.png|thumb|450px|center|]]

The eigenvalues are the squared normal mode frequencies. If all the eigenvalues are positive, the frequencies are all real, indicating a minimum point on the PES. If one eigenvalue is negative, there is one imaginary frequency, indicating a TS.

Two different quantum chemical methods are used in this lab: Density functional method B3LYP (DFT) and Semi-empirical method PM6. The semi-empirical methods makes many approximations and obtain some parameters from empirical data, therefore it is much quicker. However, the optimization is less prefect. The DFT method doesn't include any empirical or semi-empirical parameters in their equations. It derives those parameters directly from theoretical principles, no experimental data needed. This method is more accurate, but it is slower as greater computational effort is required. It is also necessary to choose a basis set, which is a set of functions used to represent the electronic wave function within the linear combination of atomic orbitals.<ref>Joseph J W McDouall, Computational Quantum Chemistry: Molecular Structure and Properties in Silico, Royal Society of Chemistry, Cambridge, 2013.,pp 1-62</ref>

== Results and Discussion ==

=== Exercise 1: Reaction of Butadiene with Ethene ===

[[File:E1_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Butadiene with Ethene reaction.]]

This is a Dials-Alder reaction. The ethene acting as the dienophile, reacts with the s-cis butadiene. Cyclohexene is formed.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Ethene
! center; style="background: #0D4F8B; color: white;" | Butadiene
! center; style="background: #0D4F8B; color: white;" | Transition State
! center; style="background: #0D4F8B; color: white;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 12; measure 1 4</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 3 4; measure 1 2; measure 1 4</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 54; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>E1_PRODUCT_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. Optimized Stuctures at PM6 level.
|}

==== Bond Length Analysis ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" |sp<sup>3</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Double bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Single bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |VDW radius of C
|-
| style="background: #0D4F8B; color: white;" |Typical Bond Length (Å)
| 1.54
| 1.33
| 1.47
| 1.50
| 1.70
|+ Table 2. Typical C-C Bond Length.<ref>E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008</ref>
|}

{| class="wikitable" style="margin: auto;"
|-
| [[File:ZZY_E1_NUMBERING.png|thumb|none|350px|center|Figure 2. Numbering of TS Carbons.]]
|rowspan="2" |[[File:E1_BONDDISTANCES_ZZY.png|thumb|none|500px|center|Figure 3. Bond distances versus IRC.]]
|-
| [[File:ZZY_E1_DISTANCE_FOCUS.png|thumb|none|350px|center|Figure 4. Zoom-in of Bond distances versus IRC Graph.]]
|-
|+ Table 3. Change in Bond Distances During The Reaction.
|}

The length of the partially formed C-C sigma bonds (C1-C8, C4-C9) in the TS is shorter than 2 x Van Der Waals radius of carbon, indicating formation of bonds between them. As the reaction proceeds, their length shortens and reaches the typical sp<sup>3</sup> C-sp<sup>3</sup>C single bond length at the end of the reation. The bond length between C7-C10 in the TS is shorter compared to the typical sp<sup>2</sup> C-sp<sup>2</sup>C single bond length. This indicating the formation of C-C pi bond between them. The bond length between C1-C4 at TS is longer than the typical C-C double bond length, indicating the pi bond breaking during the reaction. The bond length between C7-C8, C9-C10 is longer than the typical C-C double bond length, indicating the breaking of pi bond between them. It reaches the typical sp<sup>2</sup> C-sp<sup>3</sup>C bond length at the end.

==== Frequency and IRC Analysis ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | TS Bond Forming/Breaking Vibration
! center; style="background: #0D4F8B; color: white;" | Frequency Calculation
|-
| [[File:ZZY_TS_VIBRATION.gif]] || [[File:ZZY_E1_FREQUENCY.PNG|350px|thumb|center |]]
|-
|+ Table 4. Transition State Vibrational Frequencies
|}

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Trajectory
! center; style="background: #0D4F8B; color: white;" | IRC Path
|-
| [[File:ZZY_IRC.gif]] || [[File:ZZY_E1_IRC_PATH.PNG|350px|thumb|center |]]
|-
|+ Table 5. IRC Path of Reaction
|}

There is only one imaginary vibration (negative vibration) for the TS calculated, confirming that the TS is optimized correctly. Transition state corresponds to the highest potential energy point along the minimum energy path. At TS, the first derivative of energy graph is zero and the second derivative is negative. The frequency represents the second derivative of the energy. Therefore a single negative frequency indicates that the structure is the maximum point in only one degree of freedom but minimum in all others. That is the correct transition state.

The IRC plots also show the correct optimization of TS. The maximum energy point corresponds to zero RMS gradient,showing the geometry is optimized at that point.

The animation of vibration at -949 cm<sup>-1</sup> shows that the formation of bonds in this reaction is synchronous. They form at the same time.

==== MO Analysis ====
{| class="wikitable" style="margin: auto;"
!
! center; style="background: #0D4F8B; color: white;" | HOMO
! center; style="background: #0D4F8B; color: white;" | LUMO
! colspan="2" center; style="background: #0D4F8B; color: white;" | MO Diagram
|-
| center; style="background: #0D4F8B; color: white;" | Butadiene
|<jmol>
<jmolApplet>
<title>HOMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2" colspan="2"|[[File:E1_MO_ZZY_NEW.png|thumb|none|450px|center|]]

|-
| center; style="background: #0D4F8B; color: white;" | Ethene
|<jmol>
<jmolApplet>
<title>HOMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| center; style="background: #0D4F8B; color: white;" | Transition state
|<jmol>
<jmolApplet>
<title>HOMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
|+ Table 6. MO Diagrams
|}

The MO diagram is constructed based on the energies of MOs calculated at PM6 level. The diene has a smaller HOMO-LUMO energy gap as the HOMO and LUMO are neither the lowest energy bonding MO nor the highest energy antiboning MO, which is the case for the ethene. Noticed that the energy of HOMO/HOMO-1 of TS is higher than expected and the energy of the LUMO/LUMO+1 of TS is lower than expected (real energy levels indicated by red lines in the graph). This is because the MO diagram is based on the transition state MO energies, not on product as we used to do. In the TS, the new bonds are not completely formed. Therefore the "bonding orbitals" are higher in energy and the "anti-bonding orbitals" are lower in energy than expected.

Due to the larger energy gap between interacting MOs of ethene and diene, this reaction is not efficient. This can be improved by adding electron donating groups to the diene and adding electron withdrawing groups to the dienophile. By doing this, the energy leveles of diene are raised and that of the dienophile are lowered. This leads to better overlap as MOs closer in energy. The reaction is more efficient.

As shown by the MO visualization, reactants' MOs of the same symmetry overlap and give the TS MOs. This indicates that only interactions between MOs of the same symmetry are allowed. Mis-symmetry interactions are forbidden, i.e. they don't interact.

The overlap between MOs is described by the orbital overlap integral <math>S</math>. It is defined as:
<center><math>S=\int {\psi_1\psi^*_2 d\tau}</math></center>
<center><small> ''Equation 1: Equation of the Overlap Integral'' </small> </center>
<math>\psi_1</math> and <math>\psi^*_2</math> are the wavefunctions of the interacting MOs.
It is known that integral of asymmetric functions is zero. The product of an asymmetric and a symmetric function is asymmetric as the product of two functions of the same symmetry is symmetric. In conclusion, the overlap integral of two MOs of different symmetry is zero and the overlap integral of two MOs of the same symmetry is non-zero. This is consistent to the symmetry requirement mentioned before as reaction can't happen with zero overlap.

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

[[File:E2_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 5. Reaction Scheme of Cyclohexadiene and 1,3-Dioxole Reaction.]]

This a Diels-Alder reaction. The 1,3-Dioxole acts as the dienophile. There are two possible products: endo and exo.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
|+ Table 7: ''' Optimized Stuctures at PM6 Level and BY3LP 6-31(d) Level '''
!
!center; style="background: #0D4F8B; color: white;" |Cyclohexadiene
!center; style="background: #0D4F8B; color: white;" |1,3-dioxole
!center; style="background: #0D4F8B; color: white;" |Endo TS
!center; style="background: #0D4F8B; color: white;" |Exo TS
!center; style="background: #0D4F8B; color: white;" |Endo Product
!center; style="background: #0D4F8B; color: white;" |Exo Product
|-
|center; style="background: #0D4F8B; color: white;" |PM6
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |B3LYP/6-31G(d)
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |Frequency values at B3LYP/6-31G(d) Level
|[[File:E2_DIENE_ZZY.png|185px|thumb|center |]]
|[[File:E2_OXO_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_ZZY.png|185px|thumb|center |]]
|-
|}

The structures above are optimized as confirmed by the frequency calculation. None of them has more than one negative frequencies. There is only one negative frequency for both TS structures, indicating they are correctly optimized.

==== MO Analysis ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | ENDO MO
! style="background: #0D4F8B; color: white;" | EXO MO
|-
| [[File:E2_ENDO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
| [[File:E2_EXO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
|-
|+ Table 8. MO Diagrams for Endo and Exo Reactions
|}

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene HOMO
! style="background: #0D4F8B; color: white;" | Cyclohexadiene LUMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole HOMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | EXO TS HOMO
! style="background: #0D4F8B; color: white;" | EXO TS LUMO
! style="background: #0D4F8B; color: white;" | EXO TS HOMO-1
! style="background: #0D4F8B; color: white;" | EXO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO-1
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|+ Table 9. Relevant MOs to the MO Diagram
|}

The MO diagram is constructed based on the energies of MOs calculated at BY3LYP/6-31(d) level.

This is an inverse demand DA reaction. The frontier molecular orbitals of the dienophile are higher in energy than that of the diene, i.e. the diene is electron poor while the dienophile is electron rich. In result of that, the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub> are more similar in energy compared to the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub>. The strongest orbital interaction is between FMOs that are closest in energy, in this case, that are the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub>. In a normal demand DA reaction, the strongest orbital interaction is between the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub> and the diene is electron rich as the dienophile is electron poor.

This can be rationalized as the dienophile of this reaction: 1,3-dioxole, is relatively electron rich. The neighbouring oxygen atoms donate electron density into the double bond, raise the energy of the double bond MOs. The reaction proceeds in an inverse demand fashion.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energies Calculated From B3LYP/631G(d) (kJmol<sup>-1</sup>)
| -612584.1026
| -701187.072
| -1313621.484
| -1313613.647
| -1313848.695
| -1313845.101
|-
|+ Table 10. Energies for All Species
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 150
| -77.5
|-
| style="background: #0D4F8B; color: white;" | Exo
| +157
| -73.9
|-
|+ Table 11. Calculated Activation and Reaction Energy
|}

The reaction barrier and the reaction energy were calculated by using the energy data from the BY3LYP/6-31G(d) results.
<center>Reaction barrier = Energy of TS - Sum of energy of reactants</center>
<center>Reaction energy = Energy of product - Sum of energy of reactants</center>

For this reaction, the endo reaction has a more negative reaction energy and a lower activation energy. Therefore the endo product is both the kinetically and thermodynamically favourable products. The endo product is more stable and less energy is required to overcome the reaction barrier of the endo reaction. Noticed both the endo and exo reactions are exothermic, i.e. the products are lower in energy compared to the reactants.

==== Secondary Orbital Interaction ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
|-
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|[[File:ZZY_E2_ENDO_2.png|thumb|center]]
|[[File:ZZY_E2_EXO_steric.png|thumb|center]]
|-
|+ Table 12. Secondary Orbital Interactions
|}

As shown in the graph, only the endo TS has the secondary orbital interactions between diene and dienophile. The lone pair orbitals of oxygen atoms interact with the LUMO of cyclohexadiene. This interaction stabilizes the endo transition state, lowering the reaction barrier. According to the Hammond's Postulate, the transition state of a reaction resembles either the reactants or the products, to whichever it is closer in energy. In this reaction, the energy of both TS are closer in energy to the product, hence the structure of the TS resembles the product. Consequently, the secondary orbital interactions which stabilizes the endo TS, also stabilizes the endo product. This explains the endo selectivity of this reaction.

For the exo TS, there is no secondary orbital interactions and the steric clash between the diene and dienophile destablizes the exo TS and product. This results in disfavouring of the exo reaction.

=== Exercise 3: Diels-Alder vs Cheletropic ===

[[File:E3_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 6. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 63; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_TS_ZZY_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 65; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 134; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo Product
! center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 119; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 85; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 1; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 13. Optimized stuctures at PM6 level
|}

==== IRC Analysis ====

{| class="wikitable" style="margin: auto;"
|-
| style="background: #0D4F8B; color: white;" | Endo
| [[File:ZZY_E3_ENDO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Exo
| [[File:ZZY_E3_EXO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| [[File:ZZY_E3_CHE_DONG.gif]]
|-
|+ Table 14. Approach Trajectory of xylylene with SO<sub>2</sub>
|}

Ortho-xylylene has 8 <math>pi</math> electrons. According to the Huckle's rule (4n+2), it is not aromatic. However, it is planar as all carbons are sp<sup>2</sup> hybridised. When SO<sub>2</sub> approaches o-xylylene, the two ortho bonds stick out of the 6-membered ring plane towards the SO<sub>2</sub> and form new bonds with it while the <math>pi</math> bonds in the two ortho double bonds break. This leaves 6 <math>pi</math> electrons within the ring and the ring establishes aromaticity. Then the molecule adjusts to such that the original 8 carbons of the o-xylylene back to the same plane. The formation of aromatic ring and new sigma bonds are the driving force for the reactions.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Cheletropic TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
! style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +237.7678009
| +241.7506826
| +260.0871666
| +56.96807393
| +56.32220122
| -0.013127494
|-
|+ Table 15. Energies calculated from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 79.8
| -101.0
|-
| style="background: #0D4F8B; color: white;" | Exo
| +83.8
| -101.6
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| +102.2
| -157.9
|-
|+ Table 16. Calculated Activation and Reaction Energy
|}

[[File:ZZY_E3_ENERGY_PROFILE.PNG|centre|frame|Fig.7: Energy profiles of Endo, Exo and Cheletropic reactions]]

(This level of precision is far too high [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:18, 7 March 2018 (UTC))

The Diels-Alder reactions have lower reaction barrier than the Cheletropic reaction. They are kinetically favoured. The endo reaction has the lowest reaction barrier and it is the most favoured kinetically. The reaction energy of the endo and exo reactions are very close with the exo one slightly lower (probably due to less steric hindrance). Hence thermodynamically, they are favoured similarly. However, the Cheletropic reaction has a much lower reaction energy, i.e. the Cheletropic product is the most stable. The Cheletropic reaction is thermodynamically the most favoured reaction.

=== Extension: Second Cis-butadiene Fragment in O-xylylene ===

[[File:EX_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 8. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Exo Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 1; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 99; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 69; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 101; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 17. Optimized stuctures at PM6 level
|}

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +267.9846671
| +275.8217811
| +172.2537282
| +176.7223272
|-
|+ Table 18. Energies from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 110.1
| +14.3
|-
| style="background: #0D4F8B; color: white;" | Exo
| +117.9
| +18.8
|-
|+ Table 19. Calculated Activation and Reaction Energy
|}

The reaction barrier for both endo and exo reactions is much higher than that of the reactions with the other cis-butadiene fragment in Exercise 3. More energy required to overcome the barrier. In addition, the reaction energy for both endo and exo is positive, i.e. the products are more unstable than the reactants. Thus, this reaction with the cis-butadiene fragment within the ring is thermodynamically and kinetically unfavoured.

== Conclusion ==

In this experiment, the transition structures for three pericyclic reactions were located and characterized using two electronic structure methods: the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP in Gaussian. The structures were visualized in GaussView. An Intrinsic Reaction Coordinate (IRC) calculation on the correctly located TS showed the trajectories of the reactions and the change in physical parameters such as bond lengths and energy during the reaction. The TS MO diagram of these reactions were constructed based on the MO energy calculated from Gaussian. This showed the interacting orbitals and symmetry requirement for the reaction. The demand of the Diel-Alder reactions (normal/inverse) was also determined by analysis of the TS MO. Analysis of energy of optimized products, reactants and transition states demonstrated which products or route of reactions are more kinetically or thermodynamically favoured.

== References ==

<references />

== Appendix ==

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Ethene
|[[File:E1_SM_ALKENE_OP_PM6.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Butadiene
|[[File:DIENE_OP_PM6_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | TS
|[[File:REACTANT_TS_PM6_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexene
|[[File:E1_PRODUCT_OP_PM6.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | IRC
|[[File:E1_TS_IRC_PM6.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
!center; style="background: #0D4F8B; color: white;" | BY3LYP/6-31(d)
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexadiene
|[[File:ZZY_E2_DIENE_OP_PM6.LOG]]
|[[File:ZZY_E2_DIENE_OP_631.log]]
|-
|center; style="background: #0D4F8B; color: white;" | 1,3-dioxole
|[[File:ZZY_E2_DIOXOLE_OP_PM6.LOG]]
|[[File:ZZY_E2_DIOXOLE_OP_631.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:ZZY_E2_ENDO_TS_PM6_J.LOG]]
|[[File:ZZY_E2_ENDO_TS_631_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:ZZY_E2_EXO_TS_PM6_J.LOG]]
|[[File:ZZY_E2_EXO_TS_631_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:ZZY_E2_ENDO_OP_PM6.LOG]]
|[[File:ZZY_E2_ENDO_OP_631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:ZZY_E2_EXO_OP_PM6.LOG]]
|[[File:ZZY_E2_EXO_OP_631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:ZZY_E2_ENDO_IRC_PM6.LOG]]
|
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:ZZY_E2_EXO_IRC_PM6.LOG]]
|
|-
|}

=== Exercise 3: Diels-Alder vs Cheletropic ===

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:E3_XYLYLENE_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:E3_SO2_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:E3_ENDO_TS_ZZY_2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:E3_EXO_TS_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|[[File:E3_CHE_TS_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:E3_ENDO_Product_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:E3_EXO_Product_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|[[File:E3_CHE_Product_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:E3_ENDO_IRC_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:E3_EXO_IRC_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic IRC
|[[File:E3_CHE_IRC_ZZY.LOG]]
|}

=== Extension ===
{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:EX_ENDO_TS_ZZY_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:EX_EXO_TS_ZZY_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:EX_ENDO_PRODUCT_ZZY_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EX_EXO_PRODUCT_ZZY_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:EX_ENDO_IRC_ZZY_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:EX_EXO_IRC_ZZY_J.LOG]]
|}

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-03-07T12:10:15Z

Tam10: /* Exercise 3 */

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. 5.
[[File:Reaction_scheme_ex3_zwl115.PNG|left|frame| Figure 5. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

(Please check and understand the JMol code that you're using. You're asking for a particular MO number when you mean frame number [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:10, 7 March 2018 (UTC))

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system and are highly stabilised. On the contrary, compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable due to the filling of anti-bonding orbitals.<sup>9</sup> O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex3_1_zwl115.PNG|centre|frame|Figure 6. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure 7. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure 8. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures 6 and 8, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

==References==

9. Aromaticity and the Hückel 4n + 2 Rule. Chemistry Libretexts.

Rep:Mod:cej15 Transition States

2018-03-07T12:04:12Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

==Introduction==
===Transition State===
[[File:TS_cej.png|thumb|left|400px]]
A transition state of a particular reaction is the point where the reaction reaches its maximum potential energy. The activated complex would then either proceed to form the product, or return to its reagents, as shown in the graph. When the gradient in the reaction profile reaches zero and the second derivative is negative, then that represents the transition state.

===Potential Energy Surface===
The transition state can also be defined as a surface in configuration space that divides reactants from products and passes through the saddle point of the potential-energy surface<ref> Donald G. Truhlar, and Bruce C. Garrett Acc. Chem. Res., 1980, 13 (12), pp 440–448</ref>. The potential energy surface is a three-dimensional illustration of the reaction profile. A saddle point is when the gradient is zero but the second derivatives do not represent maxima or minima.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Optimisation and Determination of Transition State===
Both structures for the reactants and the structure for the product were constructed in Gaussian and optimised to a PM6 level. The bond lengths and bond angles for the optimised product were altered to resemble the transition state, and this assumed transition state was then optimised to a Berny Transition State.
In order to confirm if the transition state was correct or not, frequency calculations were made and the Intrinsic Reaction Coordinate was determined. The frequency of the transition state was -948.65 cm<sup>-1</sup> and the gifs for the vibrations and IRC are shown below.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto" border=1
! Vibrations || IRC
|-
| [[File:Exercise_1_vibration_cej.gif]] || [[File:Exercise_1_irc_cej.gif]]
|}

===MO Analysis===
For two molecular orbitals to interact, they must be of the same symmetry, which could also be shown in the table below, meaning that antisymmetric orbitals can only interact with antisymmetric orbitals and same for symmetric ones. This is because MOs would interact to form a non-zero overlap orbital. Mathematically, an antisymmetric function would have an overall integral of zero and combining a symmetric function and an antisymmetric function would produce this result, and this is why this kind of interacting is forbidden. Therefore, symmetric-antisymmetric interactions produce zero overlapping while symmetric-symmetric and antisymmetric-antisymmetric interactions produce non-zero overlaps.
{| class="wikitable" style="text-align: center" border=1
! Ethene MO !! 1,3-Butadiene MO || Symmetry || Transition State MOs || MO Diagram
|-
| rowspan="2" | [[File:ETHYLENE_LUMO_cej1.jpg|thumb|center|<div style="text-align: center">LUMO]] || rowspan="2" | [[File:BUTADIENE_HOMO_cej.jpg|thumb|center|<div style="text-align: center">HOMO]] || rowspan="2" | <math>a</math> || [[File:HIGHEST_MO_CEJ1.jpg|thumb|center|<div style="text-align: center">Highest MO]] || rowspan="4" | [[File:Exercise_1_MO_cej.png|500px]]
|-
| [[File:TS_lowest_MO_cej1.jpg|thumb|center|<div style="text-align: center">LUMO+1]]
|-
| rowspan="2" | [[File:ETHYLENE_HOMO_cej.jpg|thumb|center|<div style="text-align: center">HOMO]] || rowspan="2" | [[File:BUTADIENE_LUMO_cej.jpg|thumb|center|<div style="text-align: center">LUMO]] || rowspan="2" | <math>s</math> || [[File:TS_HOMO_CEJ1.jpg|thumb|center|<div style="text-align: center">HOMO]]
|-
| [[File:TS_LUMO_cej1.jpg|thumb|center|<div style="text-align: center">LUMO]]
|}

===Bond Length Analysis===

Shown below is a table of the bond lengths for each substance related in this reaction. A typical sp<sub>2</sub> C-C bond length is around 147 pm and a carbon double bond is around 133 pm, as shown for the bond lengths for butadiene and ethylene. A typical sp<sub>3</sub> C-C bond length is around 154 pm. Shown below is also a graph showing the change in bond lengths during the whole reaction.

{| style="text-align: center; " border=1
|+ '''Bond Lengths (Unit = pm)'''
! Carbons !! Butadiene !! Ethylene !! Transition State !! Product
|-
| C1-C2 || 134 || 133 || 138 || 149
|-
| C2-C3 || 147 || || 211 || 154
|-
| C3-C4 || 134 || || 138 || 154
|-
| C4-C5 || || || 211 || 154
|-
| C5-C6 || || || 138 || 149
|-
| C6-C1 || || || 141 || 133
|}

[[File:C_bond_change.png|600px]]

===Log File Uploads===
[[:File:BUTADIENE_OPT.LOG|Butadiene]]

[[:File:Ethene_opt_cej.log|Ethylene]]

[[:File:TS_opt_cej1.log|Transition State]]

[[:File:IRC_cej1.log|Intrinsic Reaction Coordinate]]

[[:File:PRODUCT_OPT_CEJ1.LOG|Cyclohexene]]

==Exercise 2: Reactions of Cyclohexadiene and 1,3-Dioxole==
===Optimisation and Determination of Transition State===
The same procedure was performed for this reaction as that of exercise 1. The vibration frequencies obtained for the endo adduct and the exo adduct are -935.85 cm<sub>-1</sub> and -959.61 cm<sub>-1</sub>. The intrinsic reaction coordinates are shown below.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto" border=1
! Endo Adduct || Exo Adduct
|-
| [[File:Exercise_2_endo_irc_cej.gif]] || [[File:Exercise_2_exo_irc_cej.gif]]
|}

===MO Analysis===

Shown below are the MO digrams of both the endo and exo transition states and the MO orbitals obtained from Gaussview.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto" border=1
! Endo MO diagram || Exo MO diagram
|-
| [[File:ENDO_MO_cej.png|thumb|500px]] || [[File:EXO_MO_cej.png|thumb|500px]]
|}

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto" border=1
! Cyclohexadiene MO !! 1,3-Dioxole MO || Symmetry || Endo Transition State MOs || Exo Transition State MOs
|-
| rowspan="2" | [[File:CYCLOHEXADIENE_HOMO_CEJ.PNG|thumb|center|<div style="text-align: center">HOMO]] || rowspan="2" | [[File:DIOXOLE_LUMO_CEJ.PNG|thumb|center|<div style="text-align: center">LUMO]] || rowspan="2" | <math>a</math> || [[File:ENDO_LOWEST_CEJ.PNG|thumb|center|<div style="text-align: center">LOWER MO]] || [[File:EXO_LOWEST_CEJ.PNG|thumb|center|<div style="text-align: center">LOWER MO]]
|-
| [[File:ENDO_HIGHEST_CEJ.PNG|thumb|center|<div style="text-align: center">HIGHER MO]] || [[File:EXO_HIGHEST_CEJ.PNG|thumb|center|<div style="text-align: center">HIGHER MO]]
|-
| rowspan="2" | [[File:CYCLOHEXADIENE_LUMO_CEJ.PNG|thumb|center|<div style="text-align: center">LUMO]] || rowspan="2" | [[File:DIOXOLE_HOMO_CEJ.PNG|thumb|center|<div style="text-align: center">HOMO]] || rowspan="2" | <math>s</math> || [[File:ENDO_HOMO_CEJ.PNG|thumb|center|<div style="text-align: center">HOMO]] || [[File:EXO_HOMO_CEJ.PNG|thumb|center|<div style="text-align: center">HOMO]]
|-
| [[File:ENDO_LUMO_CEJ.PNG|thumb|center|<div style="text-align: center">LUMO]] || [[File:EXO_LUMO_CEJ.PNG|thumb|center|<div style="text-align: center">LUMO]]
|-
|}

From comparing the transition state HOMOs for the exo and endo adducts, it can be suggested that the endo adduct is kinetically favoured. This is because there are non-bonding interactions present between the reactive site of cyclohexadiene and the p-orbitals of the oxygen atoms on the 1,3-dioxole. This would stabilise the transition state and reduce its energy.

===Energies and Analysis===

{| class="wikitable floatright" style="text-align: center" border=1
|+ '''Reactant and Product Energies (kJmol<sup>-1</sup>)'''
! !! Compound || <math>\varepsilon_0 + G_{corr}</math>
|-
| rowspan="2" | Reactant || Cyclohexadiene || -233.32
|-
| 1,3-Dioxole || -267.07
|-
| rowspan ="2" | Product || Exo Diels-Alder Adduct || -500.43
|-
| Endo Diels-Alder Adduct || -500.42
|}
The table to the right shows the sum of electronic and thermal free energies of the reactants and the products. This can be used to calculate the change in the standard Gibbs Free Energy for both reactions using the equation below:

<div align="center"><math>\Delta_rG^{\ominus}(298.15K) = \sum_{products} (\varepsilon_0 + G_{corr}) - \sum_{reactants} (\varepsilon_0 + G_{corr})</math></div>

which turns out to be:

<div align="center"><math>\Delta_rG^{\ominus}(298.15K) = -500.43 - (-233.32 + -267.07) = -0.04 kJ/mol</math></div> for the exo adduct and,

<div align="center"><math>\Delta_rG^{\ominus}(298.15K) = -500.42 - (-233.32 + -267.07) = -0.03 kJ/mol</math></div> for the endo adduct.

The two is very similar as shown, with a very small difference of 0.01 kJ/mol. This suggests that both is favourable, but due to the fact that the exo adduct did have a larger change in gibbs free energy, the exo adduct is supposed to be more thermodynamically stable, while the endo adduct is more kinetically stable. This could be due to the endo adduct having better orbital overlaps than the exo adduct, but the exo adduct reduces repulsion more than the endo adduct.

The activation energy was also calculated by using the energies for the reactants and the energies at the transition state. Results for the activation energy of the endo and exo adducts are shown below respectively:

<div align="center"><math>\Delta_rG^{\ddagger}(298.15K) = -500.33 - (-233.32 + -267.07) = + 0.06 kJ/mol</math></div>

<div align="center"><math>\Delta_rG^{\ddagger}(298.15K) = -500.33 - (-233.32 + -267.07) = + 0.06 kJ/mol</math></div>

As the activation energy values for both are the same at 2 decimal places, both transition states are very similar in stability.

===Log File Uploads===
[[:File:CYCLOHEXADIENE_OPT_CEJ.LOG|Cyclohexadiene]]

[[:File:DIOXOLE_OPT_CEJ.LOG|Dioxole]]

[[:File:ENDO_TS_CEJ.log|Transition State for Endo Product]]

[[:File:EXO_TS_CEJ.log|Transition State for Exo Product]]

[[:File:ENDO_IRC_CEJ.log|Intrinsic Reaction Coordinate of Endo Product]]

[[:File:EXO_IRC_cej.log|Intrinsic Reaction Coordinate of Exo Product]]

[[:File:ENDO_product_cej.log|Endo Product]]

[[:File:EXO_PRODUCT_CEJ.LOG|Exo Product]]

==Exercise 3: Diels-Alder vs Cheletropic==
===Optimisation and Determination of Transition State===
The transition states for the Diels-Alder reaction and the Cheletropic product were both determined and optimised and had vibrational frequencies of -351.62 cm<sup>-1</sup> and -486.44 cm<sup>-1</sup> respectively. Shown below are the intrinsic reaction coordinates of the two reactions.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto" border=1
! Diels-Alder || Cheletropic
|-
| [[File:Exercise_3_DA_irc_cej.gif]] || [[File:Exercise_3_Chele_irc_cej.gif]]
|}

===Energies and Analysis===

{| class="wikitable floatright" style="text-align: center" border=1
|+ '''Reactant and Product Energies (kJmol<sup>-1</sup>)'''
! !! Compound || <math>\varepsilon_0 + G_{corr}</math>
|-
| rowspan="2" | Reactant || Xylylene || -309.50
|-
| Sulfur Dioxide || -548.60
|-
| rowspan ="2" | Product || Diels-Alder || -853.60
|-
| Cheletropic || -853.53
|}

(The energies quoted by Gaussian are in Hartree/particle. You have also swapped over activation and reaction energies. It seems that your product was the wrong structure (wrong number of atoms probably?). Unfortunately you've uploaded the PM6 geometries instead so I can't see what's happened. There is also the endo-DA reaction you've missed [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:04, 7 March 2018 (UTC))

The energy values of the reactants and products are shown in the table on the right. The same method of calculation was used as that of the previous exercise and the results are shown in the table below.

{| class="wikitable floatleft" style="text-align: center" border=1
|+ '''Change in Free Energies and Calculation of Activation Energies (kJmol<sup>-1</sup>)'''
! !! <math>\Delta_rG^{\ominus}(298.15K)</math> || <math>\Delta_rG^{\ddagger}</math>
|-
| Diels-Alder Product || + 4.50 || +0.01
|-
| Cheletropic Product || +4.57 || + 0.03
|}

The differences between the two are also very small but it could still be seen that the Diels-Alder product was more favourable as the change in free energy is more negative than that of the cheletropic product. The general energy profiles of the two can be shown in the graph below.

[[File:Reaction_profile_cej.png|centre|600px]]

(This diagram doesn't correspond to the data you have provided [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:04, 7 March 2018 (UTC))

===Log File Uploads===
[[:File:SO2_opt_cej.log|Sulfur Dioxide]]

[[:File:XYLYLENE_OPT_CEJ.LOG|Xylylene]]

[[:File:DA_TS_CEJ3.log|Diels-Alder Transition State]]

[[:File:Chele_TS_cej.log|Cheletropic Transition State]]

[[:File:DA_IRC_cej3.log|Diels-Alder Intrinsic Reaction Coordinate]]

[[:File:Chele_IRC_cej.log|Cheletropic Intrinsic Reaction Coordinate]]

[[:File:DA_PRODUCT_cej3.log|Diels-Alder Product]]

[[:File:PRODUCT_CHELETROPIC_CEJ.LOG|Cheletropic Product]]

Rep:Dy815

2018-03-07T11:11:51Z

Tam10: /* Exercise 3 */

==Introduction==

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

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

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

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

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

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

where the middle part is called Hessian matrix.

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

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

==Exercise 1==

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

===Calculation files list===

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

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

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

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

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

==Exercise 2==

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The new comparison method follows:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=== Reaction energy analysis===

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

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

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

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

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

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

The reason why the '''endo''' product is the thermodynamic product can be rationalised by considering the steric clash in '''exo''', which raises the energy level of '''exo''' product. Therefore, with the increased product energy level, the reaction energy for '''exo''' product is smaller than '''endo''' one.

[[File:DY815 Ex2 Steric clash of products.PNG|thumb|centre|Figure 11. different products with different steric clash |700x600px]]

====Secondary molecular orbital overlap====

[[File:DY815 Secondary orbital effect.PNG|thumb|centre|Figure 12. Secondary orbital effect|700x600px]]

As seen in '''figure 12''', the secondary orbital effect occurs due to a stablised transition state where oxygen p orbitals interact with π <sup>*</sup> orbitals in the cyclohexadiene. For '''exo''' transition state, only first orbital interaction occurs. This is the reason why '''endo''' product is the kinetic product as well.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 11. Frontier molecular orbital to show secondary orbital interactions
!<jmol>
<jmolApplet>
<title>ENDO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>black</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DY815 EX2 TS2-B3LYP(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

'''Table 11''' gives the information of the frontier molecular orbitals.

===Calculation files list===

Energy calculation for the '''endo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 ENDO MO.LOG]]

Energy calculation for the '''exo''' transition state combined with reactants has been done in the same '''PES''':[[Media:DY815 EX2 EXO MO 2222.LOG]]

Frequency calculation of endo TS:[[Media:DY815 EX2 ENDO-TS2-B3LYP(FREQUENCY).LOG]]

Frequency calculation of exo TS:[[Media:DY815 EX2 TS2-B3LYP(FREQUENCY).LOG]]

Energy calculation for endo TS vs exo TS:[[Media:DY815 EX2 ENDOTS VS EXOTS ENERGYCAL.LOG]]

Energy calculation for EX1 dienophile vs EX2 dienophile:[[Media:DY815 COMPARISON FOR EX1 AND EX2 DIENOPHILE.LOG]]

Energy calculation for comparing HOMO and LUMO for cyclohexadiene vs 1,3-dioxole:[[Media:(ENERGY CAL GFPRINT) FOR CYCLOHEXADIENE AND 13DIOXOLE.LOG]]

==Exercise 3==

In this section, Diels-Alder and its competitive reaction - cheletropic reaction will be investigated by using '''PM6''' method in GaussView. Also, the side reactions - internal Diels-Alder and electrocyclic reaction will be discussed. The figure below shows the reaction scheme ('''figure 13''').

'''Note''': All the calculations done in this part are at '''PM6''' level.

[[File:DY815 EX3 Reaction scheme.PNG|thumb|center|Figure 13. Secondary orbital effect|500px]]

===IRC calculation===

IRC calculations use calculated force constants in order to calculate subsequent reaction paths following transition states. Before doing the IRC calculation, optimised products and transition states have been done. The table below shows all the optimised structures ('''table 12'''):

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center
|+|table 12: Table for optimised products and transition states
!
! endo Diels-Alder reaction
! exo Diels-Alder reaction
! cheletropic reaction
|-
! optimised product
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! optimised transition state
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| |<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

After optimising the products, set a semi-empirical distances (C-C: 2.2 Å) between two reactant components and freeze the distances. IRC calculations in both directions from the transition state at '''PM6''' level were obtained. The table below shows IRC calculations for '''endo''', '''exo''' and '''cheletropic''' reaction. As shown in the IRC gif, '''the six-member ring''' became the '''aromatic system''' during the reactions processing.

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 13. IRC Calculations for reactions between o-Xylylene and SO<sub>2</sub>
!
!Total energy along IRC
!IRC
|-
|IRC of Diels-Alder reaction via endo TS
|[[File:DY815 EX3 ENDO IRC capture.PNG]]
|[[File:Diels-alder- endo-movie file.gif]]
|-
|IRC of Diels-Alder reaction via exo TS
|[[File:DY815 EX3 EXO IRC capture.PNG]]
|[[File:DY815 Diels-alder- exo-movie file.gif]]
|-
|IRC of cheletropic reaction
|[[File:DY815 EX3 Cheletropic IRC capture.PNG]]
|[[File:DY815 Cheletropic-movie file.gif]]
|}

===Reaction barrier and activation energy===

The thermochemistry calculations have been done and presented in the tables below:

{| class="wikitable"
|+ table 14. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS
! 0.092077
! 241.748182
|-
! EndoTS
! 0.090562
! 237.770549
|-
! Cheletropic TS
! 0.099062
! 260.087301
|-
! Exo product
! 0.027492
! 72.1802515
|-
! Endo Product
! 0.021686
! 56.9365973
|-
! Cheletropic product
! 0.000002
! 0.0052510004
|}

(Your xylylene energy is a bit too high. If you had included the log file for it we could have seen what happened [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:11, 7 March 2018 (UTC))

The following figure and following table show the energy profile and the summary of activation energy and reaction energy.

[[File:DY815 EX3 Enrgy profile.PNG|thumb|centre|Figure 14. Energy profile for ENDO, EXO and CHELETROPIC reaction|500px]]

(You should include values on this diagram to make comparison easier. It's not immediately obvious which way around the profile is, so typically it's better to show where reactants/TS/products are as well. Excel is not the easiest program to do this with. Remember it doesn't need to be to scale if you have individual values on, so you can make it tidier if there's overlap [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:11, 7 March 2018 (UTC))

{| class="wikitable"
|+ table 15. Activation energy and reaction energy(KJ/mol) of three reaction paths at 298K
!
! Exo
! Endo
! Cheletropic
|-
! Activation energy (KJ/mol)
! 83.69570
! 79.71806
! 102.03481
|-
! Reaction energy (KJ/mol)
! -85.87224
! -101.11589
! -158.04724
|}

(Too many significant figures. The precision is an indication of trust and lack of error [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:11, 7 March 2018 (UTC))

By calculation, the cheletropic can be considered as thermodynamic product because the energy gain for cheletropic pathway is the largest. The kinetic product, here, is '''endo''' product (the one with the lowest activation energy) just like as what was expected before.

===Second Diels-Alder reaction (side reaction)===

The second Diels-Alder reaction can occur alternatively. Also, for this second DA reaction, '''endo''' and '''exo''' pathways can happen as normal DA reaction do.

[[File:DY815 EX3 Internal DA Reaction scheme.PNG|thumb|centre|Figure 15. Second Diels-Alder reaction reaction scheme|500px]]

The '''table 16''' below gives the IRC information and optimised transition states and product involved in this reaction:

{| class="wikitable" style="margin-left:auto;margin-right: auto;border:none; text-align:center"
|+Table 16. for TS IRC and optimised products for THE SECOND DA reaction between o-Xylylene and SO<sub>2</sub>
!
!exo pathway for the second DA reaction
!endo pathway for the second DA reaction
|-
!optimised product
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(EXO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>black</color>
<size>150</size>
<script>frame 2; </script>
<uploadedFileContents>INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!TS IRC
|[[File:Internal-diels-aldermovie file(EXO).gif]]
|[[File:DY815 Internal-diels-aldermovie file(ENDO).gif]]
|-
!Total energy along IRC
|[[File:Dy815 ex3 IDA-EXO IRC capture.PNG]]
|[[File:DY815 IDA-ENDO IRC capture.PNG]]
|}

The table below (in '''table 17''') gives the information of energies calculation:

{| class="wikitable"
|+ table 17. Summary of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! Components
! Energy/Hatress
! Energy/kJmol<sup>-1</sup>
|-
! SO2
! -0.118614
! -311.421081
|-
! Xylylene
! 0.178813
! 469.473567
|-
! Reactants energy
! 0.060199
! 158.052487
|-
! ExoTS (second DA reaction)
! 0.102070
! 267.984805
|-
! EndoTS (second DA reaction)
! 0.105055
! 275.821924
|-
! Exo product (second DA reaction)
! 0.065615
! 172.272196
|-
! Endo Product (second DA reaction)
! 0.067308
! 176.717167
|}

The energy profile for the second Diels-Alder reaction is shown below (shown in '''figure 16'''):

[[File:Second DA enrgy profile.PNG|thumb|centre|figure 16. Energy profile for the second Diels-Alder reaction|500px]]

And the activation energy and reaction energy for the second Diels-Alder reaction has been tabulated below. From this table, it can be concluded that the kinetic product is '''endo''' as expected, and the relative thermodynamic product here is '''endo''' as well.

{| class="wikitable"
|+ table 18. Activation energy and reaction energy(KJ/mol) of second DA reaction paths at 298K
!
! Exo (for second DA reaction)
! Endo (for second DA reaction)
|-
! Activation energy (KJ/mol)
! 109.93232
! 117.76944
|-
! Reaction energy (KJ/mol)
! 14.21971
! 18.66468
|}

===Comparing the normal Diels-Alder reaction and the second Diels-Alder reaction (side reaction)===

[[File:DY815 Combined energy profile.PNG|thumb|centre|figure 17. combined energy profile for five reaction pathways|600px]]

(Perhaps keep the colours consistent throughout the exercise? [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:11, 7 March 2018 (UTC))

As seen in '''figure 17''', the combined energy profile has been shown to compare the activation energies and reaction energies. The energy profile illustrates that both '''endo''' and '''exo''' for second DA reaction is side reactions because their gain in reaction energy are both positive values. The positive values indicate that the second diels-Alder reactions are not thermodynamically favourable compared with the normal Diels-Alder reactions and cheletropic reaction. If we see the products formed by the second DA pathway, very distorted structures can be found, which means the products for the second DA pathway are not stablised.

The second DA reaction are not kinetically favourable, reflected by the activation energies for both '''side reaction''' pathways. The activation energies for '''side reaction''' are higher than the activation energies for other three normal reaction pathways (as shown in '''figure 17''').

===Some discussion about what else could happen (second side reaction)===

Because o-xylyene is a highly reactive reactant in this case, self pericyclic reaction can happen photolytically.

[[File:DY815-Electrocyclic rearragenment.PNG|thumb|centre|figure 18. Electrocyclic rearrangement for reactive o-xylyene|500px]]

While this reaction is hard to undergo under thermal condition because of Woodward-Hoffmann rules (this is a 4n reaction), this reaction can only happen only when photons are involved. In this case, this reaction pathway is not that kinetically competitive for all other reaction pathways, except the photons are involved.

In addition, in this side reaction, the product has a four-member ring, which means the product would have a higher energy than the reactant. This means this side reaction is also not that competitive thermodynamically.

(This is not true. You can perform the calculations to determine which is more stable. The important thing is whether it is kinetically viable. [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:11, 7 March 2018 (UTC))

===Calculation file list===

Log file for CHELETROPIC IRC:[[Media:DY815-CHELETROPIC-IRC.LOG]]

Log file for CHELETROPIC PRODUCT:[[Media:DY815 EX3 CHELETROPIC-PRO1(FREQUENCY).LOG]]

Log file for CHELETROPIC TS:[[Media:DY815 EX3 CHELETROPIC-TS2(FREQUENCY).LOG]]

Log file for DIELS-ALDER ENDO IRC:[[Media:DY815 DIELS-ALDER- ENDO-IRC.LOG]]

Log file for DIELS-ALDER ENDO PRODUCT:[Media:DY815 EX3 DIELS-ALDER- ENDO-PRO1(FREQUENCY).LOG]]

Log file for DIELS-ALDER ENDO TS:[[Media:DY815 EX3 DIELS-ALDER- ENDO-TS2(FREQUENCY).LOG]]

Log file for DA EXO IRC:[[Media:Dy815-DIELS-ALDER- EXO-IRC.LOG]]

Log file for DA EXO PRODUCT:[[Media:DY815 EX3 DIELS-ALDER- EXO-PRO1(FREQUENCY).LOG]]

Log file for DA EXO TS:[[Media:DY815 EX3 DIELS-ALDER- EXO-TS2(FREQUENCY).LOG]]

Log file for SECOND DA IRC (ENDO):[[Media:INTERNAL-DIELS-ALDER-IRC(ENDO).LOG]]

Log file for SECOND DA IRC (EXO):[[Media:INTERNAL-DIELS-ALDER-IRC(EXO).LOG]]

Log file for SECOND DA PRODUCT (ENDO):[[Media:INTERNAL-DIELS-ALDER-P1(ENDO) (FREQUENCY).LOG]]

Log file for SECOND DA PRODUCT (EXO):[[Media:INTERNAL-DIELS-ALDER-P1(EXO).LOG]]

Log file for SECOND DA TS (ENDO):[[Media:INTERNAL-DIELS-ALDER-TS2(ENDO) (FREQUENCY).LOG]]

Log file for SECOND DA TS (EXO):[[Media:INTERNAL-DIELS-ALDER-TS2(EXO) (FREQUENCY).LOG]]

==Conclusion==

For all the works, GaussView shows reasonably good results, especially for predicting the reaction process.

In '''exercise 1''' - Diels-Alder reaction between butadiene and ethene have been discussed, and in this exercise, necessary energy levels for molecular orbitals have been constructed and compared. Bond changes involved in the reaction have also been discussed, which illustrated that the reaction was a synchronous reaction.

In '''erexcise 2''' - Diels-Alder reaction for cyclohexadiene and 1,3-dioxole, MOs and FMOs were constructed, followed by the energy calculations for the reaction. Although for working out '''endo''' MO diagram was a bit problematic by using individual energy calculation, it can be solved by constructing a non-interactive reactant-transition-state calculation. The MO diagram obtained is reasonably good, in terms of correct MO energies. In the last bit, via calculation, '''endo''' was determined as both kinetic and thermodynamic product.

In '''exercise 3''' - reactions for o-xylyene and SO<sup>2</sup>, the IRC calculations were presented to visualise free energy surface in intrinsic reaction coordinate at first. The calculation for each reaction energies were compared to show natures of the reactions.

For all calculation procedures, including all three exercises, products were firstly optimised, followed by breaking bonds and freezing these bonds at empirically-determined distances for specific transition states. The next step was to calculate 'berny transition state' of the components and then IRC was required to run to see whether the correct reaction processes were obtained.

Rep:Mod:ha3915TS

2018-03-07T10:48:40Z

Tam10: /* Exercise 3: Diels-Alder vs Cheletropic */

== Transition States and Reactivity Computational Lab ==

=== Introduction ===

==== Potential Energy Surface ====
[[File:Ha3915pes.jpg|thumb|'''Figure 1: '''A potential energy surface with labels to describe the properties of a transition state<ref>HARE, S.R., and TANTILLO, D. J., 2017. Post-transition state bifurcations gain momentum – current state of the field. Pure Appl. Chem. 89(6), pp. 679–698</ref>]]
A potential energy surface (PES) is a depiction of the relationship between a reaction's geometry parameters and the potential energy. The dimensionality of such surface is determined by 3N-6, where N is the number of atoms involved in the reaction. As such the dimensionality is proportional to the number of degrees of freedom of the molecule. Although the PES is found for multiple progress variables, one can minimise all other degrees of freedom such that only one reaction coordinate remains variable, giving the energy profile of the reaction.

A Transition State (TS) is a maximum on the minimum energy pathway; this is usually the pathway taken by the reaction where the reactants and products are minima with the maximum transition state between them. It is thus a saddle point on the multi-dimensional PES as all second derivatives are positive except that of the reaction coordinate.

All stationary points on the PES have first derivatives of 0 with respect to all degrees of freedom. For a minimum point, the second derivative will be positive since it describes the curvature of the surface and any fluctuation at a minimum will cause an increase in the potential energy since it has a positive curvature. The opposite case, where the curvature is negative, describes a maximum; any fluctuation would decrease the potential energy. A TS is a saddle point, only some fluctuations cause a decrease in energy whilst others can cause an increase in energy. Since the TS is a maximum on the energy profile it will have a negative curvature (negative second derivative) with respect to one degree of freedom (the reaction coordinate that gives the minimum energy pathway or energy profile) and positive curvature (positive second derivative) for all other degrees of freedom. The matrix of partial second derivatives of a multivariable function is known as the Hessian matrix, as such, the eigenvalues of the matrix can be examined to determine the curvatures at each point.

Such an energy landscape can be dense with saddle points, however only a few are relevant transition states, since by definition, the transition state is a saddle point on the PES with a single negative Hessian eigenvalue.

The negative Hessian eigenvalue means that the force constant for that vibration is negative. The vibrational frequency is calculated by:

<center><math>\nu = \frac{1}{2 \pi c} \sqrt{\frac{k}{\mu}}</math></center>

where ν is the wavenumber, c is the speed of light, k is the force constant and µ is the reduced mass. As such, the vibrational frequency is imaginary; thus every TS has an imaginary vibrational frequency; this phenomenon was used to confirm the success of the calculations.

==== Computational Methods ====
Three methods were used to locate the transition state of the reaction as described in the tutorial, these were:
# Guessing a transition state, then placing the reactants in a similar position and orientation, then optimise - some transition state may be found, however this method is unreliable but it's quick.
# Similar to method 1, however the bonds which are thought to form during the transition state between the interacting atoms are frozen in length during optimisation - this makes it more likely to find the transition state for more complex reactions but is slower than method 1.
# The product was drawn and optimised to a minimum, the bonds which are thought to be formed in the reaction are broken and frozen as above in 2. Then the transition state was calculated - this method was the most successful but was the slowest.
In order to optimise the geometry of the transition state, Gaussian did step-wise calculations for the single point energy as an attempt to solve the Hamiltonian matrix of the system for each possible geometry until the energy converged and the minimum energy structure was found.

Gaussian assumes the linear combination of atomic orbitals to calculate MO energies - this is defined mathematically as <math> |\Psi > =\sum_{i}^{N}c_{i}\Phi _{i}</math> , where ''φ<sub>i</sub>'' is the atomic orbital, ''c<sub>i</sub>'' is a weighting coefficient and ''|Ψ>'' the wavefunction vector in Hilbert space. This is done using the Hamiltonian, which in bra-ket notation is defined as <math> E=< \Psi |H|\Psi > </math>

To solve the Hamiltonian matrix, two different algorithms were used. PM6 and B3LYP. PM6 is a semi-empirical method in which some terms in the matrix are assumed by approximation. As such, the optimisations are less accurate than B3LYP. B3LYP however, utilises a 6-31G(d) basis set and is a DFT-hybrid technique (Density Functional Theory and the Hartree-Fock methods); this means that the Hamiltonian matrix is solved as a function of electron density and there are no integral approximations; B3LYP also accounts for the exchange integral and the electron correlation exchange energy. Both methods utilise the Hartree-Fock method, which uses a set of electron wavefunctions to approximate the motion of electrons in a field of atomic nuclei by assuming that the wavefunction can be approximated by a single Slater determinant (an expression that describes a multi-fermionic (electrons are fermions) and satisfies Pauli's exclusion principle) made up of one spin orbital per electron.<ref>Slater, J., ''A Simplification of the Hartree-Fock Method'', MIT, 1950.</ref><ref>Froese Fischer, Charlotte (1987). "General Hartree-Fock program". ''Computer Physics Communication''. '''43''' (3): 355–365.</ref> Since B3LYP is a hybrid many more properties of the system can be determined more accurately; Hartree-Fock is a quantum mechanical method of approximation that best describes the exchange correlation but can't determine the dynamic electron correlation accurately, this is where DFT is used - which can exactly determine the dynamic electron correlation is used.

== Exercise 1: Reaction of Butadiene with Ethylene ==
This Diels Alder reaction was investigated using PM6 to determine the transition state. This was achieved by using method 2 mentioned above. Figure 2 shows the reaction scheme:
[[File:Ha3915 ex1 mech.jpg|centre|thumb|'''Figure 2:''' Reaction Scheme and mechanism for the Diels Alder reaction of Butadiene with Ethylene]]
This pericyclic cycloaddition reaction has a <sub>π</sub>4<sub>s </sub>and a <sub>π</sub>2<sub>s</sub> component (butadiene and ethylene respectively) and is thus thermally allowed as satisfied by the Woodward-Hoffman rules.

Upon transition state optimisation, an Intrinsic Reaction Coordinate (IRC) calculation was performed, again with PM6, to confirm that a transition state has been found. The IRC results and MO diagram are shown below.
[[File:Ha3915 ex 1 IRC PATH.PNG|centre|thumb|'''Figure 3:''' IRC Path for exercise 1 - Butadiene and ethylene]]

==== MO Analysis ====
[[File:Ha3915 ex1 mo.png|centre|thumb|'''Figure 4:''' MO Diagram for exercise 1 - Butadiene and ethylene]]According to frontier molecular orbital theory, the transition state orbitals are formed by the interactions of the frontier orbitals of the reactants (the HOMO and LUMO). The MOs of the reactants and TS are shown below, matching those depicted in the MO diagram. The relative energy positions of these orbitals were calculated through a single point energy calculation. The labels "s" and "a" in the MO diagram describe whether the MO is symmetric or asymmetric.

It can be seen that the butadiene HOMO interacts with the LUMO of the ethylene as they are of the same symmetry. This results in the formation of a transition state bonding/antibonding pair (the HOMO - 1 and the LUMO + 1) which are of the same symmetry as the interacting reactant orbitals, antisymmetric. Likewise, the symmetric ethylene HOMO interacts with the butadiene LUMO to form a further two symmetric transition state orbitals.

It is important to note that only orbitals of the same symmetry interact to form transition state orbitals of the same symmetry as the reactants' interacting orbitals. This is due to the overlap integral being non-zero, only when the two interacting orbitals are of the same symmetry. The overlap integral is defined as:

<center><math>S_{P_A, P_B} = \int \Psi_A \Psi_B dV </math><ref>Martin, D., ''Quantum mechanics of diatomic molecules:overlap integrals, coulomb integrals and ab initio calculations on imidogen'', Iowa State University Press, 1968, p.168.</ref></center>

Where <math>\Psi_A</math> and <math>\Psi_B</math> are orbital wavefunctions. In order to achieve a non-zero integral the integrated function must not be odd; this is true when the symmetry of the orbitals is the same, as such, the integrand becomes even and there is constructive interference so the orbitals can interact.

This reaction follows a 'normal electron demand' for a Diels Alder reaction as the HOMO of the diene and the LUMO of the dienophile (the asymmetric fragment orbital pair) have the largest splitting when forming the transition state MOs.

The MOs for the reactants and the transition state are shown below:
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Butadiene HOMO</title>
<size>200</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 BUTADIENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Butadiene LUMO</title>
<size>200</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 BUTADIENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Ethylene HOMO</title>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 ETHYLENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Ethylene LUMO</title>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 ETHYLENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>TS HOMO - 1</title>
<size>200</size>
<script>frame 34; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915TS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>TS HOMO</title>
<size>200</size>
<script>frame 34; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915TS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>TS LUMO</title>
<size>200</size>
<script>frame 34; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915TS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>TS LUMO + 1</title>
<size>200</size>
<script>frame 34; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915TS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Bond Length Analysis ===

{| class="wikitable" border="1" style="margin-left: auto; margin-right: auto; border: none; text-align:center; caption-side: bottom;"
|+
! Carbons !! Reactants Bond Length / Angstrom !! TS Bond Length / Angstrom !! Products Bond Length / Angstrom
|-
| C1-C2 || 1.3334 ||1.3798 ||1.5009
|-
| C2-C3 || 1.4706 ||1.4111 ||1.3370
|-
| C3-C4 || 1.3334 ||1.3798 ||1.5008
|-
| C4-C5 || N/A ||2.1143 ||1.5372
|-
| C5-C6 || 1.3273 ||1.3818 ||1.5346
|-
| C6-C1 || N/A ||2.1151 ||1.5372
|-
| colspan="4" |Literature values for bond lengths<ref>CRAIG, N. C., GRONER, P., and MCKEAN, D. C., 2006. Equilibrium Structures for Butadiene and Ethylene: Compelling Evidence for Π-Electron Delocalization in Butadiene. J. Phys. Chem. A, 110(23), pp. 7461–7469. DOI: 10.1021/jp060695b</ref>: Butadiene C-C: 1.454 ; Butadiene C=C: 1.338 ; Ethene C=C: 1.331
|-
|+ Table 1ː Change in C-C bond lengths as the reaction proceeds. The carbons are numbered as they are in the reaction scheme in figure 2.
|}

From this data it can be seen that in the product, there is one double bond where as in the reactants there are three; this agrees with the reaction scheme and the mechanism as predicted in figure 2.

The bond lengths in the transition state are not traditional as with the literature values; this is because the double bonds elongate as they become single bonds - the bond lengths are therefore intermediate between a single and double bond. This represents a change in hybridisation from sp2 carbons to sp3 carbons.

However in the C2-C3 pair a double bond is formed when electrons are moved during the pericyclic reaction, thus the bond gets shorter in the transition state to become of double bond length in the products. This can be rationalised by Hammond's postulate which states that the transition state of a reaction resembles either the reactants or the products depending on which it is closer to in energy; in this case, as confirmed by the IRC path in figure 2, the transition state resembles the product.

The Van der Waals radius of a carbon atom is 1.7 Å<ref>Batsanov, S.S., ''Van der Waals Radii of Elements'', Centre for High Dynamic Pressures, 2001, vol.37.</ref>. In the transition state, the bond length of the newly formed bonds are 2.115 Å which is less than 2x1.7, suggesting that a bond is actually forming and there are attractive interactions between the two atoms so a sigma bond can form.

=== Vibrational TS Analysis ===
The JSmol below shows the imaginary transition state vibration as discussed in the introduction.

<jmol>
<jmolApplet>
<title></title><color>white</color><size>400</size>
<uploadedFileContents>Ha3915TS3.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 35; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Show vibration</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
This shows the butadiene carbons getting closer to the ethylene; since symmetry is maintained throughout the vibration, both fragments must be moving at the same rate. the bond forming process is therefore synchronous which confirms the concerted nature of Diels Alder reactions<ref name=":0">CLAYDEN, J., GREEVES, N. and WARREN, S., 2012. Organic chemistry. Oxford: Oxford University Press, pp. 884-887</ref>. This is confirmed by the IRC animation of the reaction below.[[File:Ha3915 ex1 IRC MOVIE.gif|centre|frame|'''Figure 5: '''IRC animation for the formation of cyclohexene from butadiene and ethylene]]

=== LOG files ===
[[Media: Ha3915 BUTADIENE OPT.LOG| Butadiene]]

[[Media: Ha3915 ETHYLENE OPT.LOG| Ethylene]]

[[Media: Ha3915TS3.LOG| Transition State]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
This reaction is another Diels Alder cycloaddition which is thermally allowed, however in this case, the addition could be endo or exo depending on the approach trajectory of the reactants and their geometrical orientation, this is shown in the reaction scheme below.
[[File:CHD Diox Scheme.png|centre|thumb|'''Figure 6ː''' Reaction scheme for the reaction of cyclohexadiene and 1,3-Dioxole showing the exo and endo products.
]]

=== MO Analysis ===
[[File:Ha3915 MO DIAGRAM EXO AND ENDO.png|centre|thumb|'''Figure 7: '''MO diagram for the reaction of cyclohexadiene and 1,3-Dioxole in both conformations. Endo as shown in the black lines and Exo shown in red.]]The MO diagram above shows the MOs and relative energies for both the Endo (black) and Exo (red) reactions.

This reaction follows an 'inverse electron demand' as the diene LUMO/ dienophile HOMO gap is smaller than the diene HOMO/dienophile LUMO gap. This could be rationalised by the presence of electron donating oxygen atoms in the Dioxole being able to donate more electron density into the pi bond; thus raising the HOMO and LUMO energies of the dienophile. It should also be noted that the Exo TS has a higher energy HOMO and a lower energy LUMO comparing to the Endo.
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene HOMO</title>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 R1 B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene LUMO</title>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 R1 B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>1,3-Dioxole HOMO</title>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 R2 B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>1,3-Dioxole LUMO</title>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 R2 B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS HOMO-1</title>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS HOMO</title>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS LUMO</title>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo TS LUMO+1</title>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 EXO TS B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<color>white</color>
<title>Endo TS HOMO-1</title>
<size>200</size>
<script>frame 40; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 ENDO TS B3LYP NOEIGEN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Endo TS HOMO</title>
<size>200</size>
<script>frame 40; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 ENDO TS B3LYP NOEIGEN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Endo TS LUMO</title>
<size>200</size>
<script>frame 40; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 ENDO TS B3LYP NOEIGEN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<title>Endo TS LUMO+1</title>
<size>200</size>
<script>frame 40; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ha3915 ENDO TS B3LYP NOEIGEN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Analysis ===
The LOG files produced by Gaussian were inspected for the Gibbs free energy, which is the sum of electronic and thermal free energies. These energies are shown below
{| class="wikitable" border="1" style="margin-left: auto; margin-right: auto; border: none; text-align:center; caption-side: bottom;"
|+
! Molecule !! Gibbs Free Energy / E<sub>h</sub>
|-
| Cyclohexadiene || -233.324
|-
| 1,3-Dioxole || -267.068
|-
| Exo TS || -500.329
|-
| Endo TS || -500.332
|-
|+ Table 2ː Gibbs free energy values of reactants and transition states
|}
The reaction barrier was then calculated by subtracting the energy of the reactants from the transition state energy for each of the products. The results are shown in the table below.

{| class="wikitable" border="1" style="margin-left: auto; margin-right: auto; border: none; text-align:center; caption-side: bottom;"
|+
{| class="wikitable"
!Reaction
!Reaction Barrier / kJ mol<sup>-1</sup>
!Overall Reaction Energy / kJ mol<sup>-1</sup>
|-
|Exo
|166.310
|<nowiki>-65.154</nowiki>
|-
|Endo
|158.467
|<nowiki>-68.749</nowiki>
|}
|+ Table 3ː Reaction barriers and energies for Endo and Exo.
|}
These energies were calculated using the B3LYP method and 6-31G(d) basis set. It can be seen from the reaction barrier energy that the Endo TS is lower in energy than the Exo TS (see MO diagram). This suggests that the kinetic product is the Endo product; thus if the reaction was irreversible it would be selective towards the Endo product. The endo product also has a lower overall reaction energy and the endo product is more stable, thus the endo product is also the thermodynamic product. The lower reaction barrier are due to the favourable secondary orbital interactions between the lone pair on each oxygen atom in the p orbital on the dioxole and the π orbitals on the cyclohexadiene, stabilising the TS. In the exo product, the interaction between the O atoms and the π orbitals ceases to exist as they are simply too far away.

There was a large discrepancy between the energies calculated by B3LYP compared with PM6. The B3LYP energies are much more accurate, however a pre-optimisation was done with PM6 to save computational time as B3LYP is much more intensive. This made is easier and quicker to find the minimum as B3LYP was used on an already somewhat optimised structure.

=== LOG Files ===

[[Media: Ha3915 R1 B3LYP.LOG| Cyclohexadiene]]

[[Media: Ha3915 R2 B3LYP.LOG| 1,3-Dioxole]]

[[Media: Ha3915 EXO TS B3LYP.LOG| Exo Transition State]]

[[Media: Ha3915 ENDO TS B3LYP NOEIGEN.LOG| Endo Transition State]]

[[Media: Ha3EXO B3LYP.LOG| Exo Product]]

[[Media: Ha3ENDO B3LYP.LOG| Endo Product]]

== Exercise 3: Diels-Alder vs Cheletropic ==
[[File:Ha3915 ex3 reaction scheme.png|centre|thumb|<b>Figure 8ː</b> Reaction scheme for exercise 3 of the Diels Alder (both Endo and Exo) and Cheletropic reactions of SO<sub>2</sub> and Xylylene. ]]

(Be careful: you're showing bonds between S and the Cs in the TS as having bond order 1.5 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:48, 7 March 2018 (UTC))

The reaction between Xylylene and SO<sub>2 </sub>was invesigated. Both Endo and Exo Diels alder reactions were optimised and the transition states calculated. This was again a <sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s </sub>pericyclic reaction and was therefore thermally allowed in accordance with Woodward-Hoffman analysis.

A cheletropic reaction of xylylene and SO<sub>2 </sub> was also investigated. This is also a pericyclic reaction, where two new sigma bonds form to the same atom forming the five membered ring as shown in figure 8.

All the calculations were performed using PM6 as it gave relatively accurate geometrical optimisations for the purposes of this investigation. Although the energies are most likely inaccurate.

IRCs were also calculated to confirm the transition state, these are analysed below.

=== IRC analysis ===
<center>
{| class="wikitable"
![[File:Ha3915EXO IRC.gif|centre|frame|'''Figure 9:''' IRC animation for the formation of the Exo adduct]]
|-
![[File:Ha3915ENDO IRC.gif|frame|'''Figure 10:''' IRC animation for the formation of the Endo adduct|centre]]
|-
![[File:Ha3915CHELE IRC.gif|frame|'''Figure 11:''' IRC animation for the formation of the cheletropic product|centre]]
|}
</center>It can be seen from the IRC animations that the sigma bonds formed in the Endo and Exo Diels Alder reactions are not formed simultaneously; the reaction is thus described to be an asynchronous cycloaddition. On the other hand, the cheletropic IRC shows both bonds forming simultaneously to the S atom; it is thus a synchronous reaction. The formation of the aromatic ring in these reactions is a strong driving force due to the stabilisation energy of aromatics.

=== Energy Analysis ===
The table below shows the reaction barrier energies and the overall reaction energies for the three reactions above, these were calculated the same was as in exercise 2 but with the PM6 method.
{| class="wikitable" border="1" style="margin-left: auto; margin-right: auto; border: none; text-align:center; caption-side: bottom;"
|+
! Reaction !! Reaction Barrier / kJ mol<sup>-1</sup> !! Overall Reaction Energy / kJ mol<sup>-1</sup>
|-
| Exo || 88.398 || -98.531
|-
| Endo || 84.420 || -96.369
|-
| Cheletropic || 106.734 || -153.358
|-
|+ Table 4ː Reaction barriers and energies for the three reactions.
|}
As in exercise 2, the Endo approach is more kinetically favourable as the reaction barrier is smaller, and since this is an exothermic reaction<ref name=":0" />, according to Hammond's postulate, the product is much more likely to be formed. Again, the reaction barrier for the Endo transition state is smaller due to stabilising secondary orbital overlap of the π systems. However in this case, the discrepancy in activation energies between the Endo and Exo reactions is small; this is due to the size of the dienophile (sulfur dioxide) being very small such that the secondary orbital overlap effect is limited.

The Cheletropic reaction has the highest activation energy but the lowest reaction energy; this could be rationalised by considering the stabilisation from the extra S=O double bond in the cheletropic product. This makes it the most favourable thermodynamic product. The high activation barrier can be rationalised by the ring strain in the five membered ring that is formed which is larger compared to the ring strain in the six membered ring that is formed in the Diels Alder reactions.

=== Endocyclic reaction at alternative site ===
[[File:Ha3915altda.png|centre|thumb|'''Figure 12:''' Reaction scheme for the alternate endocyclic reactions that could occur, both Exo and Endo]]Xylylene could also react with SO<sub>2</sub> through its cis-butadiene fragment forming the two possible endocyclic products shown in the reaction scheme above. The transition state for both of these reactions was calculated and an IRC was performed - the IRC animations are shown below
[[File:ALT EXO IRC.gif|centre|frame|'''Figure 13:''' IRC animation for the formation of the endocyclic exo product]]
[[File:Ha3915ALT ENDO IRC.gif|centre|frame|'''Figure 14:''' IRC animation for the formation of the endocyclic endo product]]Since this is also a Diels Alder reaction, it can be seen in the IRC that the bonds don't form simultaneously and is therefore asynchronous.

==== Energy Analysis ====

{| class="wikitable" border="1" style="margin-left: auto; margin-right: auto; border: none; text-align:center; caption-side: bottom;"
|+
! Reaction !! Reaction Barrier / kJ mol<sup>-1</sup> !! Overall Reaction Energy / kJ mol<sup>-1</sup>
|-
| Exo || 122.472 || 23.356
|-
| Endo || 114.642 || 18.906
|-
|+ Table 5ː Reaction barriers and energies for the two reactions.
|}
Comparing these energies with the exocyclic reactions above, it can be concluded that an endocyclic reaction at the cis-butadiene site is unlikely due to the higher activation energy; this could be rationalised by the increased ring strain. The free energy of the reaction from both endo and exo approaches are positive which means that the reaction is not spontaneous and thus is thermodynamically unfavourable; this could be rationalised by considering the lack of aromatisation as compared with the exocyclic reactions.

=== Energy profile ===
[[File:Ha3915 reaction prof.png|centre|'''Figure 15:''' Energy profile for the formation of the 5 products|thumb]]

=== LOG files ===

[[Media: Ha3 SO2 PM6.LOG| Sulfur dioxide]]

[[Media: Ha3 XYLENE PM6.LOG| Xylylene]]

[[Media: Ha3 DA EXO TS PM6.LOG| Exo Transition State]]

[[Media: Ha 3 DA ENDO TS PM6.LOG| Endo Transition State]]

[[Media: Ha3 DA EXO PM6.LOG| Exo Product]]

[[Media: Ha3 DA ENDO PM6.LOG| Endo Product]]

[[Media: Ha3 CHELE PM6.LOG| Cheletropic Product]]

[[Media: Ha3 CHELE TS PM6.LOG| Cheletropic Transition State]]

[[Media: Ha3 DA ALT EXO PM6.LOG| Alternative Exo Product]]

[[Media: Ha3 DA ALT ENDO PM6.LOG| Alternative Endo Product]]

[[Media: Ha3 DA ALT EXO TS PM6.LOG| Alternative Exo Transition State]]

[[Media: Ha3 DA ALT ENDO PM6.LOG| Alternative Endo Transition State]]

== Conclusion ==
PM6 and B3LYP were two methods that were used to attempt to understand a reaction's pathway through optimising and finding transition states. A set of exercises dealing with pericyclic reactions showed that the transition states can be calculated with both methods for complex reactions.

From the exercises, it seems that in most cases, the endo reaction barrier was lower than the exo reaction barrier due to stabilising secondary orbital overlap between the p-orbitals on the dienophile and the diene orbitals. The exo product is also usually the most thermodynamically favourable due to steric hindrance, however as shown in exercise 2, even an exo product can become unfavourable because of sterics as the discrepancy is not large.

== References ==
<references />

Rep:Mod:tyy15 y3TS

2018-03-07T10:35:55Z

Tam10: /* Exercise 3 */

= Transition States and Reactivity =

== Introduction ==

Locating and examining the transition state has always been challenging in the field of chemistry before computational methods are developed. Since transition states are very short-lived, using experimental techniques in the laboratory to determine the structure of the transition state has proven to be very difficult or nearly impossible. Hammond's Postulate has helped scientist to give first approximation on what the transition might look like, by stating that the transition state structure will closely resemble the structure of product or reactant depending on which one is closer in energy with the transition state. The emergence and development of computational chemistry has not only helped to locate the transition state and provide you with the structure of the transition state, it can also be used to calculate the relative energy of reactants, T.S, and product in order to comparison between experimental data obtained in lab. Better understanding of the mechanism of the reaction can be brought about through knowing the transition state.

Transition state can be considered as the highest energy state within the reaction coordinate. Transition state will have a gradient of zero with a negative second derivative on the curve. The reaction coordinate we usually plot represents varying only one degree of freedom while keeping other degrees of freedom in equilibrium. An equilibrium mode would mean that those modes are kept in their lowest energy state, such that these structures (those not shown on the reaction coordinate) are said to be minimised. Minimised structure can be found on the PES, such that they will have value of zero for the first derivative, and a positive value for the second derivative. A saddle point is then said to be located. A useful reaction coordinate requires knowing which degree of freedom to vary depending on which degree.

In this exercise conducted below, we will explore a few Diels-Alder reactions and try to examine and analyse the Transition State, Potential Energy Surface and MOs of these structures. The reactions are run using Gaussview and each of the structure presented below are optimised by either the semi-empirical PM6 method or the Density Functional Theory method using B3LYP/6-31G(d) basis set. The molecules are drawn and optimised in Gaussview, by calculating the potential energy of all degrees of freedom of the molecule. The degrees of freedom are represented as various normal vibrational modes in each molecule. Linear molecules will possess (3N-5) vibrational modes and non-linear molecules will possess (3N-6) vibrational modes. N is representing the number of atoms in the molecule.

The program uses quantum chemistry to examine the wavefunction of each of the molecule. In each case, the Schrodinger equation is solved by using LCAO method. The overall wavefunction is the sum of individual degrees of freedom added together. Since there are so many degrees of freedom, a Hessian matrix can be employed to evaluate this complex Schrodinger equation. This will provide a solution for the Schrodinger equation. Then, the program will evaluate the energy of the system by applying the Hamiltonian operator to the Schrodinger equation.

The two methods that we use to optimise our structures and calculate energies represent the different ways in solving the Hessian matrix as discussed above. The PM6 method is a semi-empirical method, which stands for parameterization method 6. This method examines the Hessian matrix by correlating the functions to experimental data in the program. Therefore, it doesn't calculate all the values in the matrix, but it uses empirical values that speeds up the calculation. This is therefore called a semi-empirical method and the calculation does not that that long. For the other method that we use, it was the Density Functional Theory (DFT) method which uses the B3LYP/6-31G(d) basis set. This method again evaluates the Hessian Matrix, by calculating the electron density of each term in the matrix. The B3LYP/6-31G(d) basis set gives a hybrid function which correlates the energy calculated by DFT to the Hartree-Fork theory. The calculations are done from first principle, meaning that it will take a longer time for the calculations to run. It makes sense that our B3LYP calculations are done on the optimised structure from PM6 method, which should speed up the calculation by not starting from scratch. The IRC calculation that we ran represents the intrinsic reaction coordinate. It locates the minimum pathway on the potential energy surface between two minima. This is found through displacing our structure at the highest energy point in both directions, which is our transition state, and calculating the minimum energy pathway. Transition state will have a first derivative of zero and a negative second derivative. This leads to one imaginary (negative) frequency being able to be observed at the transition state. Other minima will have a positive second derivative at the minima, hence will not show a negative frequency of vibrations and would help us to distinguish between reactants/products and transition states.

== Exercise 1 ==
In this exercise, we have explored the [4+2] cycloaddition reaction between butadiene and ethylene. It can also be classified as a Diel-Alder reaction. Its reaction scheme can be found below in Figure.1. Analyses were conducted to explore the transition state, in relation to the reactants and the products. All the reactants, transition states, and the product was optimised using the PM6 method.

[[File:Tyy15 fg1 ex1 reaction scheme.PNG|400px|center|thumb|Figure 1: Reaction Scheme for reaction between butadiene and ethylene]]

=== Molecular Orbital Diagram ===

The energy of the different MO of the reactants and transition state was calculated using the optimised structures and their values can be compared. A MO diagram was constructed to probe the relative energy levels of the transition state, in comparison to the two reactants: ethylene and butadiene. The MO diagram can be found below in Figure.2.

[[File:Tyy15 fg2 ex1 MO.PNG|500px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital Diagram of Reaction between Butadiene and Ethylene]]

The HOMO and LUMO of the two reactants are the MOs that would participate in bonding in this reaction. They are displayed here as Jmol objects, helping us to understand the geometry of the orbitals and how they can participate in bonding. Each of the two reactants has its corresponding HOMO and LUMO and can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:tyy15_y3TS_ex1_reactants '''here''']. These four original individual MOs will linearly combine and give four MOs for the transition state. The interaction between these orbitals can be seen in our MO diagram in Figure.2 as well as a Jmol file from our calculation [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:tyy15_y3TS_ex1_ts '''here'''].

We can see from the calculation that the resulting MOs from the transition state consists of two bonding orbitals as well as two anti-bonding orbitals. It is seen that the two antisymmetric MOs of the reactants combined to give two antisymmetric MOs in the transition state, namely the 2π and the 5π*orbitals. Conversely, the two symmetric MOs of the reactants combined to give two symmetric MOs in the transition state, namely the 3π and the 4π* orbital. Through this, we can conclude that the same symmetry between the two fragments is required to be the same in order for a linear combination of the MOs to occur. This suggests that the orbital overlap integral will be zero for a symmetric-antisymmetric combination as confirmed by the non-interacting nature of these orbitals. In the case of symmetric-symmetric interaction and antisymmetric-antisymmetric interaction between the orbitals, the orbital overlap integral will be non-zero as found from the linear combinations between these orbital leading to the formation of the transition state. Therefore, it can be determined that the reaction is allowed when the MOs of same symmetry combine while the reaction is disallowed when the MOs of different symmetry is combined. This gives rise to the selection rule when different MOs interact together.

=== Bond Length Analysis ===

Bond length analysis was also conducted for the reactants, transition state and the product to probe its changes throughout the reaction. The result can be found in Figure.3 below. These values can then be compared to Table.1 below, which includes the literature values of typical sp3 and sp2 bond lengths as well as Van der Waals radius of C atom.

[[File:Tyy15 fg3 ex1 bond length.PNG|600px|center|thumb|Figure 3: Bond Length between Different Carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #4682B4; color: white;" |
! style="background: #4682B4; color: white;" | C<sub>sp<sup>3</sup></sub>-C<sub>sp<sup>3</sup> </sub> (single bond) <ref> H. J. Bernstein, Trans. Faraday Soc., 1961,57, 1649-1656 </ref>
! style="background: #4682B4; color: white;" | C<sub>sp<sup>2</sup></sub>=C<sub>sp<sup>2</sup></sub> (double bond)<ref> N C. Craig; P. Groner and D. C. McKean, J. Phys. Chem. A, 2006, 110 (23), pp 7461–7469 </ref>
! style="background: #4682B4; color: white;" | Van der Waals Radius of C atom <ref> A. Bondi, J. Phys. Chem., 1964, 68, 441–451 </ref>
|-
! style="background: #4682B4; color: white;" |Bond Length / Å
| 1.54
| 1.34
| 1.77
|}

A change in bond length between the carbon atoms can be observed throughout the reaction. A noticeable change can be observed between C1 and C2. These two atoms are the two carbons from the original ethylene, which has a double C-C sp2 bond between them and has a bond length of 1.33Å. However, during transition state, the bond length has increased to 1.38 Å, which can be explained by the formation of a partial double bond instead of a full double bond between C1 and C2. This value agrees with literature, which is a bond length between C-C sp3 and C-C sp2.This bond further increases the bond length to 1.53 Å, which suggest the formation of single C-C sp3 bond when compared to literature. Similar observation can be found between C3-C4 and C5-C6, which the double bond from reactant is turned into single bond in the product.

An opposite effect is seen between C4 and C5, where the single bond is turned into a double bond from reactants to product. The bond length changes from 1.47 Å to 1.34 Å which suggests the change from C-C sp3 bond to C-C sp2 bond. These values also agree closely with the literature values presented in Table.1.

Another interesting result that was obtained was the newly formed bonds between C2 and C3, as well as C6 and C1, during the reaction. We would expect that the distance of C2-C3 and C6-C1 will be slightly shorter than twice of the Van der Waals radius of carbon. This is because we have established in the previous section (See Molecular Orbital Diagram above) that there are interactions between the MOs of ethylene and butadiene during the transition state. This would mean that the MOs will overlap and hence leading to a shorter bond between the carbons. This is confirmed by the results we obtained, which bond lengths of 2.11 Å were found for these two bonds and is smaller than 3.4 Å (twice of Van der Waals radius).

=== Vibrational Analysis ===

The IRC and the vibrational frequencies were also probed in this exercise. During the transition state, an imaginative(negative) frequency should be found since a saddle point that contains a negative second derivative is situated at the point. The imaginative frequency found was - 948.74 cm<sup> -1</sup>. Both IRC and imaginary frequency can be found below in GIF.1 and GIF.2. Through this computational stimulation, we observe that the ethylene approaches the butadiene in a synchronous and concerted fashion during the transition state, leading to the bond formation.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ GIF.1 (Left): IRC of Reaction of Butadiene with Ethylene ; GIF.2 (Right) Imaginary Frequency at The Transition State (cm<sup>-1</sup>)
! style="background: #4682B4; color: white;" | IRC
! style="background: #4682B4; color: white;" | Imaginary Frequency at The Transition State
|-
| [[File:Tyy15 Ex1 IRC.gif|centre|500px]]
| [[File:Tyy15 Ex1 negative freq.gif|centre|500px]]
|}

== Exercise 2 ==

In this exercise, we have explored the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole. We will determine whether this Diels-Alder reaction is a normal or inverse electron demand reaction. Both the exothermic and endothermic product were probed and their results were compared. The reactants, transition states, and products were first optimised using the PM6 method, followed by the B3LYP/6-31G(d) method. IRC and frequency calculations were conducted for the transition states. The reaction scheme can be found below in Figure. 4.

[[File:Tyy15 fg4 ex2 reaction scheme.PNG|600px|center|thumb|Figure 4: Reaction Scheme of Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ]]

=== Molecular Orbital Diagram ===

MO diagrams were constructed for both the exothermic and endothermic transition state. They are put next to each other for ease of comparison. This can be found below in Figure.5.

[[File:Tyy15 fg5 ex2 MO.PNG|900px|900xp|center|thumb|Figure 5:Molecular Orbital Diagram of Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ]]

The HOMO and LUMO of the transition state of the exothermic and endothermic product can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:tyy15_y3TS_ex2_exo '''here'''] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:tyy15_y3TS_ex2_exo '''here'''] respectively as Jmol files. Using the theories established above from exercise 1, we again see that linear combination between MOs with the same symmetry has resulted in a non-zero orbital integral overlap.

The HOMO and LUMO for both exothermic and endothermic transition state were symmetric in nature and were formed by the interaction between the symmetric π orbital of the 1,3-dioxole fragment and the π*<sub>u</sub> fragment of the cyclohexadiene. Their interaction forms the 3π HOMO and the 4π* LUMO in the resulting transition states.

By running a single point energy calculation on the reactants geometry on the IRC calculations, we can calculate the energy of the different orbitals, hence able to determine their relative energy level on the MO diagram on Figure.5. From the results obtained, we have found that the formation of the HOMO and LUMO of the transition state is from the interaction between HOMO of the dienophile, 1,3-dioxole, and the LUMO of the diene, cyclohexadiene. This shows that the reaction is an inverse electron demand Diels-Alder Reaction, as the diene LUMO has a higher energy than the dienophile HOMO. The Diels-Alder reaction is between an electron-rich dienophile and an electro-poor diene. The two oxygen atoms on the 1,3-dioxole are electron donating in nature, leading to the interaction between LUMO of cyclohexadiene and HOMO of 1,3-dioxole. These two orbitals have energy levels that are closer in energy than the LUMO of 1,3-dioxole and HOMO or cyclohexadiene.

The energy of the HOMO and LUMO of the endothermic and exothermic transition states were also examined. Their relative energies were placed on the MO diagram according to the calculation. It can be seen that the HOMO-LUMO gap for the exothermic reaction is smaller as compared to the endothermic reaction. When examining the transition state, the HOMO of the endothermic transition state will be at lower energy as compared to the HOMO of the exothermic transition state. This is because, in an endothermic transition state, the p-orbitals of the oxygen on 1,3-dioxole will interact and overlap with the p-orbital of the cyclohexadiene. This in turns means that the HOMO of the transition is lowered and the LUMO is raised, leading to a larger HOMO-LUMO gap for the endothermic reaction.

=== Activation and Reaction Energies ===

Calculation regarding the activation energies and the reaction energies was done and recorded in Table.2 below. The energy of reactants, transition states, and products was extracted from their optimised structure using method described above. The reactants energies were calculated by summing the two individual reacts together, assuming that they are placed at infinite distances before the reaction occur and hence no interaction was made possible. To visualise the reaction better, a reaction coordinate was drawn below a well in Figure.6.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Energies of Reactants, Transition States and Products for Both Endothermic and Exothermic Pathways
|-
! rowspan="2" style="background: #4682B4; color: white;" | Pathway
! colspan="5" style="background: #4682B4; color: white;" | Energy / kJ mol<sup>-1</sup>
|-
! style="background: #4682B4; color: white;" | Reactants
! style="background: #4682B4; color: white;" | Transition States
! style="background: #4682B4; color: white;" | Products
! style="background: #4682B4; color: white;" | Activation Energy
! style="background: #4682B4; color: white;" | Reaction Energy
|-
! style="background: #4682B4; color: white;" | Endo
| -1313781.87
| -1313622.06
| -1313849.28
| 159.81
| -67.41
|-
! style="background: #4682B4; color: white;" | Exo
| -1313781.87
| -1313614.23
| -1313845.68
| 167.64
| -63.81
|}
|
|
|
|
| [[File:Tyy15 fg6 ex2 reaction coordinate.PNG|700px|centre|thumb|Figure 6: Reaction Coordinate of Reaction between Cyclohexadiene and 1,3-Dioxole]]
|}

For this Diels-Alder reaction, we would expect the endothermic product to the kinetic product. This is because transition state is stabilised by the p orbital overlap between the oxygen atoms on the 1,3-dioxole and the diene of cyclohexadiene. This is both supported by the Jmol files uploaded above and also the MO diagrams above. The endothermic pathway has a lower activation energy, hence it is classified as the kinetic product. For the exothermic reaction, no secondary orbital interaction is observed as the p orbital of the oxygen atoms are no longer below the diene p orbital. This means that the transition state cannot be stabilised. This effect is shown in Figure.7.

In a typical Diels-Alder reaction, the exothermic product is supposed to be the thermodynamic product as the endothermic product is susceptible to experience 1,3-diaxial interaction, which disfavours its formation. Placing the substituents on the equatorial position, such that in the exothermic product, should help to relieve the apparent repulsion experience in the endothermic product. However, the energy that was calculated suggests otherwise. The endothermic product is also the thermodynamic product as suggested by data as it as a lower reaction energy. This can be explained by the steric clash that might be experienced by the exothermic product, which the hydrogen on dioxole ring is sterically clashing with the bridging hydrogen as depicted in Figure.7. This destabilises the exothermic product and raises its energy. The endothermic product is therefore both the kinetic and thermodynamic product.

[[File:Tyy15 fg7 ex2 steric clash.PNG|700px|center|thumb|Figure 7: Secondary Orbital Effect in the Endothermic Transition State (LEFT) ; Steric Clash between hydrogen on dioxole ring and bridging hydrogen (RIGHT) ]]

== Exercise 3 ==

In this exercise, two kinds of reactions were probed by reacting O-xylylene and SO<sub>2</sub>. A hetero Diels-Alder reaction was examined to probe the endothermic and exothermic products. The other reaction that was probed was the cheletropic reaction. The reaction scheme is shown below in Figure.8. It can be seen that a Diels-Alder reaction will yield a 6-membered ring while a cheletropic reaction will yield a 5 membered ring. All the reactants, transition states, and products were optimised using the semi-empirical PM6 method. IRC calculations were conducted for all three transition states.

[[File:Tyy15 fg8 ex3 reaction scheme.PNG|700px|center|thumb|Figure 8: Reaction Scheme of Reaction between O-xylylene and SO<sub>2</sub>]]

=== IRC Calculations ===

Using IRC calculations, the total energy along the IRC can be measured, as well as visualising the reaction coordinate. This becomes helpful when we try to examine and analyse the transition states, as well as understanding the reaction trajectory. The calculations can be found in Table. 3 below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC Calculations and Total Energy along IRC for Different Pathways
! style="background: #4682B4; color: white;" | Pathway
! style="background: #4682B4; color: white;" | IRC
! style="background: #4682B4; color: white;" | Total Energy along IRC
|-
! Endothermic Diels-Alder Reaction
| [[File:Tyy15 Ex3 da endo IRC.gif |centre|500px]]
| [[File:Tyy15 ex3 da endo IRC.PNG|centre|500px]]
|-
! Exothermic Diels-Alder Reaction
| [[File:Tyy15 Ex3 da exo IRC.gif|centre|500px]]
| [[File:Tyy15 ex3 da exo IRC.PNG |centre|500px]]
|-
! Cheletropic Reaction
| [[File:Tyy15 Ex3 che IRC.gif|centre|500px]]
| [[File:Tyy15 ex3 che IRC.PNG |centre|500px]]
|}

=== Activation and Reaction Energies ===

Not only the IRC of the reaction was calculated, further investigation was done to examine the relative energies of the reactants, transition states and products. The data collected are represented below in Table.4. Same with exercise 2, the reactants were the sum of individual energy of O-xylylene and SO2. Assumptions were again made such that we assume the two reactants were placed at an infinite distance apart so that there will not be any interaction between the two molecules. A reaction coordinate diagram, Figure 9 was also produced to accompany the data collected from Table.4.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #4682B4; color: white;" | Pathway
! colspan="5" style="background: #4682B4; color: white;" | Energy / kJ mol<sup>-1</sup>
|-
! style="background: #4682B4; color: white;" | Reactants
! style="background: #4682B4; color: white;" | Transition States
! style="background: #4682B4; color: white;" | Products
! style="background: #4682B4; color: white;" | Activation Energy
! style="background: #4682B4; color: white;" | Reaction Energy
|-
! style="background: #4682B4; color: white;" | Endo Diels-Alder
| 158
| 238
| 57.0
| 79.8
| -101
|-
! style="background: #4682B4; color: white;" | Exo Diels-Alder
| 158
| 242
| 56.3
| 83.8
| -102
|-
! style="background: #4682B4; color: white;" | Cheletropic
| 158
| 260
| 0.00
| 102
| -158
|}
|
|
|
|
| [[File:Tyy15 fg9 ex3 reaction coordinate.PNG |700px|centre|thumb|Figure 9: Reaction Coordinate on Reaction between O-xylylene and SO<sub>2</sub>]]
|}

(Your reactants energy is too high and if you had included the log files I would have been able to see why [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:35, 7 March 2018 (UTC))

Each of the reaction is colour-coded and their activation energy and reaction energy are shown in the diagram. As depicted in Figure.9, we can see that despite having the highest activation energy, the cheletropic reaction forms that most stable product and it is thermodynamically favoured. This can be due to the fact that the two strong S=O bonds are retained, as well as the formation of the aromatic ring on the other side. Conversely, the Diels-Alder reactions have lower activation energies. Amongst which, the endothermic transition state has a lower activation energy than the exothermic transition state. This can be explained using the same principle as described above, in which secondary orbital interaction has played a role in stabilising the transition state of the endothermic product, giving it the kinetic product amongst those three reactions. The reaction energy for both the exothermic and endothermic reaction is quite similar, with the exothermic product being slightly more stable. This might be due to the steric clash experience between the oxygen on S=O and the H atoms on the 6-membered ring.

=== Discussion: Possible Side Reaction between o-xylylene &SO<sub>2 </sub> - Internal Diels-Alder Reaction ===

By closely examining our reactants, we can also observe that there are two cis-butadiene presents in the molecule. The above discussion mainly dealt with the reaction between the terminal diene and SO2. Here, we discuss the possibility of an internal Diels-Alder Reaction, where the cis-butadiene in the close 6-membered ring reacts with SO<sub>2</sub>. The reaction scheme of this reaction is found below in Figure.10. These reactions are stimulated using Gaussian and the structures for the transition states and products are optimised using the semi-empirical PM6 method.

[[File:Tyy15 fg10 ex3 reaction scheme internal.PNG |700px|center|thumb|Figure 10: Reaction Scheme for Internal Diels-Alder Reaction]]

Same with the reactions above, the activation energies and reaction energies of the two internal Diels-Alder product: Endothermic and Exothermic, are calculated and tabulated in the Table.5 below. The reaction coordinate of this reaction is also drawn alongside with the original Diels-Alder reaction for ease of comparison. The reaction coordinate of this internal Diels-Alder reaction is presented in Figure.11 below.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: Energies of Reactants, Transition States and Products for Internal Diels-Alder Reactions
|-
! rowspan="2" style="background: #4682B4; color: white;" | Pathway
! colspan="5" style="background: #4682B4; color: white;" | Energy / kJ mol<sup>-1</sup>
|-
! style="background: #4682B4; color: white;" | Reactants
! style="background: #4682B4; color: white;" | Transition States
! style="background: #4682B4; color: white;" | Products
! style="background: #4682B4; color: white;" | Activation Energy
! style="background: #4682B4; color: white;" | Reaction Energy
|-
! style="background: #4682B4; color: white;" | Endo Diels-Alder
| 158
| 268
| 172
| 110
| 14.3
|-
! style="background: #4682B4; color: white;" | Exo Diels-Alder
| 158
| 276
| 177
| 118
| 18.8
|}
|
|
|
|
| [[File:Tyy15 fg11 ex3 reaction coordinate internal da.PNG |700px|centre|thumb|Figure 11: Reaction Coordinate of Terminal and Internal Diels-Alder Reaction ]]
|}

As we can see from the calculations for both the activation energy and reaction energy, both the internal Diels-Alder reaction are kinetically unfavourable as well as thermodynamically unfavourable. The internal Diels-Alder reactions have higher activation energy as compared to the original Diels-Alder reaction. Following the same reason as above, the endothermic reaction has a lower activation energy than exothermic reaction due to the secondary orbital stabilisation of the endothermic transition state. This internal Diels Alder reaction is unfavourable since there is a larger change in structure as compared to the original terminal Diels-Alder Reaction. The cyclohexadiene ring has to change from its planar geometry to a chair/ boat confirmation, which is indicated by the change from largely sp2 hybridised C-C bond in reactants to sp3 hybridised C-C bond in the product.

IRC calculations were also conducted and can be found below on Table.7

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Internal Diels-Alder Reaction
! style="background: #4682B4; color: white;" | Pathway
! style="background: #4682B4; color: white;" | IRC
! style="background: #4682B4; color: white;" | Total Energy along IRC
|-
! Endothermic Diels-Alder Reaction
| [[File:Tyy15 Ex3 int da endo IRC.gif |centre|500px]]
| [[File:Tyy15 ex3 int da endo IRC.PNG|centre|500px]]
|-
! Exothermic Diels-Alder Reaction
| [[File:Tyy15 Ex3 int da exo IRC.gif|centre|500px]]
| [[File:Tyy15 ex3 int da exo IRC.png |centre|500px]]
|}

=== Discussion : Possible Side Reaction of o-xylylene - Electrocyclic Reaction ===

Other possible side reaction also includes an electrocyclic reaction of the xylylene itself, which forms benzocyclobutane. The reaction scheme is found in Figure.12 below.

[[File:Tyy15 fg12 ex3 reaction scheme electrocyclic.PNG|400px|center|thumb|Figure 12: Electrocyclic Reaction of o-Xylylene]]

If such reaction was to occur, it would result in the formation of an aromatic ring, which is thermodynamically favourable, and also the formation of a 4 membered ring. The electrocyclic reaction would undergo a conrotation reaction, as suggested by the HOMO of xylylene as depicted below in Figure.13. In order for the two terminal alkenes to interact and form a sigma bond, a conrotation reaction must happen.

[[File:Tyy15 fg15 ex3 Electrocyclic HOMO.png|400px|center|thumb|Figure 13: HOMO of xylylene ]]

However, such formation is not observed when we optimise xylylene. The optimised structure remains as xylylene instead of forming benzocyclobutane. This means that even though the structure is thermodynamically stabilised, it is not kinetically favoured. This must imply that energy gained from the formation of the aromatic ring is not enough to overcome the activation barrier it has for such electrocyclic reaction to occur. One possible explanation is that the formation of the 4-membered cyclobutane is energetically more costly than the energy released from bond formation. Ring strain is present in the 4 membered ring, which the 90<sup>o</sup> bond angle has caused energy penalty for sp3 hybridised carbon which prefers 109.5<sup>o</sup>. This electrocyclic reaction obeys the Woodward Hoffmann where there are 4n π electrons and n=1. This suggests that the reaction is conrotatory and also thermally allowed.

(No this isn't true. Optimisations will bring you to a local minimum. benzocyclobutane is in another part of the PES. If you start near benzocyclobutane then you can minimise to it. What you are thinking about is a barrierless reaction which is an intrinsic instability. The TS that links them is fairly straightforward to find using the methods we've provided [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:35, 7 March 2018 (UTC))

== Conclusion ==

All in all, the exercises that we have conducted have helped us to explore Diels-Alder reaction between different substrates. Three kinds of Diels-Alder reaction were stimulated and analysed using Gaussview: standard Diels-Alder reaction, Inverse electron demand Diels-Alder reaction, and heteroatom-substituted Diels-Alder reaction. All three reactions are either optimised using the semi-empirical PM6 method or Density Functional Theory method to B3LYP/6-31G(d) level.

In Exercise 1, we have conducted the standard Diels-Alder reaction, which we analysed the molecular orbitals of the transition state and reactants. We have also conducted a bond length analysis to find that our calculated values agree closely with the literature values. A vibrational analysis was done and confirmed that the transition state of our reaction was correctly located, as it contains only one imaginary frequency.

In Exercise 2, we have conducted an inverse electron demand Diels-Alder reaction. As the dienophile is no longer ethylene, we can stimulate the reaction to probe the formation of both endothermic and exothermic products. Molecular orbital diagram for both of the endothermic and exothermic transition states was drawn and compared. It is found, by running single point energy calculation, that the HOMO-LUMO gap for endothermic transition state is bigger than that of the exothermic transition state. Activation energy and reaction energy was also calculated for the reactions and was found that the endothermic pathway is both the kinetic and thermodynamic product. This can be explained by the secondary orbital interaction effect that stabilises the endothermic transition state, as well as the steric clash that the exothermic product which destabilises the product.

In Exercise 3, a heteroatom-substituted Diels-Alder reaction is conducted. In this case, not only the Diels-Alder reaction is present, the cheletropic reaction between the SO<sub>2</sub> fragment and xylylene can also be calculated. IRC calculations have helped us to visualise the reaction progress between the different reactions and aid us to understand the reaction trajectory. Activation energy and reaction energy was also tabulated for these reactions and being compared to each other. The cheletropic pathway is found to be the thermodynamically preferred pathway, while the endothermic Diels-Alder reaction pathway has yield the kinetic product. Other possible reacts, such as the internal Diels-Alder reaction and the electrocyclic reaction are also calculated and compared against the normal reactions. These reactions are found to have higher activation energy or are thermodynamically not favourable hence they are not competing process of the reaction.

== References ==

Rep:LH3115TSS

2018-03-06T15:13:25Z

Tam10: /* Exercise 3 */

==Transition State Structures==
===Introduction===

Gaussian basis functions have been used to calculate wavefunctions for a long time, like Hartree-Fock functions. The Hartree-Fock method uses a series of approximations to solve the time ondependent Schrödinger Equation and because Molecular Orbitals are linear combinations of atomic orbitals, this involves solving matrices. However due to the time-consuming nature of these calculations, reducing the number of iterations becomes necessary for big systems<ref name="1970one" />. In this experiment two methods have been used to calculate the Molecular Orbitals of 3 different reactions. The first used is a semi empirical method called PM6 (Parameterization Method 6), is a relatively quick method that doesn’t calculate all the values of the matrices to evaluate the MO, instead it uses empirical values <ref name="PM6" />. The other one is under DFT (Density Functional Theory) methods called B3LYP method, which is a hybrid function that uses both Hatree-Fock and DFT methods. The 6-31G basis set was used for all B3LYP calculations in this experiment <ref name="DFT" />.

In this experiment 3 reactions were investigated, each with its different Transition State to result in different products. In a 3 dimensional molecule there are 3N-6 (N = number of atoms in molecule)degrees of freedom for vibrations. The TS is located by calculating the second derivative at a particular vibration. The TS will be at the saddle point, which will have one negative second derivative frequency as a saddle point has a first derivative equal to 0 in one direction (vibrations in this case) and a negative second in the same direction, all other directions would increase the energy of the reaction at that point. All minimum points (Reactants and Products)have no negative frequencys as the second derivative at a minimum is positive in all directions.

===Exercise 1===
====Diels-Alder reaction====
[[File:DA_reaction_profile_LH3115.PNG|400px|thumb|center|Figure 1:Reaction scheme of the Diels-Alder reaction of Ethene and Butadiene.]]

The Reactant, Product and Transition State structures of the [4+2] cycloaddition shown in figure 1 were calculated using the PM6 method. According to the calulations the Ethene approaches the Butadiene from below or above resulting in a stacked TS.

====Molecular Orbitals====
[[File:MO_diagram_LH3115.PNG|400px|thumb|center|Figure 2:MO Diagram of the Diels-Alder reaction of Ethene and Butadiene.]]

In the MO diagram in figure 2 one can see the relative different Energie-levels which correspond to the energies calculated from Gaussview 5.0. In the MO diagram one can see that only orbitals interact that have the same symmetry, so it can be concluded that a reaction is only allowed if orbitals of the same symmetry can interact. The orbitals overlap is zero for all antisymmetric-symmetric interactions and non-zero for all interaction of antisymmetric-antisymmetric and symmetric-symmetric interactions. Note that reactant orbitals that are closer in energy to the TS state orbitals contribute more to the bonding which is illustrated in the MO diagram.
<br>

====J mol files====

The following link is to the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=LH3115TSS_ex1jmol Jmols of the Reactant MOs and Transition state MOs] seen in figure 2.
====C - C bond lengths====

[[File:C_Ctable_ex1_LH3115.PNG|1000px|thumb|left|Table 1:Table of the different bond lengths and types of the Reactant, Product and Transition State structures.]]
[[File:C_Ctable_lit_table_LH3115.PNG|1000px|thumb|right|Table 2:Table of the typical bond lengths found in literature <ref name="cclengths" />.]]
[[File:C_Ctable_lit_hex_table_LH3115.PNG|1000px|thumb|Table 3:Table of the bond lengths of cyclohexene found in literature <ref name="cclengthshexene" />.]]

The distances in table 1 correspond to the results obtained from the optimizations using the PM6 method while table 2 gives the typical bond lengths found in literature.

During the reaction the 3 C-C double bonds break to form 2 new single bonds, connecting the Ethene and the Butadiene and creates a new double bond.
Due to the change in bonding and hybridization of the C atoms all of the bond lengths change. All of the single bonds of the products are within 0.01 Å of the typical single bond lengths for all the different hybridizations present, while the double bond in the product is off by 0.015 Å. However the literature values for the bond lengths in cyclohexene show that the calculated values are almost identical with data from literature seen in table 3.<ref name="cclengthshexene" />This suggests that the difference in bond lengths from the typical values is due to the structural strain of the ring and and not due to the accuracy of the method used. Given the accuracy of the values obtained from the PM6 method, any further optimization with the B3LYP method is not necessary.

For the reactants the bond lengths are within 0.015 Å of the typical values in table 2. In this case the differences seem to be due to the method used and a optimization with the B3LYP would most likely result in more accurate bond lengths. However the obtained values are still very close to the typical values.

The Bond lengths of the Transition state reflect the stage at which the reaction is very well as the newly formed single bond of C2-C3 and C6-C1 are the longest as they being newly formed. These are the only once that have a bond length larger than that of the Van der Walls radius of carbon seen in table 2. However the length is less than twice the VDW radius of C, which means that there is a orbital interaction between the atoms.
All other Transition bonds have distance more similar to the reactant distances with fits with Hammond's postulate , which states that the Transition State is closest in structure to the structure that it is closest in energy to. As this reaction is endothermic, the reactants total energie are closer in energy to the transition state.

Figure 3 visualizes how bond lengths are changing in the course of the reaction compared to each other.

[[File:C-Cbond_lengthovertime_LH3115.png|700px|thumb|center|Figure 3:C-C bond lengths over the course of the reaction obtained from IRC run using method PM6.]]

==== Reaction ====
[[File:IRCfileex1mov_LH3115.gif|400px|thumb|center|GIF 1:IRC of the Diels-Alder reaction of Ethene and Butadiene.]]

[[File:TSvibex1_LH3115.gif|400px|thumb|center|GIF 2:Vibration at the Transition State of the Diels-Alder reaction of Ethene and Butadiene.]]

Gif 2 shows that the formation of the two bonds is synchronous as both bonds form in the same moment. This corresponds to theory as literature says that the Diels-Alder reaction proceeds via a concerted mechanism, which makes our simulation accurate.

====Files====
[[File:Product_ex1_LH3115.LOG]]
[[File:EX1_IRC_LH3115.LOG]]

===Exercise 2===

====Reaction Scheme====

[[File:Reacschemeex2_LH3115.PNG|800px|thumb|center|Figure 4: Reaction scheme of the Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxol.]]

The reaction of 1,3-Dioxol and Cyclohexadiene gives two stereoisomers due to the dieneophiles substituent, an Endo and an Exo product. The Endo product is formed when the substituent of the dienophile is oriented towards the diene, while in the Exo product in orients away from the diene. This is illustrated in figure 4 in the Transition States, note that in this case it doesn't matter whether the dieneophile approaches from the top or from the bottom.

====MO Diagrams====

Figures 5 and 6 below show the MO diagram of the TS state energies of the Endo and Exo Products. The [https://wiki.ch.ic.ac.uk/wiki/index.php?title=LH3115TSS_ex2jmol Jmol files] for the optimized Reactants, Products and Transition States are here. All the structures were initially calculated using the PM6 method and then were further optimized using B3LYP.

Both MO diagrams were drawn with the relative size of the contributing orbitals in mind, like in exercise 1, therefore some orbitals are bigger depending on how close in Energy the relevant reactant MO is to the Transition State MO.

The Diels-Alder reaction has an inverse electron demand as the HOMO of the Dienophile and the LUMO of the Diene are closer in energy than the LUMO of the Dienophile and the HOMO of the Diene. This is because the 1,3-Dioxole is particularly electron rich, due to the electron donating oxygen, which increases the energy of it's HOMO and LUMO. However the LUMO<sub>dienophile</sub> and HOMO<sub>diene</sub> in this reaction result in a lower energy bonding orbital for the Transition State, which is unusual as the closer energy levels are the greater the energy splitting usually. This suggests that the orbital overlap is smaller, or other orbitals contribute to the overall bonding of this orbital.

{|
|[[File:MOex2_endo_LH3115.PNG|800px|thumb|Figure 5: MO diagram of the Endo-Product Transition State.]]

|[[File:MOex2exon_LH3115.PNG|800px|thumb|Figure 6: MO diagram of the Exo-Product Transition State.]]
|}

====Kinetic and Thermodynamic product====

[[File:Reaction_profile_ex2_LH3115.PNG|800px|center|thumb|Figure 7: Reaction profile of the Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxol.]]
[[File:Energytableex2_LH3115.PNG|800px|center|thumb|Table 4: Energies of the Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxol.]]

[[File:OrbitalOverlap_LH3115.PNG|800px|right|thumb|Figure 8: Orbital overlap of the Endo Transition State]]

The energies of the reaction are shown in table 4, with the activation and reaction energies visualized in a reaction profile in figure 7. In the reaction profile the Endo product is both kinetically and thermodynamically more favorable as the TS energy and Product energy is lower than those of the Exo reaction. That means that it is kinetic product has it can traverse the TS faster, as it is lower energie and it is the thermodynamic product as it is at lower energy.

The reason for the stability of the Endo product is the orbital interaction illustrated in figure 8, where the orbitals on the Oxygen atoms interact with the pi system of the diene ring resulting in increased stability of the Transition State. A similar interaction is also present in the product where the \pi orbitals interact with the orbitals on the Oxygen atoms, however due to a greater distance between these two there is less orbital overlab thus the difference in reaction energies is less than the difference in activation energies. This is called the Endo rule and due to the similarity of the 2 structures this is most likely the major effect on the energies of the system. Steric effects seem to have little impact as the angle between the dioxol and the ring in the Exo product (113.895 <sup>o</sup>) is very similar to the angle of the dioxol and the ring in the Endo structure (113.751 <sup>o</sup>).

====Files====

[[File:EX2_EXO_IRC_LH3115.LOG]]
[[File:EX2_ENDO_IRC_LH3115.LOG]]

===Exercise 3===

====Reaction Scheme====

[[File:Reaction_scheme_ex3_LH3115.PNG|600px|thumb|center|Figure 8: Reaction Scheme of the Diels-Alder and Cheletropic reaction of SO<sub>2</sub> and o-xylylene external diene.]]

The reaction of the external diene of o-xylylene with SO<sub>2</sub> is shown in figure 9, with both mechanisms. All of the possible reactions were calculated by IRC with the PM6 method and are shown in the Gifs 3 to 5.

As seen in the reaction scheme and the GIF files, in the Diels Alder reaction only the orientation of the molecules is important but not whether they approach from the top or the bottom. In the Cheletropic mechanism it is the same. Note that the SO<sub>2</sub> approaches at an angle not from the side, in order to maximize orbital overlap with the π* of the diene.

{|
|[[File:CHELEMOVIE_LH3115.gif|400px|thumb|center|GIF 3:IRC of the Cheletropic reaction of SO<sub>2</sub> and o-xylylene external diene forming the Cheletropic product.]]
|[[File:ENDOMOVIEEX3_LH3115.gif|400px|thumb|center|GIF 4:IRC of the Diels-Alder reaction of SO<sub>2</sub> and o-xylylene external diene forming the ENDO product.]]
|[[File:EXOOMOVIEEX3_LH3115.gif|400px|thumb|center|GIF 5:IRC of the Diels-Alder reaction of SO<sub>2</sub> and o-xylylene external diene forming the EXO product.]]
|}

====Energies of the Reactions====

[[File:Reacprofnotint3_LH3115.PNG|800px|thumb|center|Figure 9: Reaction profile of the Diels-Alder reaction of SO<sub>2</sub> and o-xylylene external diene.]]

(It's quite hard to read bright green on white! [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:13, 6 March 2018 (UTC))

[[File:Energytableex3_outside_LH3115.PNG|800px|center|thumb|Table 5: Energies of the Diels-Alder reaction of SO<sub>2</sub> and o-xylylene external diene.]]

The energies of the reactants and products are shown in Table 5, with the reaction profile being in figure 9. In the plot one can see that the thermodynamically preferred pathways are inverse to the kinetic ones. As the thermodynamic product is the cheletropic one, however it has the highest energy TS, while the Endo product of the Diels-Alder reaction is the kinetic product as it has the lowest TS energy but conversely has the highest final energy.

The difference in TS energies of the two Diels Alder pathways is likely due to the before mentioned (Exercise 2) orbital overlap of the oxygen substituent with the diene π orbitals.
The cheletropic pathway has no π orbitals interacting instead uses the orbitals on sulfur to the reaction which leads to a higher energy TS.

The products itself are all favorable, because of the formation of the aromatic ring which is a lot more stable than normal conjugated systems.

The cheletropic product is most likely more stable for steric reasons as the sulfur atom is much larger than a C atom, which makes a five membered ring with sulfur more stable than a six membered ring with oxygen and sulfur resulting in more strain. In the IRC files in Gifs 1 to 3 it can be seen that the final products of the Diels Alder reactions are non planar with sulfur sticking out, while the cheletropic product is planar. Orbitals have an impact on the energy too as the cheletropic product uses different orbitals to bond to the C atoms than the Diels Alder ones.

The very small difference in energy of the two DA products is most likely a result of steric strain of the oxygen with the aromatic ring in the Endo product.

====Internal Ring Reaction====
[[File:Reactprofint_LH3115.PNG|800px|thumb|center|Figure 10: Reaction profile of the Diels-Alder and Cheletropic reaction of SO<sub>2</sub> and o-xylylene internal diene.]]
[[File:Energytableex3_inside_LH3115.PNG|800px|center|thumb|Table 6: Energies of the Diels-Alder reaction of SO<sub>2</sub> and o-xylylene internal diene.]]

The reaction can theoretically also proceed with the diene within the ring of o-xylylene, however as shown in figure 10, all products of this reaction would be higher in energy than the reactants. This is because there would be no aromatic ring formation like in the reaction with the external diene. There would also be additional steric strain within the products, seen in the GIF files 6 to 8.

The reaction profile shows the big effect sterics have on this system as cheletropic product has by far the highest energy, most likely because it forms a five membered ring to the strained system while the DA products from a more open cage structure.

So in this case it would be more favorable to stay reactants at infinite seperation.

Note that the Endo product is both the thermodynamic and the Kinetic product in this reaction.

{|
|[[File:INTCHELEMOVIE_LH3115.gif|400px|thumb|center|GIF 6:IRC of the Diels-Alder reaction of SO<sub>2</sub> and o-xylylene internal diene forming the Cheletropic product.]]
|[[File:INTENDOMOVIEEX3_LH3115.gif|400px|thumb|center|GIF 7:IRC of the Diels-Alder reaction of SO<sub>2</sub> and o-xylylene internal diene forming the ENDO product.]]
|[[File:INTEXOOMOVIEEX3_LH3115.gif|400px|thumb|center|GIF 8:IRC of the Diels-Alder reaction of SO<sub>2</sub> and o-xylylene internal diene forming the EXO product.]]
|}

====Files====

[[File:EX3_XYLYLENE_LH3115.LOG]]
[[File:EX3_SO2_LH3115.LOG]]
[[File:EX3_EXO_PRODUCT_LH3115.LOG]]
[[File:EX3_EXO_TS_LH3115.LOG]]
[[File:EX3_EXO_IRC_LH3115.LOG]]
[[File:EX3_ENDO_LH3115.LOG]]
[[File:EX3_ENDO_IRC_LH3115.LOG]]
[[File:EX3_ENDO_TS_LH3115.LOG]]
[[File:EX3_CHELE_Product_LH3115.LOG]]
[[File:EX3_CHELE_IRC_LH3115.LOG]]
[[File:EXOINT_TS_LH3115.LOG]]
[[File:EXOINT_Product_LH3115.LOG]]
[[File:EXOINT_IRC_LH3115.LOG]]
[[File:ENDOINT_TS_LH3115.LOG]]
[[File:ENDOINT_Product_LH3115.LOG]]
[[File:ENDOINT_IRC_LH3115.LOG]]
[[File:CHELEINT_IRC_LH3115.LOG]]
[[File:CHELEINT_TS_LH3115.LOG]]
[[File:CHELEINT_Product_LH3115.LOG]]

===Conclusion===

The calculations run in this lab confirm the mechanisms of the Diels-Alder reaction and their predicted Transition States.

Gaussian optimizations prove a useful way analyzing molecules and predicting outcomes of reactions. It seems very useful in identifying which molecules are more the Thermodynamic and Kinetic products, enabling chemists to adapt their reaction conditions to obtain the highest yield possible. It is also a useful first step in determining whether or not a structure is energetically feasible or favorable and giving answers to why some structures are not forming. It also shows potential side products and different reaction paths, confirms mechanisms and product structures.
The MO orbitals calculated and visualized give a much better understanding in the bonding involved and how the molecule is stabilized as the calculations take into account multiple neighbour interactions.

The lab also shows the different inaccuracies of the different calculation types.

However in order for the optimizations to work, knowledge of the mechanism and the Transition State is required, especially for systems with many degrees of freedom. Given the computational costs of some calculations it is not the best way to determine the TS of a reaction.

===references===
<references>

<ref name="1970one">
T. H. Dunning Jr, J. Chem. Phys., 1970, 53, 2823-2833.
</ref>

<ref name="PM6">
Gaussian: Semi-Empirical Methods: http://gaussian.com/semiempirical/
</ref>

<ref name="DFT">
Gaussian: Density Functional (DFT) Methods: http://gaussian.com/dft/
</ref>

<ref name="cclengths">
Handbook of Chemistry & Physics (65th ed.). CRC Press. ISBN 0-8493-0465-2..
</ref>

<ref name="cclengthshexene">
J. F. Chiang and S. H. Bauer, J. Am. Chem. Soc., 1969, 91, 1898-1901.
</ref>

</references>

Rep:TSvl915

2018-03-06T12:14:14Z

Tam10: /* Ring opening of 2,3 dimethylaziridine */

== Introduction==
Chemical processes are often described in terms of the properties of their reactants, their products and their transition structures.<ref>J. J. W. Mcdouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, 2013.</ref>. Many of these properties can be obtained if the potential energy surface of the chemical system is known. The potential energy of a system depends on 3N-6 coordinates where N is the total number of atoms in the system. Product and reactant structures are located in local minima of the potential energy surface. Local minima are a special type of stationary points in which all coordinates lie at a minimum. Transition states are also a special type of stationary points in which all coordinates lie at a minimum except one which lies at a maximum. This can also be expressed using the two equations below:
[[File: Equationsvl915.PNG|800px|thumb|center|]]
where '''R''' refers to a set of coordinates and R<sub>i</sub> is the ith coordinate in that set. Every type of stationary point fulfills euqation (1). Local minima have only positive matrix elements in the matrix of second order derivatives H (also called the Hessian matrix, equation 2) whereas transition states have one single negative matrix element<ref>D. J. Wales, in Energy Landscapes, Cambridge University Press, 2013.</ref>. If a stationary point has has more than one negative matrix element it is not a transition structure as this means that it is a maximum in more than one coordinate and that there must be a lower energy pathway between the reactant and product potential energy wells. This reasoning is called the Murrell-Laidler theorem <ref>D. J. Wales, in Energy Landscapes, Cambridge University Press, 2013.</ref> and is illustrated in fig.1 :
[[File:PESfinalvl915.PNG|800px|thumb|center|Fig.1: PES illustrating the Murrell Laidler theorem and showing a transition state as well as a local minimum and a local maximum.]]
The matrix elements and the vibrational frequencies of structures are related such that correct transition state structures have one negative frequency only whereas correct minimum structures have only positive frequencies if this is not the case the structures are probably wrong.

Based on these concepts specialised software such as Gaussian can be used to model and to explore potential energy surfaces <ref>Gaussian.com, http://gaussian.com/, (accessed 27 February 2018).</ref>. In this experiment Gaussian was used to investigate three different Diels Alder reactions and a cheleotropic reaction. This included determining their transition state structures, the accurate product and reactant structures, visualising Molecular orbitals (MOs)and nuclear vibrations as well as calculating reaction energies and activation barriers. Furthermore the IRC of the reactions was determined and different bond lengths were tracked throughout the modeled reactions. For this two computational methods were used with Gaussian. The first one was PM6 a semi empirical method based on Hartree Fock theory<ref>J. J. P. Stewart, J. Mol. Model., 2007, 13, 1173–1213.</ref>. This method makes many approximations and some of its more complex terms are obtained from empirical data. It has the advantage being a relatively fast and inexpensive method but its results are unreliable as the empirical reference data may be inadequate and the assumptions made may be too inflexible<ref>J. J. P. Stewart, J. Mol. Model., 2007, 13, 1173–1213.</ref>. The other method is B3LYP/6-31G(d)) which is a density functional theory (DFT) method. These methods aim to deal with the one-electron density rather than the many-electron wavefunction which allows much less demanding computations when solving Schrödinger's equation <ref>J. J. W. Mcdouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, 2013.</ref>. B3LYP/6-31G(d))uses a basis set of s and p+d orbitals yet it is not a pure DFT method as Hartree Fock calculations are used to account for exchange correlation. B3LYP/6-31G(d)is is more expensive than PM6 and takes longer but it is also more accurate.

== Exerciese 1: Diels Alder Reaction between Ethene and Butadiene ==

=== Overview ===

[[File:Chem Draw schemevl915.png|400px|thumb|center|Fig.2: Reaction scheme showing the ethene/butadiene Diels Alder reaction (with a transition state in the middle)]]

In this exercise the Diels Alder reaction, which is a [4+2] cycloaddition, between butadiene and ethene was investigated (fig.2).

The method used was the following: Butadiene and ethene were optimised separately to a minimum at the PM6 level. To verify that the obtained minimum structures were correct it was made sure that they were converged and that they had no negative vibrations. Subsequently the transition state structure was obtained at the PM6 level using the two otpimised reactant structures. To verify that the transition state structure was correct, it was made sure that it was converged and that it had one negative vibration. An IRC was calculated from the transition state structure at the PM6 level. Finally, the product structure (cyclohexene) was obtained from the IRC and was optimised to a minimum at the PM6 level.

=== Transition State Analysis ===
[[File:MO diagram exercise 1bla.png|400px|thumb|center|Fig.3: MO diagram of the transition state of the butadiene/ethene Diels Alder reaction]]

<center>
{| class="wikitable"
!<jmol><jmolApplet><uploadedFileContents>BUTADIENE_PM_6.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>BUTADIENE_PM_6.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|-
|Butadiene HOMO
|Butadiene LUMO
|} </center>

<center>
{| class="wikitable"
!<jmol><jmolApplet><uploadedFileContents>ETHENE_GOOD_MINIMUM.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.10; mo 6; mo nodots nomesh fill translucent; mo titleformat "", rotate x 45</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>ETHENE_GOOD_MINIMUM.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.10; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|-
|Ethene HOMO
|Ethene LUMO
|} </center>
<center>
{| class="wikitable"
!<jmol><jmolApplet><uploadedFileContents>TRANSITION_STATE_GOOD_exercise1.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TRANSITION_STATE_GOOD_exercise1.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TRANSITION_STATE_GOOD_exercise1.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TRANSITION_STATE_GOOD_exercise1.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|-
|TS HOMO-1
|TS HOMO
|TS LUMO
|TS LUMO+1
|} </center>

From the transition state MOs shown above and from the transition state MO diagram (fig.3) it can be seen that MOs only interact if they are of the same symmetry (i.e. symmetric MOs interact only with symmetric MOs and not with antisymmetric ones). This implies that for a Diels Alder reaction to be 'allowed' the interacting MOs (i.e. the HOMO and the LUMO of the respective reactants) must be of the same symmetry. Conversely, if the HOMO of one reactant and the LUMO of the other reactant are of opposing symmetry the reaction does not occur.

This can be explained considering the overlap integral of the interacting orbitals. For symmetric-symmetric or antisymmetric-antisymmetric interactions the orbital overlap is non-zero as there are either in-phase or out of phase interactions so that net bonding or net antibonding MOs are generated. Meanwhile, for antisymmetric-symmetric interactions, the overlap integral is zero as the out of phase and in-phase interactions cancel out.

=== C-C bond length analysis ===

<center>
{| class="wikitable"
![[File:Bond movie.gif|400px|thumb|left|Fig.4: Animation of the butadiene/ ethene Diels-Alder reaction]]
![[File:Bond_lengths1.png|600px|thumb|left|Fig.5: C-C bond lengths plotted against the IRC starting from the adduct and progressing to the reactants of the Diels-Alder reaction]]
|} </center>

<center>
{| class="wikitable"
!Structure
!C1-C11/ Å
!C1-C4/ Å
!C4-C6/ Å
!C6-C7/ Å
!C7-C14/ Å
!C11-C14/ Å
|-
|Butadiene
|<nowiki>-</nowiki>
|1.34
|1.47
|1.34
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|-
|Ethene
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|1.34
|-
|Trasntion State Struture
|2.10
|1.38
|1.41
|1.38
|2.10
|1.38
|-
|Cyclohexene
|1.54
|1.50
|1.34
|1.50
|1.54
|1.54
|} </center>

In a Diels-Alder reaction (animated in fig.4), two new C-C sigma bonds are formed (C1-C11, C7-C14), three C=C pi bonds lengthen to become C-C sigma bonds (C11-C14, C1-C4, C6-C7) and one C-C sigma bond (C4-C6) shortens to become a pi bond. This is reflected in fig.5 where all C-C bond lengths are plotted against the intrinsic reaction coordinate (starting from the product and progressing towards the reactants).

In butadiene the C=C bond lengths (C1-C4 and C6-C7, see table) are very close to the standard C=C pi bond length (1.34 Å<ref>A. Bondi, J. Phys. Chem., 1964, 16, 1171–1223</ref>). Meanwhile, the C-C bond (C4-C6) is shorter than a typical C-C sigma bond (1.54 Å <ref>A. Bondi, J. Phys. Chem., 1964, 16, 1171–1223</ref>) which can be attributed to the effects of conjugation.

In the transition state structure the C1-C4 and C6-C7 bond lengths are lengthened compared to the bond lengths in butadiene whereas the C4-C6 bond length is shortened. The C11-C14 bond length is slightly lengthened compared to the bond length in ethene. The C1-C11 and the C7-C14 bond length is 2.1 Å which is less than the sum of two carbon van der Waals radii (3.4 Å <ref>A. Bondi, J. Phys. Chem., 1964, 16, 1171–1223</ref>) suggesting that there is some interaction between these carbon atoms.

In the product (cyclohexene) structure the C1-C4 and C6-C7 bond lengths are slightly shorter than the standard C-C bond length (where two sp<sup>3</sup> orbitals overlap) which can be attributed to an increased s character in these bonds as they can be seen as an overlap between a sp<sup>2</sup> and a sp<sup>3</sup> orbital.

=== Transitions State Vibration ===

<center>
{| class="wikitable"
![[File:TSvibrationvl915.gif|400px|thumb|center|Fig.6a: Animation of the complex vibration in the transition state for the ethene/ butadiene Diels Alder reaction]]
![[File:TSvibrationvl915.gif|400px|thumb|center|Fig.6b: Animation of the ethene/ butadiene Diels-Alder reaction]]
|} </center>

Diels-Alder reactions are known to occur via a concerted mechanism. This is underpinned by the negative vibration (animated above in fig.6a) which suggests a synchronous C-C bond formation. Figure 6b shows an animation of the whole reaction.

===Files===
IRC:[[File:IRC1vl915.LOG]]

==Exercise 2: Diels Alder reaction between Cyclohexadiene and 1,3-Dioxole ==
===Overview===

[[File:Reactionschemevl915.png|400px|thumb|center|Fig.7: Overview of the reactions investigated in exercise 2]]
In this exercise the Diels Alder reaction between cyclohexadiene and 1,3 dioxole was investigated (fig.7). In this case two different outcomes are possible, the endo and the exo product.

The method used was the following: The product (either exo or endo) was optimised to a minimum first at the PM6 level then this structure was used to find a minimum structure at the B3LYP/6-31G(d) level. To test whether a correct minimum structure was obtained in each step it was made sure that the structures were converged and that they had only positive vibrations. The optimised product structure was then used to find a transition state structure first at the PM6 level, then the PM6 structure was used to find a transition structure at the B3LYP/6-31G(d) level. To test whether a correct transition state structure was obtained in each step it was made sure that the structures were converged and that they had one negative vibration. An IRC was obtained at the PM6 level from the PM6 transition state. The reactant structures were obtained from the IRC and were optimised to a minimum separately at the B3LYP/6-31G(d) level.

===Analysis of the MOS===

<center>
{| class="wikitable"
![[File: MOdiagramendofinalvl915.png|400px|thumb|center|Fig.8a: This figure shows the MO diagram of the endo transitions state for the inverse electron-demand Dielse-Alder reaction between hexadiene and 1,3 dioxole. Energies are given in hartrees.]]
![[File:MOdiagramexofinalvl915.png|400px|thumb|center|Fig.8b: This figure shows the MO diagram of the exo transitions state for the inverse electron-demand Dielse-Alder reaction between hexadiene and 1,3 dioxole. Energies are given in hartrees.]]
|} </center>

Figure 8 (above) shows the frontier MO diagram for the transition state of the Diels-Alder reaction between cyclohexadiene and 1,3 dioxole for the endo and exo reactions, respectively. The B3Lyp/6-31G(d)-optimised MOs for the nedo and exo transition states are shown below.

The energies obtained from the B3Lyp/6-31G(d) optimisations of the reactants reveal that in this particular reaction the HOMO of the dienophile is higher in energy than the HOMO of the diene. Thus this reaction can be identified as an inverse-electron demand Diels-Alder reaction. An explanation for this is that the dieneophile is more electron-rich than the diene due to the two oxygen atoms in its structure.

=== B3Lyp/6-31G(d) optimised MOs of the transition states ===

<center>
{| class="wikitable"
!EXO HOMO-1
!EXO HOMO
!EXO LUMO
!EXO LUMO+1
|-
|<jmol><jmolApplet><uploadedFileContents>TS_B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>TS B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>TS B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>TS B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|}
{| class="wikitable"
!ENDO HOMO-1
!ENDO HOMO
!ENDO LUMO
!ENDO LUMO+1
|-
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|} </center>

=== Reaction energies and Activation barriers at the B3Lyp/6-31G(d) level===
<center>
{| class="wikitable"
!
!Reaction energy /Ha
!Reaction energy/ kJ mol<sup>-1</sup>
!Activation barrier/ Ha
!Activation Barrier/ kJ mol<sup>-1</sup>
|-
|EXO
|<nowiki>-0.024281</nowiki>
|<nowiki>-63.75</nowiki>
|0.063858
|167.66
|-
|ENDO
|<nowiki>-0.025668</nowiki>
|<nowiki>-67.39</nowiki>
|0.060876
|159.83
|} </center>
The table above shows the reaction energy and the activation energy for the endo and the exo Diels-Alder reaction. The reaction energy is negative for both reactions which means that they are both thermodynamically favourable. Meanwhile, the endo reaction is more exergonic and has a lower activation barrier and is thus thermodynamically and kinetically favoured over the exo recation. This can be explained considering two factors. Firstly, steric strain, looking at the endo product (fig.7), the (CH<sub>2</sub>CH<sub>2</sub>)-"bridge" and the 1,3 dioxole are on opposite faces of the cylcohexane ring. For the exo product they are on the same face making it more sterically strained than the endo product. The other factor to consider are secondary orbital interactions. These are bonding interactions which do not lead to a bond but contribute to lowering the energy of transition structures. These secondary orbital inetractions are only present in the endo transition structure (see below) which explains the smaller activation barrier of the endo reaction. Secondary orbital interactions generally explain the endo-selectivity of Diels-Alder reactions even in cases where the endo product is not thermodynamically favoured over the exo product.

===Closer comparison of the endo and exo transition states===

<center>
{| class="wikitable"
!ENDO TS
!ENDO TS (cartoon)
!EXO TS
!EXO TS (cartoon)
|-
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|[[File:Endotsvl915ex2.png|230px|thumb|centre|]]
|<jmol><jmolApplet><uploadedFileContents>TS B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|[[File:Exotsvl915ex2.png|200px|thumb|centre|]]
|} </center>

The table above shows the HOMO of the endo and exo transition state structures. In the case of the endo transition structure a stabilising in-phase iteraction can be seen between the p orbitals of the oxygen atoms and the centre-back lobes of the diene. The exo transition structure lacks these stabilising secondary orbital interactions and is thus higher in energy.

===Files===
1,3 dioxole:[[File:OTHER B3LYP.LOG]] cyclohexadine:[[File:CYCLOHEXADIENE B3LYP.LOG]]
Products exo:[[File:B3LYP EXO.LOG]] Product endo:[[File:ENDO B3LYP MINIMUM.LOG]]
IRC endo:[[File:IRC PM6 3.LOG]]
== Exercise 3: Diels-Alder and cheleotropic reactions between o-xylylene and sulphur dioxide ==
===Overview===
[[File:Reactionschme3vl915.png|800px|thumb|centre|Fig.9 : This reaction scheme shows the three main reactions between o-xylylene and sulphur dioxide.]]

In this exercise the possible reactions between sulphor dioxide and o-xylylene were investigated. One possible reaction path is a Diels Alder reaction wehre, just as in exercise 2, an endo and exo product can be generated (fig.9 ). Another possible reaction path is a cheleotropic reaction (fig.9). Finally, an alternative Diels-Alder where the cyclohexadiene acts as the diene (see fig.10) was considered as well.

The method used was the following: At first the products were optimised to a minimum at the PM6 level. To confirm that the right mininmum structure was obtained it was verified that the structure was converged and that all frequencies were positive. This product structure was then used to obtain the transition state structure at the PM6 level. To confirm that the right transition state structure was obtained it was verified that the structure was converged and that one negative frequency was present. Subsequently an IRC on the PM6 level was taken on the obtained transition state. The reactant structures were obtained from the IRC and optimised individually at the PM6 level. The thermochemical data of these optimised structures was used to calculate the reaction energies and the reaction barriers at the PM6 level.

===The three main reaction pathways===
<center>
{| class="wikitable"
!Exo Diels-Alder
!Endo Diels-Alder
!Cheleotropic
|-
![[File:exoIRCmovievl915.gif|400px|thumb|left|]]
![[File:endoIRCmovievl915.gif|400px|thumb|left|]]
![[File:cheleoIRCmovievl915.gif|400px|thumb|left|]]
|-
![[File:pythonIRCexo.png|400px|thumb|left|]]
![[File:pythonIRCendo.png|600px|thumb|left|]]
![[File:pythonIRCcheleo.png|600px|thumb|left|]]
|} </center>

The animations above show that during the three reactions the C-C bonds in the six-membered ring of o-xylylene shorten and that in the product structure this six-membered ring contains six C-C-bonds of equal lengths which lie between the typical C-C single and C=C double bond lengths. This is indicative of electron delocalisation and not surprising as fig.9 shows that a six-membered aromatic ring is present in the products of all three reactions. Aromatic systems are very stabilised which explains why the products are thermodynamically favoured over the reactants in all three reactions.

===Thermochemistry of the reactions===

The table below shows the reaction energies and activation barriers for the three reaction pathways calculated at the PM6 level.
<center>
{| class="wikitable"
!
!Reaction energy/ Ha
!Reaction energy/ kJ mol<sup>-1</sup>
!Activation barrier/ Ha
!Activation energy/ kJ mol<sup>-1</sup>
|-
|ENDO
|<nowiki>-0.037049</nowiki>
|<nowiki>-97.27</nowiki>
|0.031816
|83.53
|-
|EXO
|<nowiki>-0.03729</nowiki>
|<nowiki>-97.89</nowiki>
|0.033329
|87.51
|-
|Cheleotropic
|<nowiki>-0.058745</nowiki>
|<nowiki>-154.23</nowiki>
|0.040317
|105.85
|} </center>

The table above shows that as expected the activation barrier of the endo reaction is lower than the activation barrier of the exo reaction. This can again be explained by secondary orbital interactions between the p-orbital of the oxygen atom (the one not involved in the ring formation) and the lobes on the diene. In contrast to the reaction investigated in exercise 2 the exo product is less sterically strained than the endo prodcut as the oxgen atom that is not in the ring occupies the equatorial position which is less sterically strained (see fig.9). Thus the exo product is thermodynamically favoured over the endo product. The cheleotrpic product is the most stable but also has the largest activation barrier so, unless under condtions in which the Diels-Alder reacions can be reversed, it is unlikely to be generated.

=== Analternative Diels Alder reaction ===

[[File:Altdielsaldervl915.png|800px|thumb|center|Fig.10: This reaction scheme shows the alternative Diels Alder reaction of o-xylylene and sulphur dioxide.]]

<center>
{| class="wikitable"
!
!Reaction energy/ Ha
!Reaction energy/ kJ mol<sup>-1</sup>
!Activation barrier/ Ha
!Activation energy/ kJ mol<sup>-1</sup>
|-
|ENDO
|0.006865
|18.06
|0.043326
|113.78
|-
|EXO
|0.008562
|22.52
|0.046311
|121.62
|} </center>

Figure 10 shows that another couple of Diels Alder reactions than the ones mentioned so far is possible between o-xylylene and sulphur dioxide. The table above shows the reaction energies and activation barriers for this aletrnative Diels-Alder reaction calculated at the PM6 level.

The table above shows that these alernative Diels Alder reactions are clearly endergonic and therefore thermodynamically unfavourable. This can be attributed to the lack of an aromatic ring in the product structures which was present in the three reactions discussed above (see fig.9). Furthermore, the activation barriers for these Diels Alder reactions are much higher than for the reactions shown in fig.9 which makes it unlikely that they occur.

Fig.11 below summarizes the thermochemical discussion for exercise 2:
[[File:Energyschemevl9155.png|700px|thumb|center|Fig.11 : This scheme summarises the thermochemistry for all discussed reactions between o-xylylene and sulphur dioxide.]]

(I know this isn't meant to be to scale, but your diagram suggests that the alt products are similar in energy to the cheletropic TS. There are other ways of placing all this data on the same diagram [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:56, 6 March 2018 (UTC))

===Files===
sulphur dioxide:[[File:SULPHUR_DIOXIDE_FROM_IRCvl915.LOG]] o-xylylene:[[File:DIENE_3_MINIMUMvl915.LOG]]
Products exo:[[File:MINIMUM_productvl915exoex3.LOG]] Product endo:[[File:PM6_MINIMUMproduct_endovl915.LOG]] Product cheleotropic:[[File:PM6_MINIMUMproduct_endovl915.LOG]] alternative exo: [[File: MINIMUM_1altDAexoproductvl915.LOG]] alternative endo: [[File:Alternative_Diels_Alder_endo_product_minimum_PM^vl915.LOG]]
IRC endo:[[File:IRC_PM6_ex3_endovl915.LOG]] IRC exo:[[File:IRC_ON_TSex3vl915exo.LOG]] IRC cheleotropic:[[File:IRC_PM6_1cheleovl915.LOG]] alternative DA exo:[[File:IRC_1altDAexoproductvl915.LOG]] alternative DA endo:[[File:IRCalternativdielsalderendo.LOG]]
TS alternative DA: exo:[[File:TSaltDAexovl915.LOG]] endo:[[File:TSvl915alternativdielsalderendo.LOG]]
TS normal DA:exo[[File:TS_exovl915ex3.LOG]] endo:[[File:TS_PM6_ex_3_endo.LOG ]]

==Ring opening of 2,3 dimethylaziridine==
===Overview===
[[File:Dazavl915.png|500px|thumb|center|Fig.12 : This reaction scheme shows the electrociyclic ring opening of 2,3 dimethylaziridine .]]

The ring opening of 2,3 dimethylaziridine is an example of an electrocyclic reaction. Electrocyclic reactions are concerted processes in which an acyclic conjugated system is converted into a ring system by the formation of a sigma bond between the ends of the conjugated system. The reverse process is also an electrocylic reaction and these reactions are usually reversible in nature.

The method used was the following: The product structure (ring-open) was otpimised to a minimum at the PM6 level. To test if the obtained structure was correct it was verified that it was converged an that it had only positive vibrations. Subsequently a transition state structure was obtained at the PM6 level from the optimised product. To test if the transition state structure was correct it was verified that it was converged an that it had one negative vibration only. An IRC was obtained from the transition structure at the PM6 level. Finally, the reactant structure (ring closed) was obtained from the IRC and otpimised to a minimum at the PM6 level.

===The Molecular orbitals===

<center>
{| class="wikitable"
!HOMO ring closed
!LUMO ring closed
|-
!<jmol><jmolApplet><uploadedFileContents>REACTANT_MININMUMperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>REACTANT_MININMUMperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|} </center>

<center>
{| class="wikitable"
!HOMO ring open
!LUMO ring open
|-
!<jmol><jmolApplet><uploadedFileContents>RINGOPENFINALVL915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.14; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>RINGOPENFINALVL915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|} </center>

<center>
{| class="wikitable"
!HOMO-1 TS
!HOMO TS
!LUMO TS
!LUMO+1 TS
|-
!<jmol><jmolApplet><uploadedFileContents>TSperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.60; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TSperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.60; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TSperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TSperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|} </center>

(You will need to look at the same number of MOs in the reactants and products as TS MOs [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 12:14, 6 March 2018 (UTC))

===Stereochemistry and its rationalisation===
[[File:IRCpericvl915movie.gif|500px|thumb|center|Fig.13 : This is an animation of ring opening of 2,3 dimethylaziridine .]]

The animation above shows that during the ring closure the groups attached to the terminal carbons of the pi system rotate in the same direction (both clockwise). This mode of motion is called conrotation and it is these modes of motion during the electrocyclic ring closure (the counterpart of conrotation is disrotation) which determine the stereochemistry of the ring-closed product. Whether disrotation or conrotation occurs depends on the system and can be predicted by two equally successful models: Woodward-Hoffman analysis and Mobius-Huckel analysis.

Both analyses require to apply a set of rules which then allow to determine the mode of motion. Both analyses, here the rules have to be applied to a a pi system containing 4 electrons, predict conrotation for this electrocyclic reaction.

Meanwhile, whether conrotation or disrotation occurs can also be deduced, looking at the calculated ring-open HOMO.

[[File:Contehrmalvl915.png|500px|thumb|center|Fig.14 : This figure shows the effect of conrotation and dirotation on the thermal HOMO .]]

A "cartoon" of the ring-open HOMO (as shown in the Jmols above) is shown in fig. 14. It can be seen that if conrotary motion is applied, lobes of the same phase overlap (a bonding interaction) suggesting that the process is orbital symmetry allowed and that it proceeds through a low-activation energy transition state. If disrotary motion was applied to the the HOMO, lobes of opposite phase would overlap (an antibonding interaction) suggesting that the process is orbital symmetry forbidden and that it proceeds through a high-activation energy transition state. It can thus be assumed that under thermal conditions the reaction occurs with conrotary motion.

It should also be mentioned that if the Woodward Hoffman and Moebius-Hueckel analyses predict conrotation under thermal conditions for a particular system they will predict disrotation for the same system under photochemical conditions. This can also be rationalised for the 2,3 dimethylarizidine system looking at the calculated MOs. Under phtochemical conditions one electron from the HOMO is excited into the LUMO so that the LUMO (under thermal conditions) becomes the HOMO under photochemical conditions.

[[File:Conphotolvl915.png|500px|thumb|center|Fig.15 : This figure shows the effect of conrotation and dirotation on the photochemical HOMO .]]

A "cartoon" of the ring-open photochemical HOMO (see "LUMO ring open" in the Jmols above) is shown in fig. 15. If conrotary motion was applied to the the HOMO, lobes of opposite phase would overlap (an antibonding interaction) suggesting that the process is orbital symmetry forbidden and that it proceeds through a high-activation energy transition state. If disrotary motion is applied, lobes of the same phases overlap (a bonding interaction) suggesting that the process is orbital symmetry allowed and that it proceeds through a low-activation energy transition state. It can thus be assumed that under photochemical conditions the reaction occurs with disrotary motion.

===Files===
Ring closed: [[File:REACTANT_MININMUMperivl915.LOG]]
ringopen:[[File:RINGOPENFINALVL915.LOG]]
TS:[[File:TSperivl915.LOG]]
IRC: [[File:IRCperivl915.LOG]]

== Conclusion==
These three exercises show that it is possible to successfully model different Diels-Alder, cheleotropic and electrocyclic reactions with the Gaussian software using semi-empirical and DFT-based methods. Furthermore, the software also makes it possible to visualise molecular orbitals and nuclear vibrations and animations of whole reactions can be generated. The software also allows to obtain thermochemical information of the modeled reactions such as their reaction energies and activation energies. Calculations such as the ones carried out in these experiments have thus the potential to replace expensive and difficult experiments. Further work could be done on more complex cycloadditions as well as other pericyclic reactions such as [3-3] sigmatropic rearrangements for instance. A further next step could be to take into account the surrounding medium (air,solvent...) and surrounding conditions such as temperature and pressure when modelling the reactions.

==References==
<references />

Rep:TSvl915

2018-03-06T11:56:38Z

Tam10: /* Exercise 3: Diels-Alder and cheleotropic reactions between o-xylylene and sulphur dioxide */

== Introduction==
Chemical processes are often described in terms of the properties of their reactants, their products and their transition structures.<ref>J. J. W. Mcdouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, 2013.</ref>. Many of these properties can be obtained if the potential energy surface of the chemical system is known. The potential energy of a system depends on 3N-6 coordinates where N is the total number of atoms in the system. Product and reactant structures are located in local minima of the potential energy surface. Local minima are a special type of stationary points in which all coordinates lie at a minimum. Transition states are also a special type of stationary points in which all coordinates lie at a minimum except one which lies at a maximum. This can also be expressed using the two equations below:
[[File: Equationsvl915.PNG|800px|thumb|center|]]
where '''R''' refers to a set of coordinates and R<sub>i</sub> is the ith coordinate in that set. Every type of stationary point fulfills euqation (1). Local minima have only positive matrix elements in the matrix of second order derivatives H (also called the Hessian matrix, equation 2) whereas transition states have one single negative matrix element<ref>D. J. Wales, in Energy Landscapes, Cambridge University Press, 2013.</ref>. If a stationary point has has more than one negative matrix element it is not a transition structure as this means that it is a maximum in more than one coordinate and that there must be a lower energy pathway between the reactant and product potential energy wells. This reasoning is called the Murrell-Laidler theorem <ref>D. J. Wales, in Energy Landscapes, Cambridge University Press, 2013.</ref> and is illustrated in fig.1 :
[[File:PESfinalvl915.PNG|800px|thumb|center|Fig.1: PES illustrating the Murrell Laidler theorem and showing a transition state as well as a local minimum and a local maximum.]]
The matrix elements and the vibrational frequencies of structures are related such that correct transition state structures have one negative frequency only whereas correct minimum structures have only positive frequencies if this is not the case the structures are probably wrong.

Based on these concepts specialised software such as Gaussian can be used to model and to explore potential energy surfaces <ref>Gaussian.com, http://gaussian.com/, (accessed 27 February 2018).</ref>. In this experiment Gaussian was used to investigate three different Diels Alder reactions and a cheleotropic reaction. This included determining their transition state structures, the accurate product and reactant structures, visualising Molecular orbitals (MOs)and nuclear vibrations as well as calculating reaction energies and activation barriers. Furthermore the IRC of the reactions was determined and different bond lengths were tracked throughout the modeled reactions. For this two computational methods were used with Gaussian. The first one was PM6 a semi empirical method based on Hartree Fock theory<ref>J. J. P. Stewart, J. Mol. Model., 2007, 13, 1173–1213.</ref>. This method makes many approximations and some of its more complex terms are obtained from empirical data. It has the advantage being a relatively fast and inexpensive method but its results are unreliable as the empirical reference data may be inadequate and the assumptions made may be too inflexible<ref>J. J. P. Stewart, J. Mol. Model., 2007, 13, 1173–1213.</ref>. The other method is B3LYP/6-31G(d)) which is a density functional theory (DFT) method. These methods aim to deal with the one-electron density rather than the many-electron wavefunction which allows much less demanding computations when solving Schrödinger's equation <ref>J. J. W. Mcdouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, 2013.</ref>. B3LYP/6-31G(d))uses a basis set of s and p+d orbitals yet it is not a pure DFT method as Hartree Fock calculations are used to account for exchange correlation. B3LYP/6-31G(d)is is more expensive than PM6 and takes longer but it is also more accurate.

== Exerciese 1: Diels Alder Reaction between Ethene and Butadiene ==

=== Overview ===

[[File:Chem Draw schemevl915.png|400px|thumb|center|Fig.2: Reaction scheme showing the ethene/butadiene Diels Alder reaction (with a transition state in the middle)]]

In this exercise the Diels Alder reaction, which is a [4+2] cycloaddition, between butadiene and ethene was investigated (fig.2).

The method used was the following: Butadiene and ethene were optimised separately to a minimum at the PM6 level. To verify that the obtained minimum structures were correct it was made sure that they were converged and that they had no negative vibrations. Subsequently the transition state structure was obtained at the PM6 level using the two otpimised reactant structures. To verify that the transition state structure was correct, it was made sure that it was converged and that it had one negative vibration. An IRC was calculated from the transition state structure at the PM6 level. Finally, the product structure (cyclohexene) was obtained from the IRC and was optimised to a minimum at the PM6 level.

=== Transition State Analysis ===
[[File:MO diagram exercise 1bla.png|400px|thumb|center|Fig.3: MO diagram of the transition state of the butadiene/ethene Diels Alder reaction]]

<center>
{| class="wikitable"
!<jmol><jmolApplet><uploadedFileContents>BUTADIENE_PM_6.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>BUTADIENE_PM_6.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|-
|Butadiene HOMO
|Butadiene LUMO
|} </center>

<center>
{| class="wikitable"
!<jmol><jmolApplet><uploadedFileContents>ETHENE_GOOD_MINIMUM.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.10; mo 6; mo nodots nomesh fill translucent; mo titleformat "", rotate x 45</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>ETHENE_GOOD_MINIMUM.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.10; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|-
|Ethene HOMO
|Ethene LUMO
|} </center>
<center>
{| class="wikitable"
!<jmol><jmolApplet><uploadedFileContents>TRANSITION_STATE_GOOD_exercise1.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TRANSITION_STATE_GOOD_exercise1.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TRANSITION_STATE_GOOD_exercise1.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>TRANSITION_STATE_GOOD_exercise1.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|-
|TS HOMO-1
|TS HOMO
|TS LUMO
|TS LUMO+1
|} </center>

From the transition state MOs shown above and from the transition state MO diagram (fig.3) it can be seen that MOs only interact if they are of the same symmetry (i.e. symmetric MOs interact only with symmetric MOs and not with antisymmetric ones). This implies that for a Diels Alder reaction to be 'allowed' the interacting MOs (i.e. the HOMO and the LUMO of the respective reactants) must be of the same symmetry. Conversely, if the HOMO of one reactant and the LUMO of the other reactant are of opposing symmetry the reaction does not occur.

This can be explained considering the overlap integral of the interacting orbitals. For symmetric-symmetric or antisymmetric-antisymmetric interactions the orbital overlap is non-zero as there are either in-phase or out of phase interactions so that net bonding or net antibonding MOs are generated. Meanwhile, for antisymmetric-symmetric interactions, the overlap integral is zero as the out of phase and in-phase interactions cancel out.

=== C-C bond length analysis ===

<center>
{| class="wikitable"
![[File:Bond movie.gif|400px|thumb|left|Fig.4: Animation of the butadiene/ ethene Diels-Alder reaction]]
![[File:Bond_lengths1.png|600px|thumb|left|Fig.5: C-C bond lengths plotted against the IRC starting from the adduct and progressing to the reactants of the Diels-Alder reaction]]
|} </center>

<center>
{| class="wikitable"
!Structure
!C1-C11/ Å
!C1-C4/ Å
!C4-C6/ Å
!C6-C7/ Å
!C7-C14/ Å
!C11-C14/ Å
|-
|Butadiene
|<nowiki>-</nowiki>
|1.34
|1.47
|1.34
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|-
|Ethene
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|1.34
|-
|Trasntion State Struture
|2.10
|1.38
|1.41
|1.38
|2.10
|1.38
|-
|Cyclohexene
|1.54
|1.50
|1.34
|1.50
|1.54
|1.54
|} </center>

In a Diels-Alder reaction (animated in fig.4), two new C-C sigma bonds are formed (C1-C11, C7-C14), three C=C pi bonds lengthen to become C-C sigma bonds (C11-C14, C1-C4, C6-C7) and one C-C sigma bond (C4-C6) shortens to become a pi bond. This is reflected in fig.5 where all C-C bond lengths are plotted against the intrinsic reaction coordinate (starting from the product and progressing towards the reactants).

In butadiene the C=C bond lengths (C1-C4 and C6-C7, see table) are very close to the standard C=C pi bond length (1.34 Å<ref>A. Bondi, J. Phys. Chem., 1964, 16, 1171–1223</ref>). Meanwhile, the C-C bond (C4-C6) is shorter than a typical C-C sigma bond (1.54 Å <ref>A. Bondi, J. Phys. Chem., 1964, 16, 1171–1223</ref>) which can be attributed to the effects of conjugation.

In the transition state structure the C1-C4 and C6-C7 bond lengths are lengthened compared to the bond lengths in butadiene whereas the C4-C6 bond length is shortened. The C11-C14 bond length is slightly lengthened compared to the bond length in ethene. The C1-C11 and the C7-C14 bond length is 2.1 Å which is less than the sum of two carbon van der Waals radii (3.4 Å <ref>A. Bondi, J. Phys. Chem., 1964, 16, 1171–1223</ref>) suggesting that there is some interaction between these carbon atoms.

In the product (cyclohexene) structure the C1-C4 and C6-C7 bond lengths are slightly shorter than the standard C-C bond length (where two sp<sup>3</sup> orbitals overlap) which can be attributed to an increased s character in these bonds as they can be seen as an overlap between a sp<sup>2</sup> and a sp<sup>3</sup> orbital.

=== Transitions State Vibration ===

<center>
{| class="wikitable"
![[File:TSvibrationvl915.gif|400px|thumb|center|Fig.6a: Animation of the complex vibration in the transition state for the ethene/ butadiene Diels Alder reaction]]
![[File:TSvibrationvl915.gif|400px|thumb|center|Fig.6b: Animation of the ethene/ butadiene Diels-Alder reaction]]
|} </center>

Diels-Alder reactions are known to occur via a concerted mechanism. This is underpinned by the negative vibration (animated above in fig.6a) which suggests a synchronous C-C bond formation. Figure 6b shows an animation of the whole reaction.

===Files===
IRC:[[File:IRC1vl915.LOG]]

==Exercise 2: Diels Alder reaction between Cyclohexadiene and 1,3-Dioxole ==
===Overview===

[[File:Reactionschemevl915.png|400px|thumb|center|Fig.7: Overview of the reactions investigated in exercise 2]]
In this exercise the Diels Alder reaction between cyclohexadiene and 1,3 dioxole was investigated (fig.7). In this case two different outcomes are possible, the endo and the exo product.

The method used was the following: The product (either exo or endo) was optimised to a minimum first at the PM6 level then this structure was used to find a minimum structure at the B3LYP/6-31G(d) level. To test whether a correct minimum structure was obtained in each step it was made sure that the structures were converged and that they had only positive vibrations. The optimised product structure was then used to find a transition state structure first at the PM6 level, then the PM6 structure was used to find a transition structure at the B3LYP/6-31G(d) level. To test whether a correct transition state structure was obtained in each step it was made sure that the structures were converged and that they had one negative vibration. An IRC was obtained at the PM6 level from the PM6 transition state. The reactant structures were obtained from the IRC and were optimised to a minimum separately at the B3LYP/6-31G(d) level.

===Analysis of the MOS===

<center>
{| class="wikitable"
![[File: MOdiagramendofinalvl915.png|400px|thumb|center|Fig.8a: This figure shows the MO diagram of the endo transitions state for the inverse electron-demand Dielse-Alder reaction between hexadiene and 1,3 dioxole. Energies are given in hartrees.]]
![[File:MOdiagramexofinalvl915.png|400px|thumb|center|Fig.8b: This figure shows the MO diagram of the exo transitions state for the inverse electron-demand Dielse-Alder reaction between hexadiene and 1,3 dioxole. Energies are given in hartrees.]]
|} </center>

Figure 8 (above) shows the frontier MO diagram for the transition state of the Diels-Alder reaction between cyclohexadiene and 1,3 dioxole for the endo and exo reactions, respectively. The B3Lyp/6-31G(d)-optimised MOs for the nedo and exo transition states are shown below.

The energies obtained from the B3Lyp/6-31G(d) optimisations of the reactants reveal that in this particular reaction the HOMO of the dienophile is higher in energy than the HOMO of the diene. Thus this reaction can be identified as an inverse-electron demand Diels-Alder reaction. An explanation for this is that the dieneophile is more electron-rich than the diene due to the two oxygen atoms in its structure.

=== B3Lyp/6-31G(d) optimised MOs of the transition states ===

<center>
{| class="wikitable"
!EXO HOMO-1
!EXO HOMO
!EXO LUMO
!EXO LUMO+1
|-
|<jmol><jmolApplet><uploadedFileContents>TS_B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>TS B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>TS B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>TS B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|}
{| class="wikitable"
!ENDO HOMO-1
!ENDO HOMO
!ENDO LUMO
!ENDO LUMO+1
|-
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|} </center>

=== Reaction energies and Activation barriers at the B3Lyp/6-31G(d) level===
<center>
{| class="wikitable"
!
!Reaction energy /Ha
!Reaction energy/ kJ mol<sup>-1</sup>
!Activation barrier/ Ha
!Activation Barrier/ kJ mol<sup>-1</sup>
|-
|EXO
|<nowiki>-0.024281</nowiki>
|<nowiki>-63.75</nowiki>
|0.063858
|167.66
|-
|ENDO
|<nowiki>-0.025668</nowiki>
|<nowiki>-67.39</nowiki>
|0.060876
|159.83
|} </center>
The table above shows the reaction energy and the activation energy for the endo and the exo Diels-Alder reaction. The reaction energy is negative for both reactions which means that they are both thermodynamically favourable. Meanwhile, the endo reaction is more exergonic and has a lower activation barrier and is thus thermodynamically and kinetically favoured over the exo recation. This can be explained considering two factors. Firstly, steric strain, looking at the endo product (fig.7), the (CH<sub>2</sub>CH<sub>2</sub>)-"bridge" and the 1,3 dioxole are on opposite faces of the cylcohexane ring. For the exo product they are on the same face making it more sterically strained than the endo product. The other factor to consider are secondary orbital interactions. These are bonding interactions which do not lead to a bond but contribute to lowering the energy of transition structures. These secondary orbital inetractions are only present in the endo transition structure (see below) which explains the smaller activation barrier of the endo reaction. Secondary orbital interactions generally explain the endo-selectivity of Diels-Alder reactions even in cases where the endo product is not thermodynamically favoured over the exo product.

===Closer comparison of the endo and exo transition states===

<center>
{| class="wikitable"
!ENDO TS
!ENDO TS (cartoon)
!EXO TS
!EXO TS (cartoon)
|-
|<jmol><jmolApplet><uploadedFileContents>B3 LYP TS 3 ENDO.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.38; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|[[File:Endotsvl915ex2.png|230px|thumb|centre|]]
|<jmol><jmolApplet><uploadedFileContents>TS B3LYP2vl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|[[File:Exotsvl915ex2.png|200px|thumb|centre|]]
|} </center>

The table above shows the HOMO of the endo and exo transition state structures. In the case of the endo transition structure a stabilising in-phase iteraction can be seen between the p orbitals of the oxygen atoms and the centre-back lobes of the diene. The exo transition structure lacks these stabilising secondary orbital interactions and is thus higher in energy.

===Files===
1,3 dioxole:[[File:OTHER B3LYP.LOG]] cyclohexadine:[[File:CYCLOHEXADIENE B3LYP.LOG]]
Products exo:[[File:B3LYP EXO.LOG]] Product endo:[[File:ENDO B3LYP MINIMUM.LOG]]
IRC endo:[[File:IRC PM6 3.LOG]]
== Exercise 3: Diels-Alder and cheleotropic reactions between o-xylylene and sulphur dioxide ==
===Overview===
[[File:Reactionschme3vl915.png|800px|thumb|centre|Fig.9 : This reaction scheme shows the three main reactions between o-xylylene and sulphur dioxide.]]

In this exercise the possible reactions between sulphor dioxide and o-xylylene were investigated. One possible reaction path is a Diels Alder reaction wehre, just as in exercise 2, an endo and exo product can be generated (fig.9 ). Another possible reaction path is a cheleotropic reaction (fig.9). Finally, an alternative Diels-Alder where the cyclohexadiene acts as the diene (see fig.10) was considered as well.

The method used was the following: At first the products were optimised to a minimum at the PM6 level. To confirm that the right mininmum structure was obtained it was verified that the structure was converged and that all frequencies were positive. This product structure was then used to obtain the transition state structure at the PM6 level. To confirm that the right transition state structure was obtained it was verified that the structure was converged and that one negative frequency was present. Subsequently an IRC on the PM6 level was taken on the obtained transition state. The reactant structures were obtained from the IRC and optimised individually at the PM6 level. The thermochemical data of these optimised structures was used to calculate the reaction energies and the reaction barriers at the PM6 level.

===The three main reaction pathways===
<center>
{| class="wikitable"
!Exo Diels-Alder
!Endo Diels-Alder
!Cheleotropic
|-
![[File:exoIRCmovievl915.gif|400px|thumb|left|]]
![[File:endoIRCmovievl915.gif|400px|thumb|left|]]
![[File:cheleoIRCmovievl915.gif|400px|thumb|left|]]
|-
![[File:pythonIRCexo.png|400px|thumb|left|]]
![[File:pythonIRCendo.png|600px|thumb|left|]]
![[File:pythonIRCcheleo.png|600px|thumb|left|]]
|} </center>

The animations above show that during the three reactions the C-C bonds in the six-membered ring of o-xylylene shorten and that in the product structure this six-membered ring contains six C-C-bonds of equal lengths which lie between the typical C-C single and C=C double bond lengths. This is indicative of electron delocalisation and not surprising as fig.9 shows that a six-membered aromatic ring is present in the products of all three reactions. Aromatic systems are very stabilised which explains why the products are thermodynamically favoured over the reactants in all three reactions.

===Thermochemistry of the reactions===

The table below shows the reaction energies and activation barriers for the three reaction pathways calculated at the PM6 level.
<center>
{| class="wikitable"
!
!Reaction energy/ Ha
!Reaction energy/ kJ mol<sup>-1</sup>
!Activation barrier/ Ha
!Activation energy/ kJ mol<sup>-1</sup>
|-
|ENDO
|<nowiki>-0.037049</nowiki>
|<nowiki>-97.27</nowiki>
|0.031816
|83.53
|-
|EXO
|<nowiki>-0.03729</nowiki>
|<nowiki>-97.89</nowiki>
|0.033329
|87.51
|-
|Cheleotropic
|<nowiki>-0.058745</nowiki>
|<nowiki>-154.23</nowiki>
|0.040317
|105.85
|} </center>

The table above shows that as expected the activation barrier of the endo reaction is lower than the activation barrier of the exo reaction. This can again be explained by secondary orbital interactions between the p-orbital of the oxygen atom (the one not involved in the ring formation) and the lobes on the diene. In contrast to the reaction investigated in exercise 2 the exo product is less sterically strained than the endo prodcut as the oxgen atom that is not in the ring occupies the equatorial position which is less sterically strained (see fig.9). Thus the exo product is thermodynamically favoured over the endo product. The cheleotrpic product is the most stable but also has the largest activation barrier so, unless under condtions in which the Diels-Alder reacions can be reversed, it is unlikely to be generated.

=== Analternative Diels Alder reaction ===

[[File:Altdielsaldervl915.png|800px|thumb|center|Fig.10: This reaction scheme shows the alternative Diels Alder reaction of o-xylylene and sulphur dioxide.]]

<center>
{| class="wikitable"
!
!Reaction energy/ Ha
!Reaction energy/ kJ mol<sup>-1</sup>
!Activation barrier/ Ha
!Activation energy/ kJ mol<sup>-1</sup>
|-
|ENDO
|0.006865
|18.06
|0.043326
|113.78
|-
|EXO
|0.008562
|22.52
|0.046311
|121.62
|} </center>

Figure 10 shows that another couple of Diels Alder reactions than the ones mentioned so far is possible between o-xylylene and sulphur dioxide. The table above shows the reaction energies and activation barriers for this aletrnative Diels-Alder reaction calculated at the PM6 level.

The table above shows that these alernative Diels Alder reactions are clearly endergonic and therefore thermodynamically unfavourable. This can be attributed to the lack of an aromatic ring in the product structures which was present in the three reactions discussed above (see fig.9). Furthermore, the activation barriers for these Diels Alder reactions are much higher than for the reactions shown in fig.9 which makes it unlikely that they occur.

Fig.11 below summarizes the thermochemical discussion for exercise 2:
[[File:Energyschemevl9155.png|700px|thumb|center|Fig.11 : This scheme summarises the thermochemistry for all discussed reactions between o-xylylene and sulphur dioxide.]]

(I know this isn't meant to be to scale, but your diagram suggests that the alt products are similar in energy to the cheletropic TS. There are other ways of placing all this data on the same diagram [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:56, 6 March 2018 (UTC))

===Files===
sulphur dioxide:[[File:SULPHUR_DIOXIDE_FROM_IRCvl915.LOG]] o-xylylene:[[File:DIENE_3_MINIMUMvl915.LOG]]
Products exo:[[File:MINIMUM_productvl915exoex3.LOG]] Product endo:[[File:PM6_MINIMUMproduct_endovl915.LOG]] Product cheleotropic:[[File:PM6_MINIMUMproduct_endovl915.LOG]] alternative exo: [[File: MINIMUM_1altDAexoproductvl915.LOG]] alternative endo: [[File:Alternative_Diels_Alder_endo_product_minimum_PM^vl915.LOG]]
IRC endo:[[File:IRC_PM6_ex3_endovl915.LOG]] IRC exo:[[File:IRC_ON_TSex3vl915exo.LOG]] IRC cheleotropic:[[File:IRC_PM6_1cheleovl915.LOG]] alternative DA exo:[[File:IRC_1altDAexoproductvl915.LOG]] alternative DA endo:[[File:IRCalternativdielsalderendo.LOG]]
TS alternative DA: exo:[[File:TSaltDAexovl915.LOG]] endo:[[File:TSvl915alternativdielsalderendo.LOG]]
TS normal DA:exo[[File:TS_exovl915ex3.LOG]] endo:[[File:TS_PM6_ex_3_endo.LOG ]]

==Ring opening of 2,3 dimethylaziridine==
===Overview===
[[File:Dazavl915.png|500px|thumb|center|Fig.12 : This reaction scheme shows the electrociyclic ring opening of 2,3 dimethylaziridine .]]

The ring opening of 2,3 dimethylaziridine is an example of an electrocyclic reaction. Electrocyclic reactions are concerted processes in which an acyclic conjugated system is converted into a ring system by the formation of a sigma bond between the ends of the conjugated system. The reverse process is also an electrocylic reaction and these reactions are usually reversible in nature.

The method used was the following: The product structure (ring-open) was otpimised to a minimum at the PM6 level. To test if the obtained structure was correct it was verified that it was converged an that it had only positive vibrations. Subsequently a transition state structure was obtained at the PM6 level from the optimised product. To test if the transition state structure was correct it was verified that it was converged an that it had one negative vibration only. An IRC was obtained from the transition structure at the PM6 level. Finally, the reactant structure (ring closed) was obtained from the IRC and otpimised to a minimum at the PM6 level.

===The Molecular orbitals===

<center>
{| class="wikitable"
!HOMO ring closed
!LUMO ring closed
|-
!<jmol><jmolApplet><uploadedFileContents>REACTANT_MININMUMperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>REACTANT_MININMUMperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.18; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|} </center>

<center>
{| class="wikitable"
!HOMO ring open
!LUMO ring open
|-
!<jmol><jmolApplet><uploadedFileContents>RINGOPENFINALVL915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.14; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
!<jmol><jmolApplet><uploadedFileContents>RINGOPENFINALVL915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|} </center>

<center>
{| class="wikitable"
!HOMO-1 TS
!HOMO TS
!LUMO TS
!LUMO+1 TS
|-
!<jmol><jmolApplet><uploadedFileContents>TSperivl915.LOG</uploadedFileContents><size>300</size><color>white</color><script>frame 1.60; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
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|} </center>

===Stereochemistry and its rationalisation===
[[File:IRCpericvl915movie.gif|500px|thumb|center|Fig.13 : This is an animation of ring opening of 2,3 dimethylaziridine .]]

The animation above shows that during the ring closure the groups attached to the terminal carbons of the pi system rotate in the same direction (both clockwise). This mode of motion is called conrotation and it is these modes of motion during the electrocyclic ring closure (the counterpart of conrotation is disrotation) which determine the stereochemistry of the ring-closed product. Whether disrotation or conrotation occurs depends on the system and can be predicted by two equally successful models: Woodward-Hoffman analysis and Mobius-Huckel analysis.

Both analyses require to apply a set of rules which then allow to determine the mode of motion. Both analyses, here the rules have to be applied to a a pi system containing 4 electrons, predict conrotation for this electrocyclic reaction.

Meanwhile, whether conrotation or disrotation occurs can also be deduced, looking at the calculated ring-open HOMO.

[[File:Contehrmalvl915.png|500px|thumb|center|Fig.14 : This figure shows the effect of conrotation and dirotation on the thermal HOMO .]]

A "cartoon" of the ring-open HOMO (as shown in the Jmols above) is shown in fig. 14. It can be seen that if conrotary motion is applied, lobes of the same phase overlap (a bonding interaction) suggesting that the process is orbital symmetry allowed and that it proceeds through a low-activation energy transition state. If disrotary motion was applied to the the HOMO, lobes of opposite phase would overlap (an antibonding interaction) suggesting that the process is orbital symmetry forbidden and that it proceeds through a high-activation energy transition state. It can thus be assumed that under thermal conditions the reaction occurs with conrotary motion.

It should also be mentioned that if the Woodward Hoffman and Moebius-Hueckel analyses predict conrotation under thermal conditions for a particular system they will predict disrotation for the same system under photochemical conditions. This can also be rationalised for the 2,3 dimethylarizidine system looking at the calculated MOs. Under phtochemical conditions one electron from the HOMO is excited into the LUMO so that the LUMO (under thermal conditions) becomes the HOMO under photochemical conditions.

[[File:Conphotolvl915.png|500px|thumb|center|Fig.15 : This figure shows the effect of conrotation and dirotation on the photochemical HOMO .]]

A "cartoon" of the ring-open photochemical HOMO (see "LUMO ring open" in the Jmols above) is shown in fig. 15. If conrotary motion was applied to the the HOMO, lobes of opposite phase would overlap (an antibonding interaction) suggesting that the process is orbital symmetry forbidden and that it proceeds through a high-activation energy transition state. If disrotary motion is applied, lobes of the same phases overlap (a bonding interaction) suggesting that the process is orbital symmetry allowed and that it proceeds through a low-activation energy transition state. It can thus be assumed that under photochemical conditions the reaction occurs with disrotary motion.

===Files===
Ring closed: [[File:REACTANT_MININMUMperivl915.LOG]]
ringopen:[[File:RINGOPENFINALVL915.LOG]]
TS:[[File:TSperivl915.LOG]]
IRC: [[File:IRCperivl915.LOG]]
== Conclusion==
These three exercises show that it is possible to successfully model different Diels-Alder, cheleotropic and electrocyclic reactions with the Gaussian software using semi-empirical and DFT-based methods. Furthermore, the software also makes it possible to visualise molecular orbitals and nuclear vibrations and animations of whole reactions can be generated. The software also allows to obtain thermochemical information of the modeled reactions such as their reaction energies and activation energies. Calculations such as the ones carried out in these experiments have thus the potential to replace expensive and difficult experiments. Further work could be done on more complex cycloadditions as well as other pericyclic reactions such as [3-3] sigmatropic rearrangements for instance. A further next step could be to take into account the surrounding medium (air,solvent...) and surrounding conditions such as temperature and pressure when modelling the reactions.

==References==
<references />

Rep:YZ20215TS

2018-03-06T11:49:32Z

Tam10: /* Excercise 3- Diels-Alder vs Cheletropic */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure 5. Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 15. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

(You need to select the correct frame for JMols. These are just the 15th step of the optimisation [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:49, 6 March 2018 (UTC))

=== IRC calculations ===

{| class="wikitable"
|+ Table 16. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 17. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 18. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

(These levels of precision are far too high [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 11:49, 6 March 2018 (UTC))

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure 6. Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 19. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 20. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

= References =

<references />

Rep:Transition States and Reactivity - SR2815

2018-03-06T10:57:14Z

Tam10: /* Exercise 3 */

== Introduction ==
[[File:Sr2815 min saddle.png|thumb|Figure 1: Local minimum point vs. saddle point.<sup>[1]</sup>]]
When analysing a potential energy surface, there are 2 main features that are particularly important when it comes to studying a molecule's reactivity: any '''local minima''', which represent resting structures (i.e. '''reactants''' and '''products'''), and any '''saddle points''', which often link two separate local minima, and thus represent the '''transition state''' between the two.

These can be defined mathematically by their gradients and curvatures. In the case of a local minimum, this will have a gradient of '''0''', and a positive curvature in all directions. However, for a saddle point, this also has a gradient of '''0''', but instead, has a positive curvature in one direction, and a negative curvature in the perpendicular direction. This therefore gives rise to an overall '''negative''' Gaussian curvature, as opposed to local minima, whose Gaussian curvatures are '''positive'''.[[File:Sr2815 PES.gif|thumb|544x544px|left|Figure 2: Example of a potential energy surface, with labelled local minima and saddle point.<sup>[2]</sup>]]Local minima and saddle points in 3-D can be further differentiated using the partial second derivative test, whereby a 2x2 Hessian matrix consisting of partial second derivatives of a function, ''f'', is formed, and the sign of the determinant indicates what type of critical point is present. A '''positive''' determinant is indicative of a minimum or maximum point, and a '''negative '''determinant is indicative of a saddle point.

Computational methods (e.g. software such as GaussView) have proved extremely useful in analysing potential energy surfaces, as well as the structures of reactants, products, and indeed, transition states. GaussView works by acting as an interface for Gaussian, a software which performs complex mathematical calculations, specifically solving the Schrödinger equation according to what the user inputs into GaussView. Gaussian does this using various basis sets (usually in the form of a linear combination of atomic orbitals), which the user can select. These are broken down into categories based on how Schrödinger equation is solved, and these are further broken down into basis sets of various complexities. The higher the basis set, the more accurate the final result will be, '''but the longer this calculation will take'''. In this particular experiment, two different basis sets are used: a semi-empirical basis set ('''PM6'''), and a density functional theory basis set ('''B3LYP'''), the latter of which is more complex, and thus takes longer, but gives more accurate results.

One particular function of GaussView is that it is able to predict the vibrational frequencies of a given structure. In the case of a transition state, the negative Gaussian curvature gives rise to a negative force constant, ''k''. This is related to vibrational frequency as follows:

[[File:Sr2815_vib_equation.png|frameless|95x95px]]

Thus, a negative value of ''k'' gives rise to an imaginary frequency, represented in GaussView by a negative frequency. Therefore, if a structure returns '''one''' negative vibrational frequency, this is indicative that the structure is a '''transition state'''.

This particular computational experiment aims to investigate the reactivities and transition structures of various pericyclic reactions, such as Diels-Alder and Cheletropic reactions.
== Exercise 1 ==
The first exercise in this experiment was to investigate the Diels-Alder reaction between butadiene and ethylene.
[[File:Sr2815 butadiene ethylene Reaction Scheme.png|thumb|371x371px|Figure 3: Reaction scheme for the [4+2] cycloaddition of butadiene and ethylene|centre]]
The transition state structure was determined through an initial guess of the transition state, followed by freezing of the two sets of carbon atoms which form C-C bonds during the reaction, optimising the structure to a minimum, then optimising the resulting structure to a transition state (Berny). Both a frequency analysis and an IRC were carried out on said structure.

This reaction is an example of normal demand Diels-Alder, meaning that it is the LUMO of the dienophile (ethylene) that interacts with the HOMO of the diene (butadiene) in the C-C bond forming step.

{{multiple image
| align = left
| direction = vertical
| header = HOMO and LUMO of Butadiene
| width = 250

| image1 = Sr2815 BUTADIENE LUMO s.jpg
| alt1 =
| caption1 = Figure 4: LUMO of butadiene

| image2 = Sr2815 BUTADIENE HOMO a.jpg
| alt2 =
| caption2 = Figure 5: HOMO of butadiene
}}

{{multiple image
| align = right
| direction = vertical
| header = HOMO and LUMO of Ethylene
| width = 250

| image1 = Sr2815 ETHYLENE LUMO a.jpg
| alt1 =
| caption1 = Figure 10: LUMO of ethylene (π*)

| image2 = Sr2815 ETHYLENE HOMO s.jpg
| alt2 =
| caption2 = Figure 11: HOMO of ethylene (π)
}}

{{multiple image|
| align = center
| direction = horizontal
| header = MOs of Transition State
| width = 270

| image1 = Sr2815 buteth TS LUMO+1.jpg
| alt1 =
| caption1 = Figure 6: LUMO+1 of TS

| image2 = Sr2815 buteth TS LUMO.jpg
| alt2 =
| caption2 = Figure 7: LUMO of TS

| image3 = Sr2815 buteth TS HOMO.jpg
| alt3 =
| caption3 = Figure 8: HOMO of TS

| image4 = Sr2815 buteth TS HOMO-1.jpg
| alt4 =
| caption4 = Figure 9: HOMO-1 of TS
}}

[[File:Sr2815 butadiene ethylene MO Diagram.png|thumb|centre|635x635px|Figure 12: MO diagram for the [4+2] cycloaddition of butadiene and ethylene]]

[[File:Sr2815 buteth TS LUMO 2nd.jpg|thumb|Figure 13: Secondary bonding interaction in the LUMO of the TS|388x388px]]

MO analysis shows that the HOMO and LUMO of ethylene are the π and π* MOs, respectively. The HOMO and LUMO of butadiene are the the conjugated combinations of π orbitals, containing 1 and 2 nodes, respectively. It is the antisymmetric LUMO of ethylene and antisymmetric HOMO of butadiene which combine to give the HOMO-1 and LUMO+1 MOs in the final TS, which are bonding and anti-bonding, respectively. The HOMO and LUMO of the TS represent combinations of the symmetric HOMO of ethylene and the symmetric LUMO of butadiene. As can be seen from their MOs (see Figures 7 & 8), these are generally either non or anti-bonding, however, there is a slight secondary bonding interacting in the LUMO (see Figure 13).

What can therefore be concluded about this reaction is that it is only 'allowed' when two MOs of the same symmetry are close enough in energy to interact, since symmetric and antisymmetric MOs will not do so with each other. Furthermore, it is therefore also the case that the orbital overlap for antisymmetric-antisymmetric interactions is greater than 0, for antisymmetric-symmetric interactions is 0, and for symmetric-symmetric reactions, it is perhaps slightly greater than 0, due to the presence of smaller bonding interactions.

It is also possible to analyse the progression of bond lengths during the reaction. Table 1 shows the the bond lengths in the reactants, transition state, and products, in accordance with Figure 14.
[[File:Sr2815 ex1 bond lengths.png|thumb|162x162px|Figure 14: Bonds in the reaction of butadiene + ethylene|left]]
[[File:Sr2815 ex1 vibration.gif|thumb|Figure 15: C-C bond forming vibration in the TS of butadiene and ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+Table 1: Bond Lengths during the Reaction /Å
!Bond
!Reactants
!Transition State
!Product
|-
|1
|1.46835
|1.41109
|1.33766
|-
|2
|1.33530
|1.37979
|1.50034
|-
|3
|<nowiki>-</nowiki>
|2.11469
|1.54003
|-
|4
|1.32731
|1.38177
|1.54076
|-
|5
|<nowiki>-</nowiki>
|2.11479
|1.54003
|-
|6
|1.33530
|1.37977
|1.50034
|}

What is seen is that bonds which started as C=C bonds (2, 4 & 6) increase in length throughout the reaction, due to their reduction in bond order from 2 to 1, and thus elongation of the bond occurs. The opposite is true for bond 1, which starts as a C-C bond, and finishes as C=C, thus becoming shorter during the reaction. Comparing this to standard carbon-carbon bond lengths, we see that bonds in the reactants are generally shorter than the average bond length (e.g. Bonds 2, 4 & 6 < Average sp<sup>2</sup>-sp<sup>2</sup> length = '''1.47 Å'''<sup>[3]</sup>; Bond 1 < Average sp<sup>3</sup>-sp<sup>2</sup> length = '''1.50 Å'''<sup>[3]</sup>). However, in the product, bond lengths appear to be a lot closer to average bond lengths (e.g. Bonds 2 & 6 ≈ Average sp<sup>3</sup>-sp<sup>2</sup> length = '''1.50 Å'''<sup>[3]</sup>; Bonds 3, 4 & 5 ≈ Average sp<sup>3</sup>-sp<sup>3</sup> length = '''1.54 Å'''<sup>[3]</sup>). For the transition state, bonds 3 & 5 are particularly interesting, as, given that the Van der Waals radius of carbon is '''1.70 Å''',<sup>[4]</sup> bond lengths of around 2.11 Å represent the two radii of the carbons atoms overlapping, and thus the two atoms begin to become attracted.

Finally, upon performing a frequency analysis of the transition state, we can assign a vibrational frequency of '''948.57i''' '''cm<sup>-1</sup> '''(-947.57 cm<sup>-1</sup> in GaussView) to the C-C bond forming vibration, since this is the (only) imaginary frequency present (see Figure 15). This animation shows the C-C bond formation to be synchronous, also supported by roughly equal bond lengths (bond 3 & 5) in the transition state (see Table 1).

'''''Appropriate files can be found below:'''''

''Optimised butadiene [PM6] - [[File:Sr2815 BUTADIENE OPT PM6.LOG]]''

''Butadiene MOs [PM6] - [[File:Sr2815 Butadiene opt PM6.chk]]''

''Optimised ethylene [PM6] - [[File:Sr2815 ETHYLENE OPT PM6.LOG]]''

''Ethylene MOs [PM6] - [[File:Sr2815 Ethylene opt PM6.chk]]''

''Optimised transition state + frequency analysis [PM6] - [[File:Sr2815 BUTADIENE ETHYLENE TS OPTFREQ PM6.LOG]]''

''Transition state MOs [PM6] - [[File:Sr2815 Butadiene Ethylene TS OptFreq PM6.chk]]''

''Transition state IRC [PM6] - [[File:Sr2815 BUTADIENE ETHYLENE TS IRC PM6.LOG]]''

''Optimised cyclohexene [PM6] - [[File:Sr2815 CYCLOHEXENE OPT PM6.LOG]]''

== Exercise 2 ==
This exercise aimed to investigate a more complex cycloaddition, specifically that of the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole. Not only are the molecules in this example larger, but their structure means that the product has two possible stereochemistries, known as the '''exo''' and '''endo '''products. Analysis of the transition states involved in the formation of these products might give rise to an explanation as to why one is favoured over the other.
[[File:Sr2815 ex2 Reaction Scheme.png|centre|thumb|439x439px|Figure 16: Reaction scheme for the [4+2] cycloaddition of cyclohexadiene and 1,3-dioxole]]
Transition states were determined via the same method as described in exercise 1, although for this example, PM6-optimised structures were re-optimised further at a B3LYP 6-31G(d) level. IRCs were also carried out on both transition states (at a PM6 level due to time constraints, using the PM6-optimised transition states), and frequency analyses were carried out an all reactants, products and transition states.

{{multiple image
| align = right
| direction = vertical
| header = HOMO and LUMO of 1,3-Dioxole
| width = 250

| image1 = Sr2815 Dioxole LUMO.jpg
| alt1 =
| caption1 = Figure 27: LUMO of 1,3-dioxole

| image2 = Sr2815 Dioxole HOMO.jpg
| alt2 =
| caption2 = Figure 28: HOMO of 1,3-dioxole
}}

{{multiple image
| align = left
| direction = vertical
| header = HOMO and LUMO of Cyclohexadiene
| width = 250

| image1 = Sr2815 Cyclohexadiene LUMO.jpg
| alt1 =
| caption1 = Figure 17: LUMO of cyclohexadiene

| image2 = Sr2815 Cyclohexadiene HOMO.jpg
| alt2 =
| caption2 = Figure 18: HOMO of cyclohexadiene
}}

{{multiple image|
| align = center
| direction = horizontal
| header = MOs of Endo Transition State
| width = 270

| image1 = Sr2815 Cyclohexadiene Dioxole endo TS LUMO+1.jpg
| alt1 =
| caption1 = Figure 19: LUMO+1 of Endo TS

| image2 = Sr2815 Cyclohexadiene Dioxole endo TS LUMO.jpg
| alt2 =
| caption2 = Figure 20: LUMO of Endo TS

| image3 = Sr2815 Cyclohexadiene Dioxole endo TS HOMO.jpg
| alt3 =
| caption3 = Figure 21: HOMO of Endo TS

| image4 = Sr2815 Cyclohexadiene Dioxole endo TS HOMO-1.jpg
| alt4 =
| caption4 = Figure 22: HOMO-1 of Endo TS
}}

{{multiple image|
| align = center
| direction = horizontal
| header = MOs of Exo Transition State
| width = 270

| image1 = Sr2815 Cyclohexadiene Dioxole Exo TS LUMO+1.jpg
| alt1 =
| caption1 = Figure 23: LUMO+1 of Exo TS

| image2 = Sr2815 Cyclohexadiene Dioxole Exo TS LUMO.jpg
| alt2 =
| caption2 = Figure 24: LUMO of Exo TS

| image3 = Sr2815 Cyclohexadiene Dioxole Exo TS HOMO.jpg
| alt3 =
| caption3 = Figure 25: HOMO of Exo TS

| image4 = Sr2815 Cyclohexadiene Dioxole Exo TS HOMO-1.jpg
| alt4 =
| caption4 = Figure 26: HOMO-1 of Exo TS
}}
[[File:Sr2815 MO Exo Diagram.png|thumb|809x809px|Figure 30: MO diagram for the exo [4+2] cycloaddition of cyclohexadiene and 1,3-dioxole]]
[[File:Sr2815 MO Endo Diagram.png|left|thumb|800x800px|Figure 29: MO diagram for the endo [4+2] cycloaddition of cyclohexadiene and 1,3-dioxole]]

The order of energy levels of the two reactants is slightly different in this example than that seen in exercise 1, however, analysis of MOs shows that this reaction is still a normal demand Diels-Alder reaction, in which the antisymmetric LUMO of the dienophile (1,3-dioxole) interacts with the antisymmetric HOMO of the diene (cyclohexadiene) to give the primary C-C bond forming interaction ('''HOMO-1''' and '''LUMO+1''' orbitals). However, in this example, there is also a clear interaction between the two symmetric orbitals (the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole), which gives rise to the '''HOMO '''and '''LUMO '''of the transition states, which are largely bonding and anti-bonding, respectively.

What proves to be more significant, however, are the differences in the MOs between the endo and exo transition states. Specifically, looking at the HOMOs of both TS's, the endo TS has a very clear secondary orbital interaction between the π orbitals of the two oxygen atoms of 1,3-dioxole, and two π orbitals of the conjugated π system in cyclohexadiene (see Figure 21). This interaction undoubtedly stabilises the endo transition state, and since it is not present in the exo transition state, may well lead to preferential formation of the endo product.
[[File:Sr2815 ex2 Reaction Profile.png|thumb|382x382px|Figure 31: Sketch of the reaction profiles for the [4+2] cycloadditions of cyclohexadiene and 1,3-dioxole]]
This can be further investigated by analysis of the Gibbs free energies of the transition states and products, as tabled below:

{| class="wikitable"
|+Table 2: Gibbs Free Energies of Structures /kJ mol<sup>-1</sup>
!Conformation
!Reactants
!Transition State
!Product
!Reaction Barrier
!Reaction Energy
|-
|Endo
|<nowiki>-1,313,781.868759</nowiki>
|<nowiki>-1,313,622.0571995</nowiki>
|<nowiki>-1,313,849.2732205</nowiki>
|'''159.8115595'''
|'''-67.4044615'''
|-
|Exo
|<nowiki>-1,313,781.868759</nowiki>
|<nowiki>-1,313,614.220082</nowiki>
|<nowiki>-1,313,845.684162</nowiki>
|'''167.648677'''
|'''-63.815403'''
|}
Therefore, according to the calculations, the '''endo''' product proves to be both the kinetically and thermodynamically favoured product. Thermodynamically, this is most likely primarily due to the aforementioned secondary orbital overlap which stabilises the endo product. Kinetically, this is most likely due to possible steric clashes between 1,3-dioxole and the -CH<sub>2</sub>CH<sub>2</sub>- group of the cyclohexadiene ring in the exo transition state, which destabilises it more than that of the endo transition state.

'''''Appropriate files can be found below:'''''

''Optimised cyclohexadiene + frequency analysis [B3LYP 6-31G(d)] - [[File:Sr2815 CYCLOHEXADIENE OPTFREQ 6-31G.LOG]]''

''Cyclohexadiene MOs [B3LYP 6-31G(d)] - [[File:Sr2815 Cyclohexadiene OptFreq 6-31G.chk]]''

''Optimised 1,3-dioxole + frequency analysis [B3LYP 6-31G(d)] - [[File:Sr2815 DIOXOLE OPTFREQ 6-31G.LOG]]''

''1,3-Dioxole MOs [B3LYP 6-31G(d)] - [[File:Sr2815 Dioxole OptFreq 6-31G.chk]]''

''Optimised endo transition state + frequency analysis [B3LYP 6-31G(d)] - [[File:Sr2815 CYCLOHEXADIENE DIOXOLE ENDO TS OPTFREQ 6-31G.LOG]]''

''Endo transition state MOs [B3LYP 6-31G(d)] - [[File:Sr2815 Cyclohexadiene Dioxole Endo TS OptFreq 6-31G.chk]]''

''Endo transition state IRC [PM6] - [[File:Sr2815 CYCLOHEXADIENE DIOXOLE ENDO TS IRC PM6.LOG]]''

''Optimised exo transition state + frequency analysis [B3LYP 6-31G(d)] - [[File:Sr2815 CYCLOHEXADIENE DIOXOLE EXO TS OPTFREQ 6-31G.LOG]]''

''Exo transition state MOs [B3LYP 6-31G(d)] - [[File:Sr2815 Cyclohexadiene Dioxole Exo TS OptFreq 6-31G.chk]]''

''Exo transition state IRC [PM6] - [[File:Sr2815 CYCLOHEXADIENE DIOXOLE EXO TS IRC PM6.LOG]]''

''Optimised endo product + frequency analysis [B3LYP 6-31G(d)] - [[File:Sr2815 cyclodiox ENDO PRODUCT OPTFREQ 6-31G.LOG]]''

''Optimised exo product + frequency analysis [B3LYP 6-31G(d)] - [[File:Sr2815 cyclodiox EXO PRODUCT OPTFREQ 6-31G.LOG]]''

== Exercise 3 ==
This exercise continues to look at Diels-Alder reactions, in addition to another type of pericyclic reaction: a cheletropic reaction. Both reactions are seen between ortho-xylylene and SO<sub>2</sub>.
[[File:Sr2815 ex3 Reaction Scheme.png|centre|thumb|504x504px|Figure 32: Cheletropic and Diels-Alder reactions of ortho-xylylene and SO<sub>2</sub>]]

The transition states for this experiment were obtained via constructing the desired product of the reaction, optimising at a PM6 level, deleting the 2 bonds formed during the reaction, separating the reacting atoms by a suitable distance, then continuing as previously described in exercises 1 & 2 (i.e. freezing, optimising etc.). IRCs were carried out on all transition states, as well as frequency analyses on all transition states and products. The results of the IRCs can be seen below:

{{multiple image
| align = right
| direction = vertical
| header = IRC Paths for Cheletropic and Endo and Exo Diels-Alder Reactions (GIFs)
| width = 250

| image1 = Sr2815 Cheletropic TS IRC PM6.gif
| alt1 =
| caption1 = Figure 36: IRC path of cheletropic reaction

| image2 = Sr2815 DA Endo TS IRC PM6.gif
| alt2 =
| caption2 = Figure 37: IRC path of endo Diels-Alder reaction

| image3 = Sr2815 DA Exo TS IRC PM6.gif
| alt3 =
| caption3 = Figure 38: IRC path of exo Diels-Alder reaction}}

{{multiple image|
| align = center
| direction = horizontal
| header = IRC Paths for Cheletropic and Endo and Exo Diels-Alder Reactions (Energies)
| width = 450

| image1 = Sr2815 Cheletropic TS IRC PM6.png
| alt1 =
| caption1 = Figure 33: IRC path of cheletropic reaction

| image2 = Sr2815 DA Endo TS IRC PM6.png
| alt2 =
| caption2 = Figure 34: IRC path of endo Diels-Alder reaction

| image3 = Sr2815 DA Exo TS IRC PM6.png
| alt3 =
| caption3 = Figure 35: IRC path of exo Diels-Alder reaction
}}

[[File:Sr2815 ex3 Reaction Profile.png|thumb|517x517px|Figure 39: Sketch of the reaction profiles for the cheletropic and Diels-Alder reactions of ortho-xylylene and SO<sub>2</sub>]]

(Use straight lines between stationary points in the reaction profile [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:57, 6 March 2018 (UTC))

Something that can be seen from Figures 36-38 is how for each pericylic reaction, aromaticity is established in the 6 membered ring. This explains why ortho-xylylene is so unstable, as establishing aromaticity will stabilise the products majorly compared to the reactants, thus driving the reaction forward.

Similar to exercise 2, the Gibbs free energies of the reactants, transition states and products can be tabulated and analysed to work out the reaction barriers and energies for each reaction:
{| class="wikitable"
|+Table 3: Gibbs Free Energies of Structures /kJ mol<sup>-1</sup>
!Reaction
!Reactants
!Transition State
!Products
!Reaction Barrier
!Reaction energy
|-
|Cheletropic
|154.426659
|260.087281
|<nowiki>-0.0078765</nowiki>
|'''105.660622'''
|'''-154.4345355'''
|-
|Diels-Alder (Endo)
|154.426659
|237.775782
|56.983852
|'''83.349123'''
|'''-97.442807'''
|-
|Diels-Alder (Exo)
|154.426659
|241.7481635
|56.3301025
|'''87.3215045'''
|'''-98.0965565'''
|}
What can be seen from this data is that the '''cheletropic''' reaction is clearly the thermodynamically favoured reaction, possessing the largest reaction energy. However, it also possesses the largest reaction barrier, and thus it is the two Diels-Alder reactions which prove to be more kinetically favoured. Specifically, considering the two Diels-Alder reactions, the '''endo''' reaction is the more thermodynamically favoured reaction, whereas the '''exo''' is the more kinetically favoured reaction. This is most likely, once again, due to possible secondary orbital interactions in the endo product while stabilise it compared to the exo product, causing it to be lower in energy. However, for this reaction, there are no major steric clashes in the exo transition state (c.f. exercise 2), and thus the transition state for the exo reaction is lower in energy than that of the endo reaction, which causes it to be kinetically favoured.

In addition, an investigation was carried out to determine whether Diels-Alder reactions could take place at the diene of the 6-membered ring in ortho-xylylene. The following data was obtained:

{| class="wikitable"
|+Table 4: Gibbs Free Energies of Structures /kJ mol<sup>-1</sup>
!Reaction
!Reactants
!Transition State
!Products
!Reaction Barrier
!Reaction energy
|-
|Diels-Alder (Endo)
|154.426659
|267.984785
|172.2564295
|'''113.558126'''
|'''17.8297705'''
|-
|Diels-Alder (Exo)
|154.426659
|275.819277
|176.711903
|'''121.392618'''
|'''22.285244'''
|}
Therefore what can be seen is that, compared to what is seen for the Diels-Alder reactions in Table 3, both the endo and exo reactions here are both kinetically and thermodynamically unfavourable. This is most likely due to the lack or aromaticity in the final product of the reaction, as well as a greater steric influence of the ring.

'''''Appropriate files can be found below:'''''

''Optimised xylylene + frequency analysis [PM6] - [[File:Sr2815 XYLYLENE OPTFREQ PM6.LOG]]''

''Optimised SO<sub>2</sub> + frequency analysis [PM6] - [[File:Sr2815 SO2 OPTFREQ PM6.LOG]]''

''Optimised cheletropic transition state + frequency analysis [PM6] - [[File:Sr2815 CHELETROPIC TS OPTFREQ PM6.LOG]]''

''Cheletropic transition state IRC [PM6] - [[File:Sr2815 CHELETROPIC TS IRC PM6.LOG]]''

''Optimised endo transition state + frequency analysis [PM6] - [[File:Sr2815 DA ENDO TS OPTFREQ PM6.LOG]]''

''Endo transition state IRC [PM6] - [[File:Sr2815 DA ENDO TS IRC PM6.LOG]]''

''Optimised exo transition state + frequency analysis [PM6] - [[File:Sr2815 DA EXO TS OPTFREQ PM6.LOG]]''

''Exo transition state IRC [PM6] - [[File:Sr2815 DA EXO TS IRC PM6.LOG]]''

''Optimised cheletropic product + frequency analysis [PM6] - [[File:Sr2815 CHELETROPIC PRODUCT OPTFREQ PM6.LOG]]''

''Optimised endo product + frequency analysis [PM6] - [[File:Sr2815 DA ENDO PRODUCT OPTFREQ PM6.LOG]]''

''Optimised exo product + frequency analysis [PM6] - [[File:Sr2815 DA EXO PRODUCT OPTFREQ PM6.LOG]]''

''Optimised disfavoured endo transition state + frequency analysis [PM6] - [[File:Sr2815 DISFAVOURED DA ENDO TS OPTFREQ PM6.LOG]]''

''Optimised disfavoured exo transition state + frequency analysis [PM6] - [[File:Sr2815 DISFAVOURED DA EXO TS OPTFREQ PM6.LOG]]''

''Optimised disfavoured endo product + frequency analysis [PM6] - [[File:Sr2815 DISFAVOURED DA ENDO PRODUCT OPTFREQ PM6.LOG]]''

''Optimised disfavoured exo product + frequency analysis [PM6] - [[File:Sr2815 DISFAVOURED DA EXO PRODUCT OPTFREQ PM6.LOG]]''

== Conclusions ==

The results of these 3 computational investigations demonstrate the power of computational chemistry. Using software like GaussView, we are able to visualise the structures and orbitals of molecules, which in turn, through consideration of factors such as secondary orbital interactions and sterics, allows us to predict the reactivity of these molecules, on an extremely short timescale.

== References ==
[1]: Arora S., Hardt M., Vishnoi N. ''Off the Convex Path''. Available from: <nowiki>http://www.offconvex.org/2016/03/22/saddlepoints/</nowiki> [Accessed February 2018]

[2]: Sturdy Y. K., Clary D. C. Torsional anharmonicity in the conformational analysis of tryptamine. ''Phys. Chem. Chem. Phys.'' 2007;'''9''':2065-2074. Available from: doi:10.1039/B615660F

[3]: Fox, Marye Anne; Whitesell, James K. ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer; 1995. ISBN 978-3-86025-249-9.

[4]: Bondi, A. Van der Waals Volumes and Radii. ''J. Phys. Chem.'' 1964;'''68'''(3):441-451. Available from: doi:10.1021/j100785a001

Rep:Y3AS6115

2018-03-06T10:48:44Z

Tam10: /* Extensions */

=Transition State Structures=

==Introduction==
In this experiment, the transition states of several pericyclic reactions where investigated using computational techniques to acquire information about the kinetics and thermodynamics of these reactions, and analyse the molecular orbitals of these chemical systems.

A potential energy surface (PES) is a plot of the potential energy of a chemical system as a function of two or more reaction coordinates. The number of dimensions of a PES is 3N-6 (where N is the number of atoms in the molecular system being considered). In the PES the first derivative of the energy, physically representing the gradient, which is related to the force acting on the atoms whilst the second derivative, a physical measure of the curvature, is related to the force constants, k. The values of k can then be used to calculate the vibrational frequencies for each of the 3N-6 modes.

A minimum point (zero first derivative, positive second derivative) along a reaction coordinate, of the PES of the molecular system of interest, corresponds to a stable species in the reaction. This could potentially be a reactant, product or intermediates of the reaction mechanism. A transition state (TS) is a maximum point (zero first derivative, negative second derivative) along the reaction coordinate, of the PES. It is also possible that the TS for a particular reaction pathway might be a saddle point on the PES which has a zero first derivative and second derivative that is positive in some directions and negative in others. The reaction path taken can be identified form the potential energy surface by keeping the system in equilibrium whilst varying the reaction coordinates, thus elucidating the minimum energy pathway linking reactants and products via a transition state; known as the intrinsic reaction coordinate (IRC).

[[User:Nf710|Nf710]] ([[User talk:Nf710|talk]]) 10:42, 6 March 2018 (UTC) Some confusion here, A TS is always a first order saddle point. and always only has 1 dimension of negative curvature. This info is obtained by diagonalising the force constant and looking a the eigen values.

During this experiment two optimisation methods on Gaussian were used; the semi-empirical PM6 method and the density functional theory (DFT) based B3LYP. Both optimization methods are based on the Hartee-Fock model, which accounts for electron-electron interactions by assuming that any given electron in a molecule only experiences an average field from the other electrons. The relatively simpler non-ab initio PM6 method uses pre-determined empirical data in its estimation of electron density, and therefore is a relatively fast method. The B3LYP method uses 6-31(G) basis set which is essentially a mathematical representation of the atomic orbitals which make up the molecular orbitals of the molecular system being studied (i.e. LCAO theory). The B3LYP method involves the evaluation of an exchange correlation parameter term, which more accurately represents electron-electron repulsions. The purpose of these methods was to solve the time independent Schrödinger equation at each point as reaction coordinates are varied and calculate the corresponding energy, and the subsequent first and second derivatives of the energy with respect to the specific position on the PES. This allows determination of an optimised geometry. Optimised in the sense of either being a minimum and therefore a stable species involved in the reaction (by performing a minimisation calculation) or a TS (by choosing a TS(Berny) calculation). In the case of the TS optimisation calculation must have force constants calculated only once, and usually include the Gaussian keyword opt = noeigen (which in the case of multiple negative frequencies being found will prevent the calculation from terminating).

Gaussian was used to locate the TSs of the reactions studied. Several different methods were employed to find to locate the TS. Firstly, a guess-TS was built in GaussView and then optimised directly to the TS, whilst this is the fastest approach it is also the least reliable and to be of any use some prior knowledge of the TS is requires. Secondly, a guess-TS could have the interatomic distances between the atoms which are broken or formed during the reaction step fixed (‘frozen coordinates’), and then preform a minimisation calculation, before optimising to the TS. Also, a third method used involved minimising the structure of the reactants, or products, and then altering the structure and freezing the coordinates to obtain a more accruate guess-TS, which can then be optimised to the TS.

==Exercise 1: Diels-Alder reaction of butadiene with ethylene==
[[File:AS6115Excercise1scheme.png |thumb|center|300px|Figure 1: Reaction scheme of for the Diels-Alder reaction between ethylene and butadiene to form cyclohexane.]]

For this exercise the Diels-Alder reaction between ethylene and butadiene was studied (see figure 1). The method used was to first optimise the cyclohexene product to a minimum and then the two C-C bonds formed during the Diels-Alder were broken and frozen at a distance of 2.2 Å. This structure was then first minimised and then optimised to the TS.

===MO Diagram of transition state===
[[File:AS6115Mo-diagram-ts-1.png |thumb|center|600px|Figure 2: MO Diagram of the transition state formed from the Diels-Alder reaction between ethylene and butadiene. All MOs labelled with relative energy and described as symmetric, (s), and antisymmetric, (a).]]

The above figure illustrates the simplified molecular orbital (MO) diagram for the TS of the Diels-Alder reaction between ethylene and butadiene. An IRC calculation was run on the optimised TS for this reaction and from the log file initial frame, corresponding to the reactants an energy calculation reactants. This was necessary to obtain the relative energy levels of the MOs of the reactants and the TS which were comparable.

From the MO diagram (figure 2) it can be seen that the MOs of the TS formed from the linear combination of the frontier molecular orbitals of ethylene and butadiene are quite high in energy. Although this is to be expected since the transition state is the highest energy point along the reaction coordinate, and therefore the theoretical activated complex species which exists at this point, should be destabilised relative to the reactants.

===HOMO and LUMO of reactants and resultant MOs in transition state===

The table below displays the HOMOs and LUMOs of ethylene and butadiene as well as the four MOs of the TS which form because of the linear combination of the reactants frontier MOs, which are the same as does demonstrated in the above MO diagram. HOMO-1 (MO16) of the TS is the bonding orbital resulting from the net in-phase interaction (constructive interference) between the HOMO of butadiene and the LUMO of ethylene, and the LUMO +1 (MO19) of the TS is the corresponding antibonding orbital formed via an out-of-phase interaction (net destructive interference) between the butadiene HOMO and ethylene LUMO. The TS HOMO (MO17) is the bonding orbital formed because of the in-phase interaction between the ethylene HOMO and butadiene LUMO, with TS LUMO (MO18) being the antibonding orbital formed by the out-of-phase interaction between ethylene HOMO and butadiene LUMO.

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Name
! style="background: #0D4F8B; color: white;" | MO Jmol
! style="background: #0D4F8B; color: white;" | Comments
|-
| HOMO of ethylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_OPT_MIN.LOG-y3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 6

Relative energy: -0.39228

Symmetric
|-
| LUMO of ethylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_OPT_MIN.LOG-y3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 7

Relative energy: 0.04256

Antisymmetric
|-
| HOMO of butadiene
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>y3as6115BUTADIENE_OPT_MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| MO11

Relative energy: -0.35166

Antisymmetric
|-
| LUMO of butadiene
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>y3as6115BUTADIENE_OPT_MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 12

Relative energy: 0.01103

Symmetric
|-
| HOMO - 1 Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE-BUTADIENE_TS_OPT.LOGy3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 16

Relative energy: -0.32755

Antisymmetric formed as the 'bonding' MO form the interaction of the LUMO of ethylene and the butadiene HOMO
|-
| HOMO Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE-BUTADIENE_TS_OPT.LOGy3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO17

Relative energy: -0.32532

Symmetric formed as the 'bonding MO' from the interaction of the ethylene HOMO and the Butadiene LUMO
|-
| LUMO Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE-BUTADIENE_TS_OPT.LOGy3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 18

Relative energy: 0.01733

Symmetric formed as the 'antibonding MO' from the interaction of the ethylene HOMO and the Butadiene LUMO
|-
| LUMO + 1 Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE-BUTADIENE_TS_OPT.LOGy3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 19

Relative energy: 0.0366

Antisymmetric formed as the 'antibonding MO' from the interaction of the ethylene LUMO and the Butadiene HOMO
|}

Examination of the MOs of the TS exemplifies the principle of conservation of orbital symmetry; that is that only orbitals of the same symmetry can linearly combine. This can be explained by considering the orbital overlap integral, as for an overlap between orbitals of different symmetry (i.e. symmetric-asymmetric interaction) there will be equal amounts of in-phase (constructive) overlap and out-of-phase (destructive) overlap leading to a net zero overlap, hence the overlap integral for such an interaction is therefore zero. The overlap of orbitals of the same symmetry (i.e. symmetric-symmetric and asymmetric-asymmetric) have a non-zero overlap integral, as there will be either a net in-phase or out-of-phase interaction. The LUMO of ethylene and the butadiene HOMO are both asymmetric and therefore can linearly combine to generate the two asymmetric MOs of the TS (MO16 and MO19). Conversely, the Ethylene HOMO and Butadiene LUMO are symmetric can linearly combine to give the two symmetric MOs of the TS (MO17 and MO18).

===C-C bond lengths===

====For optimized reactants:====

Throughout the course of the Diels-Alder reaction the bond lengths of all C-C bonds change due to the changes in hybridisation of some of the carbons and the changes in all the bond orders, and as two additional sigma bonds are formed by the cycloaddition. The data listed below demonstrates the changes in bond lengths that occur on going from reactants to TS to product.

Ethylene C-C bond length = 1.33 Å

Butadiene central C-C bond length = 1.46 Å

Butadiene terminal C-C bond lengths = 1.34 Å

====At the optimised transition State:====

Ethylene C-C bond length = 1.38 Å

Butadiene central C-C bond length = 1.41 Å

Butadiene terminal C-C bond lengths = 1.38 Å

Partly formed new C-C bonds = 2.11 Å

====For the optimized product====
[[File:as6115-Labelled-cyclohexene.PNG |thumb|right|200px|Figure 3: Cyclohexene product labelled]]

Ethylene C-C bond length (C4-C5) = 1.54 Å

Butadiene central C-C bond length (C1-C2)= 1.34 Å

Butadiene terminal C-C bond lengths (C2-C3 & C6-C1) = 1.50 Å

Newly formed bonds (C3-C4 & C5-C6) = 1.54 Å

Typical C-C bond lengths:

C(sp<sup>3</sup>)-C(sp<sup>3</sup>) = 1.54 Å

C(sp<sup>2</sup>)-C(sp<sup>2</sup>) = 1.50 Å

C(sp<sup>3</sup>)-C(sp<sup>2</sup>) = 1.34 Å

Carbon Van der Waals radius = 1.70 Å

The C-C bond lengths in the optimised reactants and product are as expected. The C-C bond ethylene is 1.33 Å (very close to close to the typical alkene C-C sp<sup>2</sup>-sp<sup>2</sup> double bond length of 1.34Å). During this reaction, the carbon atoms (carbon atoms 4 and 5, see figure 3) of the ethylene dienophile goes from a double bond C(sp<sup>2</sup>)-C(sp<sup>2</sup>) to a single C(sp<sup>3</sup>)-C(sp<sup>3</sup>) and therefore lengthens as the reaction progresses. The C4-C5 bond length is 1.38Å which is intermediate between the shorter C-C single bond length in the optimised TS. The C4-C5 bond length in the cyclohexene product 1.54 Å, very similar typical C(sp<sup>3</sup>)-C(sp<sup>3</sup>) bond lengths. The newly formed C-C bonds in product is also at the typical C(sp<sup>3</sup>)-C(sp<sup>3</sup>) bond length and in the TS the interatomic distances between these carbon atoms (C3-C4 and C5-C6) is within the two times the van der Waals radius of carbon which indicates that there is an interaction between these two carbon atoms in the TS of the [4+2] cycloaddition. The central C-C bond of butadiene is broadly similar to typical values for a C-C single bond between two sp<sup>2</sup>hybridised carbon atoms (1.50 Å). This bond becomes progressively shorter in the reaction as in the TS the value is intermediate between the C-C bond length in the reactant and that of the C=C of an alkene, and this illustrates how the two carbon atoms come closer together in this reaction to form the π bond in the cyclohexene product (C1-C2 bond length). Like the ethylene C-C bond, the terminal C-C bond of butadiene has the typical alkene C=C bond length, and this bond lengthens as the reaction progresses with a values in intermediate of the short the C=C alkene bond and that of the typical C(sp<sup>3</sup>)-C(sp<sup>2</sup>) single bond length, at the transition state. In the product, this C-C bond length (C2-C3 and C1-C6) is as expected for a typical C(sp<sup>3</sup>)-C(sp<sup>2</sup>) length (1.50 Å).

===Vibration at the reaction path for the transition state===

{| class="wikitable"
! [[File:AS6115Ethene-butadiene-ts-vibration1.gif |centre|x400px| IRC animation]]
|-
| Figure 4 Animation of vibration of TS at the reaction path
|}

The negative frequency at -949.20 cm<sup>-1</sup> in the TS of this reaction corresponds to the vibration at the reaction path. This negative vibration is due to the negative force constant at the TS (since the force constant is related to the second derivative and at the TS, a maximum point along the reaction path, the second derivative is negative). This vibration is animated above, figure 4, and appears to represent bond formation, and provides evidence that the bond formation in this reaction is synchronous and therefore that the cycloaddition reaction is concerted.

===LOG files===

Optimised ethylene = [[File:ETHENE_OPT_MIN.LOG-y3as6115]]

Optimised butadiene = [[File:y3as6115BUTADIENE_OPT_MIN.LOG]]

Optimised TS = [[File:ETHENE-BUTADIENE_TS_OPT.LOGy3as6115]]

Optimised cyclohexene = [[File:AS6115CYCLOHEXADIENE_MIN.LOG]]

==Excercise 2: Diels-Alder reaction of cyclohexadiene and 1,3-dioxazole==

[[File:AS6115Excercise2scheme.png |thumb|centre|400px|Figure 5: Reaction scheme for the Diels-Alder reaction between 1,3-dioxole and cyclohexa-1,3-diene]]
===MOs===

For this exercise, the endo and exo reaction pathways of the Diels-Alder reaction between 1,3-dixole and cyclohexa-1,3-diene where investigated. The method employed was to first build and optimise the structures of the products and then break the two C-C bonds which formed during the reaction and freeze them at a distance of 2.2 Å, to give the exo and endo guess TS. These guess TSs where then minimised before being optimised to give the final optimised TS. In this exercise, all minimisation and TS optimisations where first preformed using PM6 method, and then using the result optimised at B3LYP level. The IRC calculations where performed at the PM6 level using the PM6 optimised TS as the input, as the corresponding IRC calculations at the B3LYP level have a significantly long run time.

{|
|[[File:AS6115-Endo-ts-mo-diagram.PNG |thumb|centre|425px|Figure 6: MO diagram of the endo transition state]]
|[[File:AS6115Exo-ts-mo-diagram1.PNG |thumb|centre|450px|Figure 7: MO diagam of the exo transition state]]
|}
The MO diagrams for the endo (figure 6) and exo (figure 7) TSs is broadly similar to the MO diagram for exercise 1, with the TS orbitals being higher in energy relative to the reactant MO levels. In a normal electron demand process the diene HOMO is higher in energy than the dienophile HOMO, and the diene HOMO-dienophile LUMO energy gap is smaller compared to the converse dienophile HOMO-diene LUMO energy gap. However, in this reaction the HOMO of the 1,3-dioxole (dienophile) is higher in energy than the cyclohexa-1,3-diene (diene) HOMO, and this means that the reaction is an inverse electron demand Diels-Alder. This is because the dienophile is relatively electron rich, as the oxygen atom substituents can donate electron density (via lone pairs in valence p orbitals) in to the alkene π bond, thus raising the orbital energy levels of the dienophile. Again, this reaction obeys the principle of orbital symmetry.

Additionally it is noticeable that the energy levels of the endo and exo transition state are different. For example the TS HOMO (MO41) for the endo TS is lower in energy than that of the exo transition state. This result is to be expected since the exo TS is higher in energy than the endo, as the endo TS has stabilising secondary orbital interactions.

The secondary orbital interaction in the endo TS can be seen when viewing the TS MOs (see figure 8), as in addition to the main frontier MO interactions, the oxygen p-orbitals interact with the back of the π-orbitals of the diene component, which provides an additional stabilising factor. This lowers the reaction barrier for the reaction, relative the reaction forming the exo product.

====Reactants====

{| class="wikitable"
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115CYCLOHEXADIENE MIN B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115DIOXAZOLE MIN B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| HOMO of Cyclohexadiene
| HOMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115CYCLOHEXADIENE MIN B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115DIOXAZOLE MIN B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| LUMO of Cyclohexadiene
| LUMO of 1,3-Dioxole
|}

====Endo Transition-State====

{| class="wikitable"
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO-TS HOMO
| ENDO-TS LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO-TS HOMO - 1
| ENDO-TS LUMO + 1
|}

====Exo Transition State====

{| class="wikitable"
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115EXO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115EXO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| EXO-TS HOMO
| EXO-TS LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115EXO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115EXO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| EXO-TS HOMO - 1
| EXO-TS LUMO + 1
|}

===Thermochemistry===

{| class="wikitable"
! Species
! Sum of electronic and thermal free energies (Hartee/particle)
|-
| 1,3-Dioxole
| -233.321
|-
| Cyclohexa-1,3-diene
| -267.068
|-
| Endo Transition State
| -500.332
|-
| Exo transition state
| -500.329
|-
| Endo product
| -500.419
|-
| Exo product
| -500.417
|}

{| class="wikitable"
! Reaction product
! Reaction Barrier (KJ / mol)
! Reaction Energy (KJ/mol)
|-
| Endo
| 151.04
| -76.18
|-
| Exo
| 158.86
| -72.59
|}

The thermochemistry section form the log file output of optimisation calculations contained the sum of electronic and thermal free energies which where subsequently used to determine the reaction barriers and reaction energies. The values for the reaction barriers and reaction energies for both the endo and exo reaction pathways are summarised in the above table. The results reveal that the endo reaction has a lower reaction barrier and a larger reaction energy (i.e. the endo product is lower in energy), compared to the exo reaction, thus the endo product is both the kinetic and thermodynamic product. The smaller activation energy for the formation of the endo product is due to the presence of stabilising secondary orbital interactions in the endo TS (which are absent in the exo TS), which means the product is kinetically favoured, . The endo product is the more stable product because it is less sterically encumbered than the exo. This because even though the exo product has the newly formed C-C in an equatorial position, they are in relatively close proximity to the CH2-CH2 bridge which results in steric clashes with the fused 5 membered ring (originating from the 1,3-dioxole). In the endo product, the 5-membered ring is in close proximity to a CH=CH bridge, and therefore experience less steric repulsion, making the more stable thermodynamically favoured product (see figure 9). Also, the greater steric repulsion may be an additional factor for the higher activation energy required for the exo relative to the endo Diels-Alder reaction.

[[File:AS6115Endo-ts-2nd-orb-inter.png |thumb|right|200px|Figure 8: MO41 of the endo transition state, displaying secondary orbital interactions]]

{| class="wikitable"
! Figure 9: Structue of exo and endo prodcut
|-
| [[File:AS6115-Unhindered-endo.PNG |thumb|center|200px|]]
|-
| Endo product
|-
| [[File:AS6115-Hindered-exo.PNG |thumb|center|200px|]]
|-
| Exo product
|}

===LOG files===

Optimised 1,3-Dioxole = [[File:AS6115DIOXAZOLE MIN B3LYP.LOG]]

Optimised cyclohexa-1,3-diene = [[File:AS6115CYCLOHEXADIENE MIN B3LYP.LOG]]

MO energy levels of reactants = [[File:AS6115REACTANTS_ENERGY.LOG]]

Optimised Endo TS = [[File:AS6115ENDO_TS_OPT_B3LYP.LOG]]

Optimised Exo TS = [[File:AS6115EXO_TS_OPT_B3LYP.LOG]]

Optimised Endo product = [[File:AS6115ENDO_PRODUCT_MIN_B3LYP.LOG]]

Optimised Exo product = [[File:AS6115EXO_PRODUCT_MIN_B3LYP.LOG]]

==Excercise 3:o-xylylene sulfur dioxide cycloadditions: Diels-Alder v. Cheletropic==

[[File:AS6115Excercise3scheme1.png|thumb|centre|300px|Figure 10: Reaction Scheme for the different possible cycloaddition reactions between SO2 and the exocyclic diene unit of o-xylylene]]

For this experiment the TSs of different possible pericyclic (figure 10) reactions were located and optimised at the PM6 level. The method used to obtain the TS was to firs build and optimise the products of each of these reactions, individually, then break and freeze the bonds which form as a result of the cycloaddition in order to generate a relatively accurate guess TS. From the optimised TSs the IRC calculations.

From the output (log files) of the optimisation calculation the free energy values for the reactants, products and TSs were collated and used to determine the reaction barriers and energies for each reaction pathway (see tables below).

===Thermochemistry===

[[File:AS6115Reaction profile 1.png |thumb|centre|500px|Figure 11: Reaction profile for the different possible cycloaddition reactions between o-xylylene and the exocyclic diene unit of o-xylylene, with reaction barriers and energies displayed]]

The reaction profile (figure 11) illustrates the data shown in the tables below. The endo product is the kinetic product ads it has the lowest reaction barrier; this is primarily due to stabilising secondary orbital interactions in the endo TS. Also the endo product has a slightly larger reaction energy than the exo product, indicating the endo product is more thermodynamically favourable than the exo. The cheletropic reaction has the highest activation energy of the pathways but also has the highest reaction energy, which means that the cheletropic product is the less kinetically favourable but more thermodynamically favourable than either the endo or exo Diels-Alder. The cheletropic reaction has the highest activation energy because the cheletropic TS is much higher in energy than the endo or exo Diels-Alder TS. This difference can be attributed to the fact that in the cheletropiuc reaction the TS involves forming a 5-membered ring which is more strained and therefore less stable than the 6-membered chair-like TS for the Diels-Alder reactions. S=O bonds are relatively strong and therefore the fact that the cheletropic reaction has two S=O bonds means it is lower in energy compared to the endo and exo products of the Diels-Alder reaction in which one of the two S=O bonds are broken. This explains why the cheletopic reaction is the thermodynamically favoured product.

{| class="wikitable"
! Species
! Sum of thermal and electronic free energies (Hartee/Particle)
|-
| Sulfur dioxide
| -0.118614
|-
| o-Xylylene
| 0.178112
|-
| Endo Transition State
| 0.090562
|-
| Exo Transition state
| 0.092078
|-
| Cheletopic Transition State
| 0.099062
|-
| Endo Product
| 0.021697
|-
| Exo Product
| 0.023829
|-
| Cheletropic reaction
| 0.000005
|}

(Your exo product hasn't fully converged to a minimum. You need to check your geometries for imaginary frequencies [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:26, 6 March 2018 (UTC))

{| class="wikitable"
! Reaction Product
! Reaction Barrier (KJ/mol)
! Reaction energy (KJ/mol)
|-
| Endo
| 81.56
| -99.24
|-
| Exo
| 85.54
| -93.65
|-
| Cheletrophic
| 103.87
| -156.20
|}

As a result of the Diels-Alder and Cheltropic reaction the 6-membered ring of the xylylene reactant is converted into an aromatic benzene ring. The aromatisation of the xylylene ring is a thermodynamic major driving force for these reactions, which explains why the o-xylylene is relatively unstable, as it is readily converted to an aromatic product, as demonstrated by the IRC animations below.

===IRC Paths===

{| class="wikitable"
! Endo pathway
! Exo pathway
! Cheletrophic
|-
| [[File:AS6115Endo reactionex3.gif |left|x550px| IRC animation]]
| [[File:AS6115EXo_reactionex3.gif |left|x400px| IRC animation]]
| [[File:AS6115Cheletrophic reaction.gif |left|x450px| IRC animation]]
|-
|}

===Alternative Diels-Alder reaction===

[[File:AS6115Excercise3scheme2.png |thumb|centre|300px|Figure 12: Reaction Scheme showing the exo and endo products of the Diels Alder reaction between sulphur dioxide and the diene unit with the 6-membered ring of o-xylylene]]

In addition to the exocyclic diene unit utilised for the Cheletropic and Diels-Alder reactions describe above, there is a second s-cis diene unit with the xylylene ring which can undergo a Diels-Alder reaction (figure 12) with sulphur dioxide. The same procedure used to locate was used to locate the TS for the endo and exo pathway for this alternative Diels-Alder reaction, and the subsequent energetic analysis, summarised in the tables below.

{| class="wikitable"
! Species
! Sum of thermal and electronic free energies (Hartee/Particle)
|-
| Sulfur dioxide
| -0.118614
|-
| o-Xylylene
| 0.178112
|-
| Endo Transition State
| 0.090562
|-
| Exo Transition state
| 0.092078
|}

{| class="wikitable"
! Reaction Product
! Reaction Barrier (KJ/mol)
! Reaction energy (KJ/mol)
|-
| Alternative Endo
| 108.09
| 16.04
|-
| Alternative Exo
| 119.61
| 20.50
|}

The data shows that this alternative Diels-Alder reaction is kinetically and thermodynamically unflavoured. Both the endo and exo TSs are higher in energy than the TSs for the cheletropic and Diels-Alder reactions, with the exocyclic diene of Xylylene. The reaction barriers for the alternative Diels-Alder reaction are very high as the approach trajectory of the sulfur dioxide to the cis-diene within the xylylene ring is sterically hindered, compared to the exocyclic diene which is more sterically accessible. Also the reaction is thermodynamically unfavourable as the reaction energies are positive (both exo and endo pathways are endothermic). This is because this Diels-Alder reaction doesn’t benefit from the aromatisation of the o-xylylene ring.

===LOG files===
Optimised sulfur dioxide = [[File:AS6115SO2_MIN.LOG]]

Optimised o-xylylene = [[File:As6115O-XYLYLENE_MIN.LOG]]

Optimised endo TS = [[File:AS6115ENDO_TS_OPT.LOG]]

Optimised exo TS = [[File:AS6115EXO_TS_OPT.LOG]]

Optimised Cheletropic TS = [[File:AS6115CHELETROPHIC_REACTION_TS_OPT.LOG]]

Optimised endo Product = [[File:AS6115ENDO_PRODUCT_MIN_PM6.LOG]]

Optimised exo Product = [[File:AS6115EXO_PRODUCT_MIN.LOG]]

Optimised Cheletropic Product = [[File:AS6115CHELETROPIC_PRODUCT_MIN.LOG]]

Alternative Diels-Alder exo TS = [[File:AS6115ALT-DA_EXO_TS_OPT.LOG]]

Alternative Diels-Alder endo TS = [[File:AS6115ALT-DA_ENDO_TS_OPT.LOG]]

Alternative Diels-Alder exo product = [[File:AS6115ALT-DA_EXO_PRODUCT_MIN.LOG]]

Alternative Diels-Alder endo product = [[File:AS6115ALT-DA_ENDO_PRODUCT_MIN.LOG]]

==Extensions==
===Electrolytic ring opening/closure===
[[File:AS6115Ext1scheme1.png |thumb|centre|400px|Figure 13: Reaction scheme for the electrocylic ring closing/opening reaction between 3,4-dichlorocyclobut-1-ene and (2Z,4E)-2,5-dichlorohexa-2,4-diene]]

The 4π-electrocyclic ring opening/closing reaction which interconverts 3,4-dichlorocyclobut-1-ene and (2Z,4E)-2,5-dichlorohexa-2,4-diene was investigated. The ring open form was first built in Gaussian and minimised, and then the carbon atoms between which the bond forms during the ring closing reaction had their coordinates frozen. This guess-TS was then optimised at the PM6 level. From this an IRC calculation was run (animation shown below). The same analysis of reaction barriers and reaction energy as done in exercises 1 and 2 was performed from this reaction. (Please note that the activation energy and reaction energy quoted in the table is specifically for the ring-opening electrocyclic reaction.)

{| class="wikitable"
! [[File:AS6115-Electrocyclic-movie2.gif |centre|x400px| IRC animation]]
|-
| Figure 14 Animation the elctrocyclic ring closing reaction
|}

As expected the ring open diene form is more stable than the cyclobutene. This is two be expected as the 4-membered ring is highly strained (it suffers from significant angle strain and torsional strain). Also the high torsional strain means that the two chlorine substituents are locked in the cis conformation and therefore the molecule also suffers from steric strain since the chlorine atoms are relatively large.

(It could be worth investigating the trans- butene to see how much sterics affects the reaction energy [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:48, 6 March 2018 (UTC))

{| class="wikitable"
! Species
! Sum of thermal and electronic free energies (KJ/mol)
|-
| (2Z,4E)-2,5-dichlorohexa-2,4-diene
| 129.8514108
|-
| Transition State
| 326.2969913
|-
| 3,4-dichlorocyclobut-1-ene
| 177.5923287
|}

{| class="wikitable"
! Reaction Barrier (KJ / mol)
! Reaction Energy (KJ/mol)
|-
| 148.70
| -47.74
|}

The reaction energy is negative which indicates that the electrocyclic ring opening is exothermic and therefore thermodynamically favourable. This is to be expeected since the ring opening process relieves the ring strain and forms the less sterically strained diene product in which the chlorine atoms are further apart.

From analysis of the stereochemistry of the products and reactants form the IRC, it can be stated that this electrocyclic reaction is conrotation (i.e. the two chlorine substituents will rotate in the same direction during the reaction). This can be explained by considering the Woodward-Hoffman rules. The Woodward-Hoffman rules is based on the principle of conservation of orbital symmetry, and states that for a thermally allowed pericyclic reaction the number of components with the correct number of which satisfy: (4q +2)s + (4r)a must be odd. Where q and r are integers and the susbscript s represents suprafacially interacting components and a represents antrafacial components. For this electrocyclic reaction can be considered as being a single component with four π-electrons and as such this means it must interact antarafacially for this reaction to be thermally allowed (see figure 15). This antrafacial interaction can only be achieved via a conrotatory mechanism. Figure 15 shows how the it is necessary for the HOMO of the diene to undergo conrotation in order for to overlap in such a fashion to form the new C-C σ bonding orbital, in the cyclobutene product.

[[File:AS6115Ext1scheme2.png |thumb|centre|400px|Figure 15: Schematic illustrating the conrotatory ring closing mechanism]]

The frontier MOs for the reactant, TS and product for this electrocyclic reaction are displayed in the table below. The HOMO and LUMO of 2,5-dichlorohexa-2,4-diene are similar to that of butadiene, allbeit with additional contribution from the chlorine atoms. Comparing the HOMO of 2,5-dichlorohexa-2,4-diene to the HOMO of the TS, seems to support the Woodward-Hoffman analysis that this reaction proceeds with conrotation. However the frontier MOs of the TS and 3,4-dichlorocyclobut-1-ene are quite complicated which makes analysis difficult. When looking at the energies it can be seen that the HOMO of the TS is higher in energy than that of the reactant and products, which is to be expected since the TS is the highest energy point in the IRC, however the opposite trend is observed for the LUMOs.

{| class="wikitable"
! Species
! HOMO
! LUMO
|-
| (2Z,4E)-2,5-dichlorohexa-2,4-diene
| [[File:AS6115Electrocyclic-dine-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.3574
| [[File:AS6115Electrocyclic-dine-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.01145
|-
| Transition State
| [[File:AS6115Electrocyclic-TS-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.33726
| [[File:AS6115Electrocyclic-TS-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.02386
|-
| 3,4-dichlorocyclobut-1-ene
| [[File:AS6115Electrocyclic-cycle-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.38986
| [[File:AS6115Electrocyclic-cycle-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.00382
|}

(You are showing the conversion of 4 pi orbitals to 2 pi and 2 sigma orbitals, and so 4 MOs are needed for the analysis. It looks like the HOMO of the products might not be so relevant to this [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:48, 6 March 2018 (UTC))

===LOG files===

Optimised (2Z,4E)-2,5-dichlorohexa-2,4-diene = [[File:AS6115EXT1-RING-OPEN-MIN.LOG]]

Optimised Transition state = [[File:As6115-Ext1CORRECT-TS-OPT.LOG]]

Optimised 3,4-dichlorocyclobut-1-ene = [[File:AS6115CORRECT(2Z4E)-25-DICHLOROHEXA-24-DIENE-MIN.LOG|AS6115CYCLOBUTENE.LOG]]

===Claisen Sigmatropic rearrangement===
[[File:AS6115Extension1scheme1.png |thumb|centre|400px|Figure 16: Reaction Scheme of the Claisen rearrangement between 3-chloro-3-(vinyloxy)prop-1-ene and (E)-5-chloropent-4-enal]]

The claisen rearrangement is a [3,3]-sigmatropic rearrangement reaction which converts 3-chloro-3-(vinyloxy)prop-1-ene to (E)-5-chloropent-4-enal was also investigated in this experiment. The method used the TS was to directly carry out a TS (Berny) optimisation of a guess-TS for the sigmatropic reaction (a chair-like structure) at the PM6 level. Following this an IRC calculation was run. From the initial and final frame of the IRC reactant and product of the Claisen (i.e. the allyl vinyl ether and unsaturated aldehyde) was obtained and optimised.

{| class="wikitable"
! [[File:AS6115Clasien-film1.gif |centre|x400px| IRC animation]]
|-
| Figure 17 Claisen rearrangement IRC
|}

{| class="wikitable"
! Species
! Sum of thermal and electronic free energies (KJ/mol)
|-
| 3-chloro-3-(vinyloxy)prop-1-ene
| 82.12887106
|-
| Transition State
| 222.5397832
|-
| (E)-5-chloropent-4-enal
| 33.55569021
|}

{| class="wikitable"
! Reaction Barrier (KJ / mol)
! Reaction Energy (KJ/mol)
|-
| 140.41
| -48.57
|}

The data in the tables above reveal that the aldehyde product is more stable than the allyl vinyl ether. This is essentially due to the fact that the C=O bond is stronger than the C=C bond. (Please note the values for the reaction barrier and reaction energy are for the sigmatropic rearrangement going from the 3-chloro-3-(vinyloxy)prop-1-ene to the (E)-5-chloropent-4-enal). The reaction is exothermic, as the reaction energy is negative, and as it is thermodynamically favourable to form the aldehyde product.

The alkene in the aldehyde product has E-stereochemistry this can be explained from the analysis of the Claisen TS. The transition state has a chair like structure and the large chlorine substituent prefers to adopt a pseudo-equatorial position, and therefore proceeds to form the E-alkene product (see figure 17).

{| class="wikitable"
! Species
! HOMO
! LUMO
|-
| 3-chloro-3-(vinyloxy)prop-1-ene
| [[File:AS6115Claisen-ether-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.36103
| [[File:AS6115Claisen-ether-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.00247
|-
| Transition State
| [[File:AS6115Claisen-TS-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.31763
| [[File:AS6115Claisen-TS-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.01767
|-
| (E)-5-chloropent-4-enal
| [[File:AS6115Claisen-CHO-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.36658
| [[File:AS6115Claisen-CHO-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.00822
|}

(Again here you have 6 electrons and 6 orbitals that you'd need to track from reactants to products. There are going to be some complicated rotations going on converting sigma and pi orbitals at the reacting sites [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:48, 6 March 2018 (UTC))

The frontier MOs of the reactant, TS and product for this claisen rearrangement along with their corresponding relative energies are listed in the table above. The MOs for this system are quite complex and it is difficult to discern how the frontier MOs develop on going from the allyl vinyl ether through the TS to the γ,δ-unsaturated aldehyde. When considering the relative energies of the frontier MOs the trend observed, is the same as that of the electrocyclic reaction, with the TS HOMO being higher in energy than the reactant and product HOMOs, whilst the TS LUMO is lower in energy than the LUMO of the reactant and product.

===LOG files===

Optimised 3-chloro-3-(vinyloxy)prop-1-ene = [[File:AS6115VINYL-ALLYL-ETHER-MIN.LOG]]

Optimised (E)-5-chloropent-4-enal = [[File:AS6115UNSATURATED-ALDEHYDE-MIN.LOG]]

Optimised TS = [[File:AS6115CLAISEN3-GUESS_TS.LOG]]

==Conclusion==

Overall this experiment used relatively complex computational techniques on Gaussian to locate the TS structures for a variety of different pericyclic reactions, as well as reveal more information about the reactions. In exercise 1 a simple Diels-Alder reaction was investigated and the MOs of the TS and reactants were explored.

In exercise 2 the endo and exo reaction pathways of an inverse electron-demand Diels-Alder was studied and again the frontier MOs of the system were considered. Also reaction barriers and reaction energies where calculated, which revealed the endo product was both the kinetic and thermodynamic product of the reaction.

In exercise 3, a range of different possible cycloaddition reactions which can take place between o-xylene and sulfur dioxide where considered and compared, in terms of activation energies and reaction energies to probe how thermodynamically and kinetically favoured each pathway is.

In addition, further work was carried out to investigate applications of these techniques to other pericyclic reactions. This included the elucidation that the electrocyclic ring opening/closing reaction was conrotatory, in accordance with the Woodward-Hoffman rules. Furthermore, an evaluation of a [3,3]-sigmatropic rearrangement TS helped reveal the stereoselectivity of the reaction.

Ultimately, the confidence that can be placed in the findings of this experiment is limited by the accuracy of the computational methods used. The experiment could be improved by using more accurate methods (e.g repeating optimisation calculations for excercises 1 and 3 at the B3LYP level). Additionally comparing the predictions of the in sillico model with experimental data would allow the validity of this computational experiment to be assessed.

Rep:Y3AS6115

2018-03-06T10:26:30Z

Tam10: /* Excercise 3:o-xylylene sulfur dioxide cycloadditions: Diels-Alder v. Cheletropic */

=Transition State Structures=

==Introduction==
In this experiment, the transition states of several pericyclic reactions where investigated using computational techniques to acquire information about the kinetics and thermodynamics of these reactions, and analyse the molecular orbitals of these chemical systems.

A potential energy surface (PES) is a plot of the potential energy of a chemical system as a function of two or more reaction coordinates. The number of dimensions of a PES is 3N-6 (where N is the number of atoms in the molecular system being considered). In the PES the first derivative of the energy, physically representing the gradient, which is related to the force acting on the atoms whilst the second derivative, a physical measure of the curvature, is related to the force constants, k. The values of k can then be used to calculate the vibrational frequencies for each of the 3N-6 modes.

A minimum point (zero first derivative, positive second derivative) along a reaction coordinate, of the PES of the molecular system of interest, corresponds to a stable species in the reaction. This could potentially be a reactant, product or intermediates of the reaction mechanism. A transition state (TS) is a maximum point (zero first derivative, negative second derivative) along the reaction coordinate, of the PES. It is also possible that the TS for a particular reaction pathway might be a saddle point on the PES which has a zero first derivative and second derivative that is positive in some directions and negative in others. The reaction path taken can be identified form the potential energy surface by keeping the system in equilibrium whilst varying the reaction coordinates, thus elucidating the minimum energy pathway linking reactants and products via a transition state; known as the intrinsic reaction coordinate (IRC).

During this experiment two optimisation methods on Gaussian were used; the semi-empirical PM6 method and the density functional theory (DFT) based B3LYP. Both optimization methods are based on the Hartee-Fock model, which accounts for electron-electron interactions by assuming that any given electron in a molecule only experiences an average field from the other electrons. The relatively simpler non-ab initio PM6 method uses pre-determined empirical data in its estimation of electron density, and therefore is a relatively fast method. The B3LYP method uses 6-31(G) basis set which is essentially a mathematical representation of the atomic orbitals which make up the molecular orbitals of the molecular system being studied (i.e. LCAO theory). The B3LYP method involves the evaluation of an exchange correlation parameter term, which more accurately represents electron-electron repulsions. The purpose of these methods was to solve the time independent Schrödinger equation at each point as reaction coordinates are varied and calculate the corresponding energy, and the subsequent first and second derivatives of the energy with respect to the specific position on the PES. This allows determination of an optimised geometry. Optimised in the sense of either being a minimum and therefore a stable species involved in the reaction (by performing a minimisation calculation) or a TS (by choosing a TS(Berny) calculation). In the case of the TS optimisation calculation must have force constants calculated only once, and usually include the Gaussian keyword opt = noeigen (which in the case of multiple negative frequencies being found will prevent the calculation from terminating).

Gaussian was used to locate the TSs of the reactions studied. Several different methods were employed to find to locate the TS. Firstly, a guess-TS was built in GaussView and then optimised directly to the TS, whilst this is the fastest approach it is also the least reliable and to be of any use some prior knowledge of the TS is requires. Secondly, a guess-TS could have the interatomic distances between the atoms which are broken or formed during the reaction step fixed (‘frozen coordinates’), and then preform a minimisation calculation, before optimising to the TS. Also, a third method used involved minimising the structure of the reactants, or products, and then altering the structure and freezing the coordinates to obtain a more accruate guess-TS, which can then be optimised to the TS.

==Exercise 1: Diels-Alder reaction of butadiene with ethylene==
[[File:AS6115Excercise1scheme.png |thumb|center|300px|Figure 1: Reaction scheme of for the Diels-Alder reaction between ethylene and butadiene to form cyclohexane.]]

For this exercise the Diels-Alder reaction between ethylene and butadiene was studied (see figure 1). The method used was to first optimise the cyclohexene product to a minimum and then the two C-C bonds formed during the Diels-Alder were broken and frozen at a distance of 2.2 Å. This structure was then first minimised and then optimised to the TS.

===MO Diagram of transition state===
[[File:AS6115Mo-diagram-ts-1.png |thumb|center|600px|Figure 2: MO Diagram of the transition state formed from the Diels-Alder reaction between ethylene and butadiene. All MOs labelled with relative energy and described as symmetric, (s), and antisymmetric, (a).]]

The above figure illustrates the simplified molecular orbital (MO) diagram for the TS of the Diels-Alder reaction between ethylene and butadiene. An IRC calculation was run on the optimised TS for this reaction and from the log file initial frame, corresponding to the reactants an energy calculation reactants. This was necessary to obtain the relative energy levels of the MOs of the reactants and the TS which were comparable.

From the MO diagram (figure 2) it can be seen that the MOs of the TS formed from the linear combination of the frontier molecular orbitals of ethylene and butadiene are quite high in energy. Although this is to be expected since the transition state is the highest energy point along the reaction coordinate, and therefore the theoretical activated complex species which exists at this point, should be destabilised relative to the reactants.

===HOMO and LUMO of reactants and resultant MOs in transition state===

The table below displays the HOMOs and LUMOs of ethylene and butadiene as well as the four MOs of the TS which form because of the linear combination of the reactants frontier MOs, which are the same as does demonstrated in the above MO diagram. HOMO-1 (MO16) of the TS is the bonding orbital resulting from the net in-phase interaction (constructive interference) between the HOMO of butadiene and the LUMO of ethylene, and the LUMO +1 (MO19) of the TS is the corresponding antibonding orbital formed via an out-of-phase interaction (net destructive interference) between the butadiene HOMO and ethylene LUMO. The TS HOMO (MO17) is the bonding orbital formed because of the in-phase interaction between the ethylene HOMO and butadiene LUMO, with TS LUMO (MO18) being the antibonding orbital formed by the out-of-phase interaction between ethylene HOMO and butadiene LUMO.

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Name
! style="background: #0D4F8B; color: white;" | MO Jmol
! style="background: #0D4F8B; color: white;" | Comments
|-
| HOMO of ethylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_OPT_MIN.LOG-y3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 6

Relative energy: -0.39228

Symmetric
|-
| LUMO of ethylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_OPT_MIN.LOG-y3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 7

Relative energy: 0.04256

Antisymmetric
|-
| HOMO of butadiene
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>y3as6115BUTADIENE_OPT_MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| MO11

Relative energy: -0.35166

Antisymmetric
|-
| LUMO of butadiene
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>y3as6115BUTADIENE_OPT_MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 12

Relative energy: 0.01103

Symmetric
|-
| HOMO - 1 Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE-BUTADIENE_TS_OPT.LOGy3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 16

Relative energy: -0.32755

Antisymmetric formed as the 'bonding' MO form the interaction of the LUMO of ethylene and the butadiene HOMO
|-
| HOMO Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE-BUTADIENE_TS_OPT.LOGy3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO17

Relative energy: -0.32532

Symmetric formed as the 'bonding MO' from the interaction of the ethylene HOMO and the Butadiene LUMO
|-
| LUMO Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE-BUTADIENE_TS_OPT.LOGy3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 18

Relative energy: 0.01733

Symmetric formed as the 'antibonding MO' from the interaction of the ethylene HOMO and the Butadiene LUMO
|-
| LUMO + 1 Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE-BUTADIENE_TS_OPT.LOGy3as6115</uploadedFileContents>
</jmolApplet>
</jmol>
| MO 19

Relative energy: 0.0366

Antisymmetric formed as the 'antibonding MO' from the interaction of the ethylene LUMO and the Butadiene HOMO
|}

Examination of the MOs of the TS exemplifies the principle of conservation of orbital symmetry; that is that only orbitals of the same symmetry can linearly combine. This can be explained by considering the orbital overlap integral, as for an overlap between orbitals of different symmetry (i.e. symmetric-asymmetric interaction) there will be equal amounts of in-phase (constructive) overlap and out-of-phase (destructive) overlap leading to a net zero overlap, hence the overlap integral for such an interaction is therefore zero. The overlap of orbitals of the same symmetry (i.e. symmetric-symmetric and asymmetric-asymmetric) have a non-zero overlap integral, as there will be either a net in-phase or out-of-phase interaction. The LUMO of ethylene and the butadiene HOMO are both asymmetric and therefore can linearly combine to generate the two asymmetric MOs of the TS (MO16 and MO19). Conversely, the Ethylene HOMO and Butadiene LUMO are symmetric can linearly combine to give the two symmetric MOs of the TS (MO17 and MO18).

===C-C bond lengths===

====For optimized reactants:====

Throughout the course of the Diels-Alder reaction the bond lengths of all C-C bonds change due to the changes in hybridisation of some of the carbons and the changes in all the bond orders, and as two additional sigma bonds are formed by the cycloaddition. The data listed below demonstrates the changes in bond lengths that occur on going from reactants to TS to product.

Ethylene C-C bond length = 1.33 Å

Butadiene central C-C bond length = 1.46 Å

Butadiene terminal C-C bond lengths = 1.34 Å

====At the optimised transition State:====

Ethylene C-C bond length = 1.38 Å

Butadiene central C-C bond length = 1.41 Å

Butadiene terminal C-C bond lengths = 1.38 Å

Partly formed new C-C bonds = 2.11 Å

====For the optimized product====
[[File:as6115-Labelled-cyclohexene.PNG |thumb|right|200px|Figure 3: Cyclohexene product labelled]]

Ethylene C-C bond length (C4-C5) = 1.54 Å

Butadiene central C-C bond length (C1-C2)= 1.34 Å

Butadiene terminal C-C bond lengths (C2-C3 & C6-C1) = 1.50 Å

Newly formed bonds (C3-C4 & C5-C6) = 1.54 Å

Typical C-C bond lengths:

C(sp<sup>3</sup>)-C(sp<sup>3</sup>) = 1.54 Å

C(sp<sup>2</sup>)-C(sp<sup>2</sup>) = 1.50 Å

C(sp<sup>3</sup>)-C(sp<sup>2</sup>) = 1.34 Å

Carbon Van der Waals radius = 1.70 Å

The C-C bond lengths in the optimised reactants and product are as expected. The C-C bond ethylene is 1.33 Å (very close to close to the typical alkene C-C sp<sup>2</sup>-sp<sup>2</sup> double bond length of 1.34Å). During this reaction, the carbon atoms (carbon atoms 4 and 5, see figure 3) of the ethylene dienophile goes from a double bond C(sp<sup>2</sup>)-C(sp<sup>2</sup>) to a single C(sp<sup>3</sup>)-C(sp<sup>3</sup>) and therefore lengthens as the reaction progresses. The C4-C5 bond length is 1.38Å which is intermediate between the shorter C-C single bond length in the optimised TS. The C4-C5 bond length in the cyclohexene product 1.54 Å, very similar typical C(sp<sup>3</sup>)-C(sp<sup>3</sup>) bond lengths. The newly formed C-C bonds in product is also at the typical C(sp<sup>3</sup>)-C(sp<sup>3</sup>) bond length and in the TS the interatomic distances between these carbon atoms (C3-C4 and C5-C6) is within the two times the van der Waals radius of carbon which indicates that there is an interaction between these two carbon atoms in the TS of the [4+2] cycloaddition. The central C-C bond of butadiene is broadly similar to typical values for a C-C single bond between two sp<sup>2</sup>hybridised carbon atoms (1.50 Å). This bond becomes progressively shorter in the reaction as in the TS the value is intermediate between the C-C bond length in the reactant and that of the C=C of an alkene, and this illustrates how the two carbon atoms come closer together in this reaction to form the π bond in the cyclohexene product (C1-C2 bond length). Like the ethylene C-C bond, the terminal C-C bond of butadiene has the typical alkene C=C bond length, and this bond lengthens as the reaction progresses with a values in intermediate of the short the C=C alkene bond and that of the typical C(sp<sup>3</sup>)-C(sp<sup>2</sup>) single bond length, at the transition state. In the product, this C-C bond length (C2-C3 and C1-C6) is as expected for a typical C(sp<sup>3</sup>)-C(sp<sup>2</sup>) length (1.50 Å).

===Vibration at the reaction path for the transition state===

{| class="wikitable"
! [[File:AS6115Ethene-butadiene-ts-vibration1.gif |centre|x400px| IRC animation]]
|-
| Figure 4 Animation of vibration of TS at the reaction path
|}

The negative frequency at -949.20 cm<sup>-1</sup> in the TS of this reaction corresponds to the vibration at the reaction path. This negative vibration is due to the negative force constant at the TS (since the force constant is related to the second derivative and at the TS, a maximum point along the reaction path, the second derivative is negative). This vibration is animated above, figure 4, and appears to represent bond formation, and provides evidence that the bond formation in this reaction is synchronous and therefore that the cycloaddition reaction is concerted.

===LOG files===

Optimised ethylene = [[File:ETHENE_OPT_MIN.LOG-y3as6115]]

Optimised butadiene = [[File:y3as6115BUTADIENE_OPT_MIN.LOG]]

Optimised TS = [[File:ETHENE-BUTADIENE_TS_OPT.LOGy3as6115]]

Optimised cyclohexene = [[File:AS6115CYCLOHEXADIENE_MIN.LOG]]

==Excercise 2: Diels-Alder reaction of cyclohexadiene and 1,3-dioxazole==

[[File:AS6115Excercise2scheme.png |thumb|centre|400px|Figure 5: Reaction scheme for the Diels-Alder reaction between 1,3-dioxole and cyclohexa-1,3-diene]]
===MOs===

For this exercise, the endo and exo reaction pathways of the Diels-Alder reaction between 1,3-dixole and cyclohexa-1,3-diene where investigated. The method employed was to first build and optimise the structures of the products and then break the two C-C bonds which formed during the reaction and freeze them at a distance of 2.2 Å, to give the exo and endo guess TS. These guess TSs where then minimised before being optimised to give the final optimised TS. In this exercise, all minimisation and TS optimisations where first preformed using PM6 method, and then using the result optimised at B3LYP level. The IRC calculations where performed at the PM6 level using the PM6 optimised TS as the input, as the corresponding IRC calculations at the B3LYP level have a significantly long run time.

{|
|[[File:AS6115-Endo-ts-mo-diagram.PNG |thumb|centre|425px|Figure 6: MO diagram of the endo transition state]]
|[[File:AS6115Exo-ts-mo-diagram1.PNG |thumb|centre|450px|Figure 7: MO diagam of the exo transition state]]
|}
The MO diagrams for the endo (figure 6) and exo (figure 7) TSs is broadly similar to the MO diagram for exercise 1, with the TS orbitals being higher in energy relative to the reactant MO levels. In a normal electron demand process the diene HOMO is higher in energy than the dienophile HOMO, and the diene HOMO-dienophile LUMO energy gap is smaller compared to the converse dienophile HOMO-diene LUMO energy gap. However, in this reaction the HOMO of the 1,3-dioxole (dienophile) is higher in energy than the cyclohexa-1,3-diene (diene) HOMO, and this means that the reaction is an inverse electron demand Diels-Alder. This is because the dienophile is relatively electron rich, as the oxygen atom substituents can donate electron density (via lone pairs in valence p orbitals) in to the alkene π bond, thus raising the orbital energy levels of the dienophile. Again, this reaction obeys the principle of orbital symmetry.

Additionally it is noticeable that the energy levels of the endo and exo transition state are different. For example the TS HOMO (MO41) for the endo TS is lower in energy than that of the exo transition state. This result is to be expected since the exo TS is higher in energy than the endo, as the endo TS has stabilising secondary orbital interactions.

The secondary orbital interaction in the endo TS can be seen when viewing the TS MOs (see figure 8), as in addition to the main frontier MO interactions, the oxygen p-orbitals interact with the back of the π-orbitals of the diene component, which provides an additional stabilising factor. This lowers the reaction barrier for the reaction, relative the reaction forming the exo product.

====Reactants====

{| class="wikitable"
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115CYCLOHEXADIENE MIN B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115DIOXAZOLE MIN B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| HOMO of Cyclohexadiene
| HOMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115CYCLOHEXADIENE MIN B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115DIOXAZOLE MIN B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| LUMO of Cyclohexadiene
| LUMO of 1,3-Dioxole
|}

====Endo Transition-State====

{| class="wikitable"
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO-TS HOMO
| ENDO-TS LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO-TS HOMO - 1
| ENDO-TS LUMO + 1
|}

====Exo Transition State====

{| class="wikitable"
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115EXO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115EXO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| EXO-TS HOMO
| EXO-TS LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115EXO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>AS6115EXO_TS_OPT_B3LYP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| EXO-TS HOMO - 1
| EXO-TS LUMO + 1
|}

===Thermochemistry===

{| class="wikitable"
! Species
! Sum of electronic and thermal free energies (Hartee/particle)
|-
| 1,3-Dioxole
| -233.321
|-
| Cyclohexa-1,3-diene
| -267.068
|-
| Endo Transition State
| -500.332
|-
| Exo transition state
| -500.329
|-
| Endo product
| -500.419
|-
| Exo product
| -500.417
|}

{| class="wikitable"
! Reaction product
! Reaction Barrier (KJ / mol)
! Reaction Energy (KJ/mol)
|-
| Endo
| 151.04
| -76.18
|-
| Exo
| 158.86
| -72.59
|}

The thermochemistry section form the log file output of optimisation calculations contained the sum of electronic and thermal free energies which where subsequently used to determine the reaction barriers and reaction energies. The values for the reaction barriers and reaction energies for both the endo and exo reaction pathways are summarised in the above table. The results reveal that the endo reaction has a lower reaction barrier and a larger reaction energy (i.e. the endo product is lower in energy), compared to the exo reaction, thus the endo product is both the kinetic and thermodynamic product. The smaller activation energy for the formation of the endo product is due to the presence of stabilising secondary orbital interactions in the endo TS (which are absent in the exo TS), which means the product is kinetically favoured, . The endo product is the more stable product because it is less sterically encumbered than the exo. This because even though the exo product has the newly formed C-C in an equatorial position, they are in relatively close proximity to the CH2-CH2 bridge which results in steric clashes with the fused 5 membered ring (originating from the 1,3-dioxole). In the endo product, the 5-membered ring is in close proximity to a CH=CH bridge, and therefore experience less steric repulsion, making the more stable thermodynamically favoured product (see figure 9). Also, the greater steric repulsion may be an additional factor for the higher activation energy required for the exo relative to the endo Diels-Alder reaction.

[[File:AS6115Endo-ts-2nd-orb-inter.png |thumb|right|200px|Figure 8: MO41 of the endo transition state, displaying secondary orbital interactions]]

{| class="wikitable"
! Figure 9: Structue of exo and endo prodcut
|-
| [[File:AS6115-Unhindered-endo.PNG |thumb|center|200px|]]
|-
| Endo product
|-
| [[File:AS6115-Hindered-exo.PNG |thumb|center|200px|]]
|-
| Exo product
|}

===LOG files===

Optimised 1,3-Dioxole = [[File:AS6115DIOXAZOLE MIN B3LYP.LOG]]

Optimised cyclohexa-1,3-diene = [[File:AS6115CYCLOHEXADIENE MIN B3LYP.LOG]]

MO energy levels of reactants = [[File:AS6115REACTANTS_ENERGY.LOG]]

Optimised Endo TS = [[File:AS6115ENDO_TS_OPT_B3LYP.LOG]]

Optimised Exo TS = [[File:AS6115EXO_TS_OPT_B3LYP.LOG]]

Optimised Endo product = [[File:AS6115ENDO_PRODUCT_MIN_B3LYP.LOG]]

Optimised Exo product = [[File:AS6115EXO_PRODUCT_MIN_B3LYP.LOG]]

==Excercise 3:o-xylylene sulfur dioxide cycloadditions: Diels-Alder v. Cheletropic==

[[File:AS6115Excercise3scheme1.png|thumb|centre|300px|Figure 10: Reaction Scheme for the different possible cycloaddition reactions between SO2 and the exocyclic diene unit of o-xylylene]]

For this experiment the TSs of different possible pericyclic (figure 10) reactions were located and optimised at the PM6 level. The method used to obtain the TS was to firs build and optimise the products of each of these reactions, individually, then break and freeze the bonds which form as a result of the cycloaddition in order to generate a relatively accurate guess TS. From the optimised TSs the IRC calculations.

From the output (log files) of the optimisation calculation the free energy values for the reactants, products and TSs were collated and used to determine the reaction barriers and energies for each reaction pathway (see tables below).

===Thermochemistry===

[[File:AS6115Reaction profile 1.png |thumb|centre|500px|Figure 11: Reaction profile for the different possible cycloaddition reactions between o-xylylene and the exocyclic diene unit of o-xylylene, with reaction barriers and energies displayed]]

The reaction profile (figure 11) illustrates the data shown in the tables below. The endo product is the kinetic product ads it has the lowest reaction barrier; this is primarily due to stabilising secondary orbital interactions in the endo TS. Also the endo product has a slightly larger reaction energy than the exo product, indicating the endo product is more thermodynamically favourable than the exo. The cheletropic reaction has the highest activation energy of the pathways but also has the highest reaction energy, which means that the cheletropic product is the less kinetically favourable but more thermodynamically favourable than either the endo or exo Diels-Alder. The cheletropic reaction has the highest activation energy because the cheletropic TS is much higher in energy than the endo or exo Diels-Alder TS. This difference can be attributed to the fact that in the cheletropiuc reaction the TS involves forming a 5-membered ring which is more strained and therefore less stable than the 6-membered chair-like TS for the Diels-Alder reactions. S=O bonds are relatively strong and therefore the fact that the cheletropic reaction has two S=O bonds means it is lower in energy compared to the endo and exo products of the Diels-Alder reaction in which one of the two S=O bonds are broken. This explains why the cheletopic reaction is the thermodynamically favoured product.

{| class="wikitable"
! Species
! Sum of thermal and electronic free energies (Hartee/Particle)
|-
| Sulfur dioxide
| -0.118614
|-
| o-Xylylene
| 0.178112
|-
| Endo Transition State
| 0.090562
|-
| Exo Transition state
| 0.092078
|-
| Cheletopic Transition State
| 0.099062
|-
| Endo Product
| 0.021697
|-
| Exo Product
| 0.023829
|-
| Cheletropic reaction
| 0.000005
|}

(Your exo product hasn't fully converged to a minimum. You need to check your geometries for imaginary frequencies [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 10:26, 6 March 2018 (UTC))

{| class="wikitable"
! Reaction Product
! Reaction Barrier (KJ/mol)
! Reaction energy (KJ/mol)
|-
| Endo
| 81.56
| -99.24
|-
| Exo
| 85.54
| -93.65
|-
| Cheletrophic
| 103.87
| -156.20
|}

As a result of the Diels-Alder and Cheltropic reaction the 6-membered ring of the xylylene reactant is converted into an aromatic benzene ring. The aromatisation of the xylylene ring is a thermodynamic major driving force for these reactions, which explains why the o-xylylene is relatively unstable, as it is readily converted to an aromatic product, as demonstrated by the IRC animations below.

===IRC Paths===

{| class="wikitable"
! Endo pathway
! Exo pathway
! Cheletrophic
|-
| [[File:AS6115Endo reactionex3.gif |left|x550px| IRC animation]]
| [[File:AS6115EXo_reactionex3.gif |left|x400px| IRC animation]]
| [[File:AS6115Cheletrophic reaction.gif |left|x450px| IRC animation]]
|-
|}

===Alternative Diels-Alder reaction===

[[File:AS6115Excercise3scheme2.png |thumb|centre|300px|Figure 12: Reaction Scheme showing the exo and endo products of the Diels Alder reaction between sulphur dioxide and the diene unit with the 6-membered ring of o-xylylene]]

In addition to the exocyclic diene unit utilised for the Cheletropic and Diels-Alder reactions describe above, there is a second s-cis diene unit with the xylylene ring which can undergo a Diels-Alder reaction (figure 12) with sulphur dioxide. The same procedure used to locate was used to locate the TS for the endo and exo pathway for this alternative Diels-Alder reaction, and the subsequent energetic analysis, summarised in the tables below.

{| class="wikitable"
! Species
! Sum of thermal and electronic free energies (Hartee/Particle)
|-
| Sulfur dioxide
| -0.118614
|-
| o-Xylylene
| 0.178112
|-
| Endo Transition State
| 0.090562
|-
| Exo Transition state
| 0.092078
|}

{| class="wikitable"
! Reaction Product
! Reaction Barrier (KJ/mol)
! Reaction energy (KJ/mol)
|-
| Alternative Endo
| 108.09
| 16.04
|-
| Alternative Exo
| 119.61
| 20.50
|}

The data shows that this alternative Diels-Alder reaction is kinetically and thermodynamically unflavoured. Both the endo and exo TSs are higher in energy than the TSs for the cheletropic and Diels-Alder reactions, with the exocyclic diene of Xylylene. The reaction barriers for the alternative Diels-Alder reaction are very high as the approach trajectory of the sulfur dioxide to the cis-diene within the xylylene ring is sterically hindered, compared to the exocyclic diene which is more sterically accessible. Also the reaction is thermodynamically unfavourable as the reaction energies are positive (both exo and endo pathways are endothermic). This is because this Diels-Alder reaction doesn’t benefit from the aromatisation of the o-xylylene ring.

===LOG files===
Optimised sulfur dioxide = [[File:AS6115SO2_MIN.LOG]]

Optimised o-xylylene = [[File:As6115O-XYLYLENE_MIN.LOG]]

Optimised endo TS = [[File:AS6115ENDO_TS_OPT.LOG]]

Optimised exo TS = [[File:AS6115EXO_TS_OPT.LOG]]

Optimised Cheletropic TS = [[File:AS6115CHELETROPHIC_REACTION_TS_OPT.LOG]]

Optimised endo Product = [[File:AS6115ENDO_PRODUCT_MIN_PM6.LOG]]

Optimised exo Product = [[File:AS6115EXO_PRODUCT_MIN.LOG]]

Optimised Cheletropic Product = [[File:AS6115CHELETROPIC_PRODUCT_MIN.LOG]]

Alternative Diels-Alder exo TS = [[File:AS6115ALT-DA_EXO_TS_OPT.LOG]]

Alternative Diels-Alder endo TS = [[File:AS6115ALT-DA_ENDO_TS_OPT.LOG]]

Alternative Diels-Alder exo product = [[File:AS6115ALT-DA_EXO_PRODUCT_MIN.LOG]]

Alternative Diels-Alder endo product = [[File:AS6115ALT-DA_ENDO_PRODUCT_MIN.LOG]]

==Extensions==
===Electrolytic ring opening/closure===
[[File:AS6115Ext1scheme1.png |thumb|centre|400px|Figure 13: Reaction scheme for the electrocylic ring closing/opening reaction between 3,4-dichlorocyclobut-1-ene and (2Z,4E)-2,5-dichlorohexa-2,4-diene]]

The 4π-electrocyclic ring opening/closing reaction which interconverts 3,4-dichlorocyclobut-1-ene and (2Z,4E)-2,5-dichlorohexa-2,4-diene was investigated. The ring open form was first built in Gaussian and minimised, and then the carbon atoms between which the bond forms during the ring closing reaction had their coordinates frozen. This guess-TS was then optimised at the PM6 level. From this an IRC calculation was run (animation shown below). The same analysis of reaction barriers and reaction energy as done in exercises 1 and 2 was performed from this reaction. (Please note that the activation energy and reaction energy quoted in the table is specifically for the ring-opening electrocyclic reaction.)

{| class="wikitable"
! [[File:AS6115-Electrocyclic-movie2.gif |centre|x400px| IRC animation]]
|-
| Figure 14 Animation the elctrocyclic ring closing reaction
|}

As expected the ring open diene form is more stable than the cyclobutene. This is two be expected as the 4-membered ring is highly strained (it suffers from significant angle strain and torsional strain). Also the high torsional strain means that the two chlorine substituents are locked in the cis conformation and therefore the molecule also suffers from steric strain since the chlorine atoms are relatively large.

{| class="wikitable"
! Species
! Sum of thermal and electronic free energies (KJ/mol)
|-
| (2Z,4E)-2,5-dichlorohexa-2,4-diene
| 129.8514108
|-
| Transition State
| 326.2969913
|-
| 3,4-dichlorocyclobut-1-ene
| 177.5923287
|}

{| class="wikitable"
! Reaction Barrier (KJ / mol)
! Reaction Energy (KJ/mol)
|-
| 148.70
| -47.74
|}

The reaction energy is negative which indicates that the electrocyclic ring opening is exothermic and therefore thermodynamically favourable. This is to be expeected since the ring opening process relieves the ring strain and forms the less sterically strained diene product in which the chlorine atoms are further apart.

From analysis of the stereochemistry of the products and reactants form the IRC, it can be stated that this electrocyclic reaction is conrotation (i.e. the two chlorine substituents will rotate in the same direction during the reaction). This can be explained by considering the Woodward-Hoffman rules. The Woodward-Hoffman rules is based on the principle of conservation of orbital symmetry, and states that for a thermally allowed pericyclic reaction the number of components with the correct number of which satisfy: (4q +2)s + (4r)a must be odd. Where q and r are integers and the susbscript s represents suprafacially interacting components and a represents antrafacial components. For this electrocyclic reaction can be considered as being a single component with four π-electrons and as such this means it must interact antarafacially for this reaction to be thermally allowed (see figure 15). This antrafacial interaction can only be achieved via a conrotatory mechanism. Figure 15 shows how the it is necessary for the HOMO of the diene to undergo conrotation in order for to overlap in such a fashion to form the new C-C σ bonding orbital, in the cyclobutene product.

[[File:AS6115Ext1scheme2.png |thumb|centre|400px|Figure 15: Schematic illustrating the conrotatory ring closing mechanism]]

The frontier MOs for the reactant, TS and product for this electrocyclic reaction are displayed in the table below. The HOMO and LUMO of 2,5-dichlorohexa-2,4-diene are similar to that of butadiene, allbeit with additional contribution from the chlorine atoms. Comparing the HOMO of 2,5-dichlorohexa-2,4-diene to the HOMO of the TS, seems to support the Woodward-Hoffman analysis that this reaction proceeds with conrotation. However the frontier MOs of the TS and 3,4-dichlorocyclobut-1-ene are quite complicated which makes analysis difficult. When looking at the energies it can be seen that the HOMO of the TS is higher in energy than that of the reactant and products, which is to be expected since the TS is the highest energy point in the IRC, however the opposite trend is observed for the LUMOs.

{| class="wikitable"
! Species
! HOMO
! LUMO
|-
| (2Z,4E)-2,5-dichlorohexa-2,4-diene
| [[File:AS6115Electrocyclic-dine-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.3574
| [[File:AS6115Electrocyclic-dine-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.01145
|-
| Transition State
| [[File:AS6115Electrocyclic-TS-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.33726
| [[File:AS6115Electrocyclic-TS-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.02386
|-
| 3,4-dichlorocyclobut-1-ene
| [[File:AS6115Electrocyclic-cycle-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.38986
| [[File:AS6115Electrocyclic-cycle-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.00382
|}

===LOG files===

Optimised (2Z,4E)-2,5-dichlorohexa-2,4-diene = [[File:AS6115EXT1-RING-OPEN-MIN.LOG]]

Optimised Transition state = [[File:As6115-Ext1CORRECT-TS-OPT.LOG]]

Optimised 3,4-dichlorocyclobut-1-ene = [[File:AS6115CORRECT(2Z4E)-25-DICHLOROHEXA-24-DIENE-MIN.LOG|AS6115CYCLOBUTENE.LOG]]

===Claisen Sigmatropic rearrangement===
[[File:AS6115Extension1scheme1.png |thumb|centre|400px|Figure 16: Reaction Scheme of the Claisen rearrangement between 3-chloro-3-(vinyloxy)prop-1-ene and (E)-5-chloropent-4-enal]]

The claisen rearrangement is a [3,3]-sigmatropic rearrangement reaction which converts 3-chloro-3-(vinyloxy)prop-1-ene to (E)-5-chloropent-4-enal was also investigated in this experiment. The method used the TS was to directly carry out a TS (Berny) optimisation of a guess-TS for the sigmatropic reaction (a chair-like structure) at the PM6 level. Following this an IRC calculation was run. From the initial and final frame of the IRC reactant and product of the Claisen (i.e. the allyl vinyl ether and unsaturated aldehyde) was obtained and optimised.

{| class="wikitable"
! [[File:AS6115Clasien-film1.gif |centre|x400px| IRC animation]]
|-
| Figure 17 Claisen rearrangement IRC
|}

{| class="wikitable"
! Species
! Sum of thermal and electronic free energies (KJ/mol)
|-
| 3-chloro-3-(vinyloxy)prop-1-ene
| 82.12887106
|-
| Transition State
| 222.5397832
|-
| (E)-5-chloropent-4-enal
| 33.55569021
|}

{| class="wikitable"
! Reaction Barrier (KJ / mol)
! Reaction Energy (KJ/mol)
|-
| 140.41
| -48.57
|}

The data in the tables above reveal that the aldehyde product is more stable than the allyl vinyl ether. This is essentially due to the fact that the C=O bond is stronger than the C=C bond. (Please note the values for the reaction barrier and reaction energy are for the sigmatropic rearrangement going from the 3-chloro-3-(vinyloxy)prop-1-ene to the (E)-5-chloropent-4-enal). The reaction is exothermic, as the reaction energy is negative, and as it is thermodynamically favourable to form the aldehyde product.

The alkene in the aldehyde product has E-stereochemistry this can be explained from the analysis of the Claisen TS. The transition state has a chair like structure and the large chlorine substituent prefers to adopt a pseudo-equatorial position, and therefore proceeds to form the E-alkene product (see figure 17).

{| class="wikitable"
! Species
! HOMO
! LUMO
|-
| 3-chloro-3-(vinyloxy)prop-1-ene
| [[File:AS6115Claisen-ether-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.36103
| [[File:AS6115Claisen-ether-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.00247
|-
| Transition State
| [[File:AS6115Claisen-TS-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.31763
| [[File:AS6115Claisen-TS-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.01767
|-
| (E)-5-chloropent-4-enal
| [[File:AS6115Claisen-CHO-HOMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.36658
| [[File:AS6115Claisen-CHO-LUMO.png |centre|x200px| IRC animation]]
Relative Energy: -0.00822
|}

The frontier MOs of the reactant, TS and product for this claisen rearrangement along with their corresponding relative energies are listed in the table above. The MOs for this system are quite complex and it is difficult to discern how the frontier MOs develop on going from the allyl vinyl ether through the TS to the γ,δ-unsaturated aldehyde. When considering the relative energies of the frontier MOs the trend observed, is the same as that of the electrocyclic reaction, with the TS HOMO being higher in energy than the reactant and product HOMOs, whilst the TS LUMO is lower in energy than the LUMO of the reactant and product.

===LOG files===

Optimised 3-chloro-3-(vinyloxy)prop-1-ene = [[File:AS6115VINYL-ALLYL-ETHER-MIN.LOG]]

Optimised (E)-5-chloropent-4-enal = [[File:AS6115UNSATURATED-ALDEHYDE-MIN.LOG]]

Optimised TS = [[File:AS6115CLAISEN3-GUESS_TS.LOG]]

==Conclusion==

Overall this experiment used relatively complex computational techniques on Gaussian to locate the TS structures for a variety of different pericyclic reactions, as well as reveal more information about the reactions. In exercise 1 a simple Diels-Alder reaction was investigated and the MOs of the TS and reactants were explored.

In exercise 2 the endo and exo reaction pathways of an inverse electron-demand Diels-Alder was studied and again the frontier MOs of the system were considered. Also reaction barriers and reaction energies where calculated, which revealed the endo product was both the kinetic and thermodynamic product of the reaction.

In exercise 3, a range of different possible cycloaddition reactions which can take place between o-xylene and sulfur dioxide where considered and compared, in terms of activation energies and reaction energies to probe how thermodynamically and kinetically favoured each pathway is.

In addition, further work was carried out to investigate applications of these techniques to other pericyclic reactions. This included the elucidation that the electrocyclic ring opening/closing reaction was conrotatory, in accordance with the Woodward-Hoffman rules. Furthermore, an evaluation of a [3,3]-sigmatropic rearrangement TS helped reveal the stereoselectivity of the reaction.

Ultimately, the confidence that can be placed in the findings of this experiment is limited by the accuracy of the computational methods used. The experiment could be improved by using more accurate methods (e.g repeating optimisation calculations for excercises 1 and 3 at the B3LYP level). Additionally comparing the predictions of the in sillico model with experimental data would allow the validity of this computational experiment to be assessed.

Rep:JJR115 TS

2018-03-05T16:04:26Z

Tam10: /* Extension */

= <div style="text-align: center;">Y3C Transition States and Reactivity</div> =
== Introduction ==

This lab explored the different computational methods involved in the location and characterisation of numerous Diels-Alder reactions. The reactions explored are as follows:

* Reaction of Butadiene with Ethylene
* Reaction of Cyclohexadiene and 1,3-Dioxole
* Diels-Alder Vs Cheletropic

When locating and characterising the transition states of these larger molecules, it is no longer possible to use fitted formulae for the energy, as changes in bond type and electron distribution are not accounted for. This lab uses MO orbital based methods to determine the location of the transition sates by solving the Schrödinger equation and rationalising potential energy surfaces.

=== Minima and Transition States ===

The transition state of a reaction is defined as the critical configuration of a reaction trajectory located at the highest point of the minimal energy pathway on the corresponding potential energy surface. It is characterised as one negative Hessian eigenvalue. The term 'critical' refers to the transition state having the highest probability of completing the reaction, bridging reactants and products <ref name="Transition state 1" />. The location of the transition state should lead to a committer of a half, with equal probability of falling to the reactants or products in a reaction system.

Potential-energy saddle points are used to determine the location of a transition state on a potential energy diagram. The transition state is defined mathematically as a first order saddle point on a potential energy surface. All the fource constants (eigenvectors) at the transition state structure can be found by diagonalising the hessian. Saddle points have at least one negative Hessian eigenvalues. The vibrational spectrum of a transition state would be characterized by one imaginary frequency, which arises when the second derivative of the potential energy surface (force constant) is negative. This effectively means that the energy is a maximum in one direction in configurational space, and a minimal in the orthogonal direction.

Calculating eigenvalues of the Hessian Matrix of second derivatives of the potential energy surface will identify minima, maxima and saddle points. For a general N-atom non-linear molecule with 3N-6 internal degrees of freedom, a potential energy surface can be constructed as a function of the degrees of freedom. At a minima on the PES, the second derivative can be equated to the vibrational force constant, where they are real and observable. By taking the hessian matrix eigenvalues, you can find the curvature of each dimension at a localised point. At a maximum (for example a transition state) the curvature will be negative in all degrees of freedom.

=== Introduction on Computational Methods ===

This lab involves the use of two electronic structure methods: PM6 and B3LYP. PM6 is a semi-empirical method, based on the Hartree-Fock methods, running a semi-empirical calculation using the PM6 Hamiltonian (with respect to electron position). This method is considered relatively inaccurate, as the calculation runs off of fewer integrals. This method requires knowledge of the transition state and often the wrong transition state will be found. experimental data is used to make up for the neglected integrals, and therefore many assumptions are taken, although this does make this method the fastest <ref name="Transition state 2" />. The average energy error for hydrogen, carbon, nitrogen and oxygen compounds is 4.6kcal/mol. In terms of bond lengths, the average error for this semi-empirical method is 0.025Å for the same elements.

The second electronic structures method used is the Density Functional theory (DFT) method; B3LYP. This method is a hybrid combination of DFT approximations while incorporating exact exchange from Hartree-Fock empirical theory. DFT improves upon Hartree-Fock calculations by including an approximation of the motions of electrons, that are only treated in an average sense in Hartree-Fock calculations <ref name="Transition state 3" />. The Hatree Fock calculation is used to account for the missing exchange correlation term. To this day, the B3LYP calculations are considered the most widely used theoretical tools in finding and characterizing transition states. The B3LYP method is considered much more accurate than the simplest PM6 calculations, and this experiment uses B3LYP to optimize PM6 generated geometries. (Noteː whenever a B3LYP optimisation is run in this investigation, the basis set is 6-31 and (d) has been chosen for the polarisation function).

The two computation calculation methods above will be used in the following three methods for finding and characterizing transition states in the experimentː

{| style="background-color:#F0FFFF;padding:0.5em;border:1px solid ##FFFFFF;"
|
{| style="background-color:#89CFF0;padding:0.1em;width:100%;"
| '''''Method 1 - Optimizing a Guess Transition state'''''
|}

This method runs a PM6 calculation and then a B3LYP optimization off of a 'guess' transition state. This assumes that the geometries selected are close to the transition state which is often not the case (wrong TS found, failed calculation, or multiple imaginary frequencies calculated). This method is very unreliable and therefore only used for small systems.

|}

{| style="background-color:#F4BBFF;padding:0.5em;border:1px solid ##FFFFFF;"
|
{| style="background-color:#C154C1;padding:0.1em;width:100%;"
| '''''Method 2 - Generating a guess transition state, freezing the reacting atoms and then optimizing using method 1'''''
|}

This method is an extension of the first method, drawing a guess transition state structure and freezing the reacting atoms. These atoms are therefore restricted from moving and the rest of the structure is minimized to find the transition state. By freezing the atoms, the system is deemed as close as possible to the true transition state and therefore optimization more reliable.
|}

{| style="background-color:#FFBCD9;padding:0.5em;border:1px solid #FFFFFF;"
|
{| style="background-color:#DE6FA1;padding:0.1em;width:100%;"
| '''''Method 3 - Start from reactants (or products, alter bond lengths and optimize via method 2.'''''
|}

This method is the most reliable of the three mentioned, as it does not require exact knowledge of the transition state structure/location. Theoretically this is a longer process, with more steps involved. The method starts from either the reactants or the product structures, and bond lengths are altered and optimized (using method 2) to find the true transition state.

|}

The three methods used can be summarized in the following diagram (fig. 1)ː

<br />

[[File:Methods JJR115.PNG|thumb|600px|center|Fig. 1 - Summary of methods used and relationship between them.]]

<br />

== Exercise 1 ==
=== Optimization, Frequency and IRC Calculation ===

Exercise 1 involves the optimization of the reaction between Butadiene with Ethene, in scheme shown in figure 2. This is a thermal [4+2] cycloaddition.

[[File:Butadiene_ethy_jjr115.PNG|thumb|center|Fig. 2. Reaction scheme of thermally allowed [4+2] cycloaddition reaction between butadiene and ethene]]

Both reactants and the transition state were optimized (energetically minimised) at the PM6 level. Method 2 of optimization was used, with the terminal carbons of the butadiene and ethene being frozen (two pairs of reacting atoms). The transition state structure was first optimized to a minimum as a 'frozen guess TS', and then unfrozen and reoptimised to the transition state. A frequency calculation was run and resulted in only one negative vibration corresponding to mode 1 at 948.68i cm-1. An IRC calculation was run in both directions (TS to products, TS to reactants). The graphs produced are shown below in figure 3, with the minima and transition state structures highlighted. This was deemed a successful, asymmetric IRC with the gradient set to zero at both minima of the reactants and products and the TS. The reactants are higher energy than the products (less stable) and so it can be concluded that this is an exothermic reaction, thermally allowed pericyclic reaction.

<br />

[[File:EX_1_IRC_JJR115.PNG|thumb|1200px|center|Fig 3. Annotated IRC graph for the reaction pathway between reactants and products passing through the transition state.]]

<br />

The product structure was optimized further to the same level as the other structures used in the calculation (PM6). The frequency analysis showed no negative vibrations, and therefore it can be concluded that the optimized product structure was indeed a minimum point (originally a negative vibration found, indicative of a saddle point, so the symmetry was broken and structure reoptimised to a minima).

=== Molecular Orbital Analysis ===

The MO's of the transition state were analysed when the correct TS was located and optimized, and used to construct the MO diagram below (figure 4). Jmols of the involved orbitals are displayed in the tables below. The interacting reactant MO's are also shown in the boxes either side of the MO diagram.

<br />

[[File:Ex_1_MO_diagram_jjr115_updated.PNG|thumb|1000px|center|Fig 4. Molecular Orbital Diagram for transition state in reaction between Butadiene and Ethene.]]

<br />

In the formation of bonding and anti-bonding molecular orbitals, atomic orbitals (or in this case, fragment orbitals) have to have the correct symmetry and similar energy for a meaningful overlap. The overlapping orbitals must therefore have the same nodal symmetry for a non zero overlap, defined by the symmetry operations of the orbitals. Fragment orbitals that do not have a similar energy/equivalent symmetry partner to overlap with, will not mix and therefore will remain non bonding. This would be classed as 'forbidden' overlap. It can be seen in the MO diagram in figure four that the fragment orbitals of equivalent symmetry (asymmetric with asymmetric, and symmetric with symmetric) form strong overlaps and therefore bonding and antibonding molecular orbitals.

The overlap integral is a term quantitatively measuring the overlap of atomic (or in this case fragment) orbitals. If the symmetry of two orbitals is the same and they overlap, there will be a finite region of overlap between their orbital wavefunctions and therefore the overlap integral will be non zero (constructive interference). If the orbitals do not overlap, the combination of these orbitals does not lead to the formation of a bonding and anti-bonding pair of molecular orbitals and therefore the overlap integral will equal zero (destructive interference). The magnitude of the overlap integral will be determined by the strength of overlap, which is dependent on the similarity of the orbital energies, spacial extent of the orbitals (the type of orbital involved) and the internuclear separation. This analysis also shows that this reaction proceeds via normal electron demand, because the HOMO<sub>butadiene</sub> - LUMO<sub>ethene</sub> energy gap is smaller than LUMO<sub>butadiene</sub> - HOMO<sub>ethene</sub> gap. Electron demand is explained further in exercise 2.

{| class="wikitable"
|-
|
{| style="border-spacing: 2px; border: 1px solid darkgray;"
|+ '''<u>Butadiene MO's</u>'''
|-
|- style="text-align: center;"
| style="border: 5px solid #E6FFEA;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -0.35900</title>
<size>300</size>
<script>frame 1.22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>OPTIMISATION_OF_BUTADIENE_2_JJR115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #E6FFEA;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = 0.01944</title>
<size>300</size>
<script>frame 1.22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>OPTIMISATION_OF_BUTADIENE_2_JJR115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- style="text-align: center;"
|'''''HOMO'''''||'''''LUMO'''''
|}
|
{| style="border-spacing: 2px; border: 1px solid darkgray;"
|+ '''<u>Ethene MO's</u>'''
|-
|- style="text-align: center;"
| style="border: 5px solid #F2CEF2;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -0.39224</title>
<size>300</size>
<script>frame 1.6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REOPT_FOR_JMOL_ETHENE_jjr115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #F2CEF2;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = 0.04252</title>
<size>300</size>
<script>frame 1.6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REOPT_FOR_JMOL_ETHENE_jjr115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- style="text-align: center;"
|'''''HOMO'''''||'''''LUMO'''''
|}
|}

{| style="border-spacing: 2px; border: 1px solid darkgray;"
|+ '''<u>Transition State MO's</u>'''
|-
|- style="text-align: center;"
| style="border: 5px solid #CEECF2;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -3.2755</title>
<size>300</size>
<script>frame 1.20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REOPRTIMISATION_TS_EX_1_jjr115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #CEECF2;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -3.2533</title>
<size>300</size>
<script>frame 1.20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REOPRTIMISATION_TS_EX_1_jjr115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #CEECF2;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = 0.01732</title>
<size>300</size>
<script>frame 1.20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REOPRTIMISATION_TS_EX_1_jjr115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #CEECF2;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = 0.03066</title>
<size>300</size>
<script>frame 1.20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REOPRTIMISATION_TS_EX_1_jjr115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- style="text-align: center;"
|'''''HOMO-1''''' || '''''HOMO''''' || '''''LUMO''''' || '''''LUMO+1'''''
|}

=== Bond Length Analysis ===

The bond lengths of the reactants, transition state and product were analysed in their optimized log files. The typical C-C Sp<sup>3</sup> bond length is around 1.54Å, and the typical Sp<sup>2</sup> C=C bond length is around 1.34Å. .<ref name="bond lengths" />

As the table shows below (Table 1), the range of bond lengths found in the optimizations lie in between a single bond and a double bond. On the transition state, these will correspond to partially formed single/double bonds as the pericyclic reaction proceeds (concerted mechanism via a cyclic transition state).

The curve on the right (Below, right) was included to highlight the bond changing process of two important bonds in the reaction, C3-C4 and C4-C5. C3-C4 starts the reaction as a double bond, but transitions into a single bond in the product. It can be seen from the graph the the bond lengthens to from 1.33 to 1.50Å, a clear lengthening of the bond from double to single. Note, the same trend is seen for bond C5-C6 by symmetry. At the same time, bond C4-C5 transitions from a 'single' bond (1.47Å) to a shorter double bond (1.34Å). In butadiene, the bond C4-C5 is already considered partially delocalised with the rest of the pi system, hence initially shorter than the typical C-C bond lengths stated above. In both of the bonds, we observe partial bond formation at the transition state. The single bonds adjacent to the pi bond in the cyclohexene structure are also shorter because one of the carbons in the bond is sp2 hybridised with more s character (hence shorter bond than expected). The transitioning of bond types described can be observed in the negative frequency vibration of the transition state, shown in the vibrational analysis section below.

{| class="wikitable"
|-
|
{| class="wikitable"
|+ Table 1. Bond Distances From PM6 Optimized Structures (Å)
|-
| style='background: #CEDAF2' |<u>Bonds</u>
| style='background: #CEDAF2' |<u>Ethene</u>
| style='background: #CEDAF2' |<u>Butadiene</u>
| style='background: #CEDAF2' |<u>Transition State</u>
| style='background: #CEDAF2' |<u>Product</u>
|-
| style='background: #E6F2FF' | '''C1-C2'''
| style='background: #E6F2FF' |1.3275
| style='background: #E6F2FF' |
| style='background: #E6F2FF' |1.3818
| style='background: #E6F2FF' |1.5345
|-
| style='background: #E6F2FF' | '''C2-C3 '''
| style='background: #E6F2FF' |
| style='background: #E6F2FF' |
| style='background: #E6F2FF' |2.1150
| style='background: #E6F2FF' |1.5371
|-
| style='background: #E6F2FF' | '''C3-C4 '''
| style='background: #E6F2FF' |
| style='background: #E6F2FF' |1.3334
| style='background: #E6F2FF' |1.3797
| style='background: #E6F2FF' |1.5008
|-
| style='background: #E6F2FF' | '''C4-C5 '''
| style='background: #E6F2FF' |
| style='background: #E6F2FF' |1.4708
| style='background: #E6F2FF' |1.4111
| style='background: #E6F2FF' |1.3370
|-
| style='background: #E6F2FF' |'''C5-C6 '''
| style='background: #E6F2FF' |
| style='background: #E6F2FF' |1.3334
| style='background: #E6F2FF' |1.3798
| style='background: #E6F2FF' |1.5009
|-
| style='background: #E6F2FF' |''' C6-C1 '''
| style='background: #E6F2FF' |
| style='background: #E6F2FF' |
| style='background: #E6F2FF' |2.1145
| style='background: #E6F2FF' |1.5372
|}
| [[File:Bond_length_graph_jjr115.PNG]]
|}

The partially formed bonds can be better understood by looking at carbon's van der Waals radius. The van der Waals radius of carbon is 1.70Å.<ref name="waals" />. The bonds that are partially made in the transition state are C6-C1 and C2-C3, with the transition state bond lengths being 2.1145Å and 2.1150Å respectively. These lengths are less than double the carbon van der Waals radii (3.4Å) which indicates the presence of partially formed bonds and electron cloud sharing (meaningful orbital overlap̠).

=== Vibration Analysis ===

<jmol>
<jmolApplet>
<color>white</color>
<title>Vib = -948.38cm-1</title>
<size>300</size>
<script>frame 1.21; vibration 1; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>REOPRTIMISATION_TS_EX_1_jjr115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

This is the only imaginary at the transition state, and corresponds to the partial formation of three single bonds (from C=C) and one double bond (from C-C). This vibration also illustrates the changes in bond length described in the section above. As the reacting atoms become closer together, the double bonds can be seen elongating, and the single bond can be seen contracting. It can also be seen that the bond making process is synchronous, with the atoms involved in bridging the two molecules together moving simultaneously. This is expected as this reaction is pericyclic, that follows a concerted mechanism by nature.

=== Log Files for Exercise 1===

*[[File:OPTIMISING_ETHENE_JJR115_LOG.LOG]]

*[[File:OPTIMISATION_OF_BUTADIENE_2_JJR115.LOG]]

*[[File:PM6_OPT_FREQ_OF_PRODUCT_ex_1_jjr115.LOG]]

*[[File:PM6_OPT_FREQ_FROZEN_GUESS_TRANSITION_STATE_ex_1_jjr115.LOG]]

*[[File:REOPRTIMISATION_TS_EX_1_jjr115.LOG]]

*[[File:IRC_both_directions_ex_1_transition_state_PM6_JJR115.LOG]]

== Exercise 2 ==
This exercise involved the analysis of the reaction of Cyclohexadiene and 1,3-dioxole. This is a standard Diels-Alder cycloaddition with the production of two productsː the endo and the exo product (see figure 5 for scheme).

[[File:Dioxole_reaction_ex_2_scheme_jjr115.PNG|thumb|500px|center|Fig. 5 Scheme showing exo/endo approach to the diels-alder cycloaddition with cyclohexadiene and 1,3 dioxole.]]

In order to find and analyse the transition state, method 3 was employed. This was done by optimizing the product first to the PM6 level and then to the B3LYP/6-31G(d) level. The product structure was then altered (bond lengths/angles etc) to illustrate what aspects of the molecule changes throughout the reaction. The method and results for the exo/endo mechanisms are discussed below.

=== Locating the Transition States ===

The Exo product was drawn and optimised to the PM6 and further to the B3LYP level. The bonds formed during the pericyclic reaction were broken and the two fragments were separated to be about 2.2Å from each other. This 'guess' transition state was optimized to a minimum with frozen bonds (pairs frozen were the two pairs involved in bridging the two reactants together in the final product). When both levels of optimization were achieved, the whole structure was optimized to a transition state (PM6 and B3LYP calculations ran) with force constant calculations set to 'once'. A frequency calculation was run on the final B3LYP Optimized Exo transition state, and a single imaginary frequency was found at 530.83 icm-1.

<jmol>
<jmolApplet>
<color>white</color>
<title>Vib = -530.83cm-1</title>
<size>300</size>
<script>frame 1.21; vibration 1; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_TRANSITION_STATE_OPTIMISATION_UNFROZEN_B3LYP_EX_2_JJR115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The method used to find the exo transition state was repeated to find the endo transition state (see section above). The frequency analysis of the final B3LYP endo transition state found a single imaginary frequency at 520.92 icm-1.

<jmol>
<jmolApplet>
<color>white</color>
<title>Vib = -520.92cm-1</title>
<size>300</size>
<script>frame 1.33; vibration 1; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_TRANSITION_STATE_UNFROZEN_OPTIMISATION_B3LYP_EX_2_JJR115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=== Molecular Orbital Analysis of Both Transition States ===

In order to understand the energetics of this reaction, an IRC was run on the system. The results of this calculation were used to understand the relative energy differences between the reactant orbitals. An energy calculation was run off of the reactants structures found in the IRC. This meant the molecular orbitals of the reactants and the transition state could be mapped, along with their relative energy positions, as seen in the molecular diagram below. Noteː this diagram could be valid (orbital orientation/overlap) for both the exo and endo transition state. This molecular orbital diagram (Fig. 6) was built from the molecular orbital diagram in exercise one, using results from the energy calculation to alter the energies of the molecular orbitals.

<br />

[[File:TS_MO_diagram_ex_2_jjr115.PNG|thumb|1000px|center|Fig. 6 - Molecular Orbital Diagram for transition state in reaction between cyclohexadiene and 1,3-dioxole. (Enlarge picture for better clarity)]]

<br />

{| style="border-spacing: 2px; border: 1px solid darkgray;"
|+ '''<u>Endo Transition State MO's</u>'''
|-
|- style="text-align: center;"
| style="border: 5px solid #FBCEB1;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -0.19648</title>
<size>300</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_2_MO_ENDO_TRANSITION_STATE_UNFROZEN_OPTIMISATION_B3LYP_EX_2_JJR115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #FBCEB1;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -0.19051</title>
<size>300</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_2_MO_ENDO_TRANSITION_STATE_UNFROZEN_OPTIMISATION_B3LYP_EX_2_JJR115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #FBCEB1;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -0.00462</title>
<size>300</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_2_MO_ENDO_TRANSITION_STATE_UNFROZEN_OPTIMISATION_B3LYP_EX_2_JJR115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #FBCEB1;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = 0.1544</title>
<size>300</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_2_MO_ENDO_TRANSITION_STATE_UNFROZEN_OPTIMISATION_B3LYP_EX_2_JJR115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- style="text-align: center;"
|'''''HOMO-1''''' || '''''HOMO''''' || '''''LUMO''''' || '''''LUMO+1'''''
|}

<br />

{| style="border-spacing: 2px; border: 1px solid darkgray;"
|+ '''<u>Exo Transition State MO's</u>'''
|-
|- style="text-align: center;"
| style="border: 5px solid #89CFF0;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -0.19801 </title>
<size>300</size>
<script>frame 1.20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>B3LYP_OPT_FREQ_UNFROZEN_EXO_STATE_FOR_WIKI_MO_PRINT_JJR115_UNFROZEN_TRANSITION_STATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #89CFF0;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -0.18560</title>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>B3LYP_OPT_FREQ_UNFROZEN_EXO_STATE_FOR_WIKI_MO_PRINT_JJR115_UNFROZEN_TRANSITION_STATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #89CFF0;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = -0.00699</title>
<size>300</size>
<script>frame 1.20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>B3LYP_OPT_FREQ_UNFROZEN_EXO_STATE_FOR_WIKI_MO_PRINT_JJR115_UNFROZEN_TRANSITION_STATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="border: 5px solid #89CFF0;"|
<jmol>
<jmolApplet>
<color>white</color>
<title>E = 0.01019</title>
<size>300</size>
<script>frame 1.20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>B3LYP_OPT_FREQ_UNFROZEN_EXO_STATE_FOR_WIKI_MO_PRINT_JJR115_UNFROZEN_TRANSITION_STATE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- style="text-align: center;"
|'''''HOMO-1''''' || '''''HOMO''''' || '''''LUMO''''' || '''''LUMO+1'''''
|}

<br />

[[File:Ex_2_electron_demand_diagrams_jjr115.PNG|thumb|right|600px|Fig 7. Summary diagram showing relative orbital energy and effect on which frontier orbital interaction. (Enlarge picture for better clarity)]]

The relative energy of the orbitals show that this reaction is under inverse electron demand. A normal electron demand reaction would involve an electron rich diene and an electron poor dienophile, as illustrated in the diagram below. The electron donating group on the diene makes it electron rich molecule with higher energy molecular orbitals. The electron withdrawing group on the dienophile decreases the energy of the molecular orbitals. In terms of the frontier MO's, this means that the HOMO of the diene (filled) will interact with the empty LUMO of the dienophile, as they are closer in energy allowing for stronger overlap .<ref name="normal electron demand" />. In the inverse scenario, the electron poor diene has lower energy molecular orbitals, and the electron rich dienophile has higher energy molecular orbitals. In terms of our reaction, the alpha oxygen's on the 1,3 - dioxole molecule act as electron donating groups via π donation. These donate more electron density than the alkyl groups on the diene, making the dienophile electron rich and the diene electron poor. In this situation, the strongest orbital interaction will be found between the LUMO of cyclohexadiene and the HOMO of 1,3 dioxole, as they are most similar in frontier MO energy (see figure 7). This system is different to the system explored in exercise one, where the cycloaddition was under normal electron demand. This can be seen by comparing the relative energy differences between the HOMO-LUMO of the reacting species.

The picture below (Fig 8) is a screen shot of the gaussview Molecular Orbital analysis window for the reactant species. The IRC was calculated and the initial reactant frame was used for an energy calculation (PM6 level). This snapshot confirms the explanation above, because it is clear that the HOMO is largely localized on the dienophile.

[[File:Ex_2_exo_reactants_MO_showing_HOMO_localised_on_dienophile_jjr115.png|thumb|center|Fig. 8 screenshot showing HOMO of system localised on the dienophile.]]

The Gaussian calculations also allowed the comparison between the endo and the exo approaches, in terms of relative transition state molecular orbital energies. Table 2 shows the relative energies of the exo and endo transition state MO's.

{| class="wikitable"
|+ Table 2. Relative energies of exo and endo TS molecular orbitals.(E<sub>h</sub>)
|-
| style='background: #F2CEE0' |<u>Molecular Orbital</u>
| style='background: #F2CEE0' |<u>Exo Energy</u>
| style='background: #F2CEE0' |<u>Endo Energy</u>
|-
| style='background: #FFE6F2' | '''HOMO-1'''
| style='background: #FFE6F2' |-0.19840
| style='background: #FFE6F2' |-0.19648
|-
| style='background: #FFE6F2' | '''HOMO'''
| style='background: #FFE6F2' |-0.18616
| style='background: #FFE6F2' |-0.19051
|-
| style='background: #FFE6F2' | '''LUMO'''
| style='background: #FFE6F2' |-0.00763
| style='background: #FFE6F2' |-0.00462
|-
| style='background: #FFE6F2' | '''LUMO+1'''
| style='background: #FFE6F2' |0.00954
| style='background: #FFE6F2' |0.01544
|-
|}

From this it can be seen that the HOMO (and HOMO-1) of the endo transition state is lower in energy relative to the exo transition state. It would therefore be fair to say at this point that endo is the more favorable product for this reaction, because its transition state molecular orbitals are lower in energy. This is explored further in the following section.

=== Thermochemistry and Orbital Interaction Analysis ===

IRC calculations were run for both the endo and exo approach to ensure the correct transition state was located. For both reactions, the product and reactant minima had gradients of zero, and an appropriate transition state was found.

With this confirmed, the thermochemistry of each system was analysed. This was done by looking at the log files (attached below) of the B3LYP/6-31(g) optimised reactant, transition state and product structures. The 'sum of electronic and thermal free energies' were tabulated and compared for the three different structures of each reaction, in order to understand the thermodynamics of the system. The result can be seen in figure 9. Note: the energies given in the log files are in Hartree units, and were converted to kJmol<sup>-1</sup> with the conversion 1 Hartree = 2625.49 kJkJmol<sup>-1</sup>

[[File:Thermochemistry_reaction_profile_ex_2_jjr115.PNG|thumb|center|600px|Figure 9. Superimposed reaction profile for Endo and Exo mechanism approaches for cycloaddition of cyclohexadiene and 1, 3 dioxole.]]

As predicted from the relative MO energies above, the endo product is in fact the most stable product of the two. Although it is considered a more sterically hindered product (thermodynamically less stable), the endo pathway has a lower activation energy barrier and the product is also lower in energy. This can be explained by secondary orbital overlaps. The lone pairs on the oxygen atom on the 1,3 dioxole species stabilises the transition state via π overlap with the diene. I have illustrated this point in figure 10 and 11 using the HOMO molecular orbital of the endo transition state as an example. Figure 10 shows the screenshot from the optimised transition state HOMO MO, and figure 11 is a schematic to highlight the overlapping atomic orbitals. The exo product in general will be higher in energy due to steric clash with the bridging carbons in the final structure. The secondary orbital interaction does not occur in the exo transition state as the oxygen p orbitals are facing away from the diene HOMO.

{| class="wikitable"
|-
| [[File:Secondary_orbital_overlap_screenshot_jjr115.PNG|thumb|Fig. 10 - Screenshot of the HOMO MO from the gaussview MO analysis of the endo transition state, optimised to B3LYP.]]
| [[File:CORRECTED_DIAGRAM_secondary_orbital_overlap_HOMO_ex_2.PNG|thumb|Fig. 11 -Schematic diagram showing secondary orbital overlap for the endo transition state, the HOMO.]]
|}

=== Log Files for exercise 2 ===
'''Reactant files'''
*[[File:OPTIMISATION_DIENE_B3LYP_ex_2_jjr115.LOG]]
*[[File:OPTIMISATION_OF_DIENE__PM6_ex_2_jjr115.LOG]]
*[[File:OPTIMISATION_OF_DIOXOLE_B3LYP_ex_2_jjr115.LOG]]
*[[File:OPTIMISATION_OF_DIOXOLE_PM6_ex_2_jjr115.LOG]]

'''Exo files'''

*[[File:B3LYP_OPT_FREQ_UNFROZEN_EXO_STATE_FOR_WIKI_MO_PRINT_JJR115_UNFROZEN_TRANSITION_STATE.LOG]]
*[[File:EXO_FROZEN_TS_B3LYP_OPT_TO_MINIMUM_EX2__JJR115.LOG]]
*[[File:EXO_FROZEN_TS_PM6_OPT_TO_MINIMUM_EX2__JJR115.LOG]]
*[[File:EXO_PRODUCT_B3LYP_OPT_EX_2_JJR_115.LOG]]
*[[File:EXO_PRODUCT_PM6_OPT_EX_2_JJR_115.LOG]]
*[[File:EXO_TRANSITION_STATE_OPTIMISATION_UNFROZEN_PM6_EX_2_JJR115.LOG]]
*[[File:ICR_ON_REOPTIMISED_PM6_EXO_TS_EX_2_JJR115.LOG]]

'''Endo files'''

*[[File:ENDO_FROZEN_TRANSITION_STATE_OPT_TO_MIN_B3LYP_JJR115.LOG]]
*[[File:ENDO_FROZEN_TRANSITION_STATE_OPT_TO_MIN_PM6_JJR115.LOG]]
*[[File:ENDO_PRODUCT_B3LYP_OPTIMISATION_EX_2_JJR115.LOG]]
*[[File:ENDO_PRODUCT_PM6_OPTIMISATION_EX_2_JJR115.LOG]]
*[[File:ENDO_TRANSITION_STATE_UNFROZEN_OPTIMISATION_PM6_EX_2_JJR115.LOG]]
*[[File:IRC_ENDO_UNFROZEN_TRANSITION_STATE_PM6_STRUCTURE_TRIAL_4_EX_2_JJR115.LOG]]
*[[File:TRIAL_2_MO_ENDO_TRANSITION_STATE_UNFROZEN_OPTIMISATION_B3LYP_EX_2_JJR115.LOG]]

== Exercise 3 ==

This experiment investigates the energy and mechanistic differences between Diels-Alder and Cheletropic reactions of o-Xylylene and SO<sub>2</sub>. The two possible reaction routes are shown in the scheme below (fig. 12).

[[File:Ex_3_reaction_scheme_JJR115.PNG|thumb|600px|center|Fig. 12 - Scheme for cheletropic and Diels-Alder reactions of o-Xylylene and SO<sub>2</sub>]]

In terms of the diels-alder reaction, there are two possible sites for the reaction to occur (two distinct dienes on the o-Xylylene). These are shown in the schematic diagram figure 13.

[[File:Corrected_two_endo_exo_sites_jjr115.PNG|thumb|Fig. 13 - Diagram showing two sites for possible diels-alder reaction to occur.]]

The reactions run in this part of this experiment wereː
* Endo/Exo Diels-Alder reaction at site A of o-Xylylene
* Endo/Exo Diels-Alder reaction at site B of o-Xylylene
* Cheletropic reaction at site B of o-Xylylene

The third method (mentioned in the introduction) was used to locate and analyse the five transition states involved in this reaction. For each mechanism (2 x endo/exo pairs for the Diels Alder, and a cheletropic mechanism) the product was drawn and optimised to find the minimum energy conformation. The reacting bonds were then broken, and the two 'reactant' species (that resemble the transition state) were pulled apart. The atoms involved in the reaction were then frozen, and the rest of the transition state structure was minimised to the lowest energy structure. This was all done to a PM6 level for time constraints (therefore error in the results is assumed). Finally, the transition state structure was optimised to a transition state with the calculate force constant parameter set to 'once'. IRC calculations were then completed in order to compare the energetics of each reaction, whilst also confirming that the true transition states were found. The results are shown and discussed below.

=== IRC Results ===
''Noteː Click to view animation''

{| class="wikitable"
|+ '''<u>Site A Diels-Alder - IRC Animations </u>'''
|-
! style="background: #CEECF2; color: black;" | Exo
! style="background: #CEECF2; color: black;" | Endo
|-
|[[File:Site_A_Exo_IRC_Animation_BETTER_ANGLE_ex_3_jjr115.gif|500px]]
|[[File:Site_A_Endo_IRC_Animation_BETTER_ANGLE_ex_3_jjr115.gif|500px]]
|}

{| class="wikitable"
|+ '''<u>Site B Diels-Alder - IRC Animations </u>'''
|-
! style="background: #CEECF2; color: black;" | Exo
! style="background: #CEECF2; color: black;" | Endo
|-
|[[File:Site_B_Exo_IRC_Animation_ex_3_jjr115.gif|500px]]
|[[File:Site_B_Endo_IRC_Animation_ex_3_jjr115.gif|500px]]
|}

{| class="wikitable"
|+ '''<u> Cheletropic Reaction - IRC Animation </u>'''
|-
|[[File:Cheletropic_IRC_animation_ex_3_jjr115.gif|500px]]
|}

The animations above show the reaction pathway from reactants to products via the transition state for all five reaction mechanisms. To understand how favorable each reaction is, the energetics were analysed in the 'thermochemistry' section in each optimized structure (reactants, products, transition state). The 'sum of electronic and thermal free energies' value for each structure allowed the following (comparative) reaction pathway to be constructed.

An interesting side note can be observed from these IRC animations. The IRC's for the endo/exo Diels-Alder reactions at the terminal diene show considerable delocalisation with the rest of the molecule before reaction with the SO<sub>2</sub> molecule. This is the beginning of the electrocyclic reaction that can occur at the terminal alkenes, forming benzocyclobutene. The scheme is shown below (fig 14)ː

[[File:Screen_Shot_2018-02-27_at_09.58.59_jjr115.png|thumb|center|Fig. 14 - Reaction scheme of the intramolecular electroclyclic reaction of o-xylylene to butacyclobutene, taken from study <ref name="xylylene" />]]

A 2000 study <ref name="xylylene" />showed that the conrotatory pathway is the lowest energy pathway, lower than the disrotatory one. The stabilisation of the aromatic product (compared to the Kekulé type reactant with alternating bonds) means this reaction occurs readily, and so xylylene is deemed unstable.

''Noteː an extension would be to run these calculations, however this was not done due to time constraints. ''

(The delocalisation into an aromatic product is indeed the driving force (thermodynamic and kinetic) of these reactions. With an MO diagram or WH analysis, you should be able to show why it occurs via conrotation [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 15:31, 5 March 2018 (UTC))

=== Thermochemistry Results ===

[[File:Thermo_data_ex_3_jjr115.png|thumb|800px|Fig. 15 - Reaction pathway diagram showing relative energy of transition states in the 5 reactions investigated. Diagram is not drawn to scale, energy values calculated from Optimized structures.]]

From the thermochemical data (fig. 15) it can be concluded that the internal diene will react much less readily than the external alkene. The activation energy for these two Diel-Alder reactions are very large compared to the other reaction routes available. Both the exo and the endo routes of this reaction mechanism are endothermic, and therefore is not enthalpically favoured. When the reaction occurs on the external diene, an aromatic ring is produced, which is largely stabilising. When the internal diene reacts, it causes an increased strain on the conformation of the molecule as a whole, and the aromaticity is disrupted (the alkenes are less conjugated than the starting material).

When looking at the reactions occuring at Diene B (terminal alkene) it can be sen that although the cheletropic transition state is considerably higher in energy than the diels-alder reactions (larger activation energy), the product is in fact the most stable of the three. This is due to the fact that the strong S=O bond is not broken in the reaction. In terms of the two diels-alder reactions, the exo product is the thermodynamic product, whereas the endo is the kinetic product (will occur faster due to a lower energy transition state. This can be explained by secondary orbital interactions, with the external S=O bond tucked in closer to the rest of the molecule, allowing for some orbital overlap that reduces the energy of the transition state intermediate.

=== Log Files Exercise 3 ===

*[[File:REACTANT_SO2_PM6_OPT_EX_3_JJR115.LOG]]
*[[File:REACTANT_XYLYLENE_PM6_OPT_EX_3_JJR115.LOG]]

'''Diels-Alder at Site A'''

*[[File:SITE_A_ENDO_FROZEN_TS_PM6_TO_MINIMUM_EX_3_JJR115.LOG]]
*[[File:SITE_A_ENDO_IRC_CALC_TS_PM6_EX_3_JJR115.LOG]]
*[[File:SITE_A_ENDO_PRODUCT_OPTIMISATION_PM6_EX_3_JJR115.LOG]]
*[[File:SITE_A_ENDO_UNFROZEN_TS_PM6_TO_TS_EX_3_JJR115.LOG]]
*[[File:SITE_A_EXO_FROZEN_TO_MIN__PM6_EX_3_JJR115.LOG]]
*[[File:SITE_A_EXO_IRC_CALC_(FROM_REDO)_PM6_EX3_JJR115.LOG]]
*[[File:SITE_A_EXO_PRODUCT_PM6_OPTIMISATION_EX_3_JJR115.LOG]]
*[[File:SITE_A_EXO_UNFROZEN_TO_TS_PM6_EX_3_JJR115.LOG]]

'''Diels Alder at Site B '''

*[[File:SITE_B_ENDO_FROZEN_TS_PM6_TO_MIN_EX_3_JJR115.LOG]]
*[[File:SITE_B_ENDO_IRC_TRANSITION_STATE_CALC_EX_3_JJR115.LOG]]
*[[File:SITE_B_ENDO_PRODUCT_OPTIMISATION_PM6_EX_3_JJR115.LOG]]
*[[File:SITE_B_ENDO_UNFROZEN_TS_PM6_TO_TS_EX_3_JJR115.LOG]]
*[[File:SITE_B_EXO_FROZEN_TS_TO_MIN_PM6_OPTIMISATION_EX_3_JJR115.LOG]]
*[[File:SITE_B_EXO_IRC_TS_PM6_CALC_EX_3_JJR115.LOG]]
*[[File:SITE_B_EXO_PRODUCT_PM6_OPTIMISATION_EX_3_JJR115.LOG]]
*[[File:SITE_B_EXO_UNFROZEN_TS_PM6_OPTIMISATION_EX_3_JJR115.LOG]]

'''Cheletropics'''

*[[File:CHELOTROPIC_FROZEN_TRANSITION_STATE_PM6_OPTIMISATION_EX_3_JJR115.LOG]]
*[[File:CHELOTROPIC_PRODUCT_PM6_OPTIMISATION_EX_3_JJR115.LOG]]
*[[File:CHELOTROPIC_TRANSITION_STATE_IRC_CALCULATION_EX_3_JJR115.LOG]]
*[[File:CHELOTROPIC_UNFROZEN_TRANSITION_STATE_PM6_OPTIMISATION_EX_3_JJR115.LOG]]

== Extension ==

This extension explores the unexpected stereochemistry for the ring opening of this cyclobutene structure with ester groups orientated in the way shown in the scheme below (figure 16). This is an interesting investigation as the unusual outcome is one of three other viable options, and is dictated by electronics of the system.

[[File:Reaction_scheme_extension_jjr115.PNG|thumb|center|Fig. 16 - Possible reaction routes of the electrolytic ring opening of cyclobutene.]]

This is a 4π electrocyclic reaction, which is thermally allowed. The equilibrium will exist largely on the right of the system towards the more strain free molecule structure. As a 4n πe reaction, under thermal conditions this will occur with conrotatory motion, but will occur with disrotatory motion of the orbitals under photochemical conditions. This follows Woodward-Hoffman rules for electrocyclic reactions. During the interconversion of the cyclobutene to butadiene (ring opening) the C2 symmetry axis is retained in the reaction under conrotatory motion. However photochemically, this two fold axis of symmetry is not retained and instead the mirror plane is retained from reactants to products, which can be seen in the scheme.

Figure 17 - is a simple diagram from source (<ref name="Butene" />) that highlights the change in orbitals throughout the ring opening process.

[[File:Screen_Shot_2018-02-27_at_10.37.16_jjr115.png|thumb|center|Fig. 17 - Diagram showing change in MO symmetry from cyclobutene to butadiene under conrotatory motion, from source (<ref name="Butene" />.)]]

(You should show these MOs so the reader knows what you mean.

===IRC Results ===
[[File:Animation_extension_jjr115.gif]]

From the animation above, the conrotatory motion of the two ester groups can be seen, as they both move in an anticlockwise direction, resulting in an asymmetric end product (one of the alkenes having E stereochemistry, and the other having Z).

{| class="wikitable"
|-
| style='background: #F2CEE0' |<u>Activation Energy kJ for Conrotatory /mol</u>
| style='background: #F2CEE0' |<u>Reaction Energy for Conrotatory kJ/mol</u>
|-
| style='background: #FFE6F2' | 163.7
| style='background: #FFE6F2' | -53.9
|-
|}

===Log Files for Extension ===

*[[File:EXTENSION_B3LYP_OPTIMISATION_OF_reactant_JJR115.LOG]]
*[[File:EXTENSION_IRC_CALC_ON_TRANSITION_STATE_PM6__JJR115.LOG]]
*[[File:EXTENSION_OPT_TO_A_MINIMUM_FROZEN_TRANSITION_STATE_JJR115.LOG]]
*[[File:EXTENSION_PM6_OPTIMISATION_OF_PRODUCT_JJR115_CORRECT.LOG]]
*[[File:EXTENSION_PM6_OPTIMISATION_OF_reactant_JJR115.LOG]]
*[[File:TRIAL_4_EXTENSION_OPTIMISATION_TO_A_MINIMUM_FROZEN_TRANSITION_STATE_JJR115.LOG]]

== Conclusion ==

To conclude, the PM6 and B3LYP methods of optimization and location of transition state were able to reasonably map the reaction pathways of the various experiments above. In exercise one, the molecular orbital analysis and IRC calculations confirmed the correct transition state was found via the computational methods used. In exercise two we were able to observe secondary orbital interactions via the molecular orbital analysis calculations in the optimised product to explain why the endo product was the most favourable. In exercise three, the cheletropic product was deemed the most thermodynamically favourable, whereas the terminal diels-alder mechanism (endo approach) was found to be the kinetic product with a lower energy barrier.

Although the PM6 calculation involves a considerable amount of doubt and error (many broad assumptions made in the calculation), combined with the more advanced B3LYP calculation, this experiment yielded good results that correlates with literature data found.

== References ==

<references>
<ref name="Transition state 1">T. Fueno, The Transition State, CRC Press, 1999, p2.</ref>
<ref name="Transition state 2" >J. J. P. Stewart, J. Mol. Model 13, 1173-1123 (2007).</ref>
<ref name="Transition state 3" >D. J, Singh, L. Nordstrom, Planewaves, Pseudopotentials and the LAPW method, 2006, p6-21.</ref>
<ref name="normal electron demand" >J. Clayden,S. Warren, N. Greeves, Organic Chemistry [e-book]. Oxford: OUP Oxford; 2012, ch. 34, p886-888</ref>
<ref name="bond lengths">P. Dewick, Essentials of Organic Chemistry, John Wiley & Sons, 2013, p44</ref>
<ref name="waals">S. Batsanov, Van der Waals Radii of Elements, Inorganic Materials, Vol. 37, No.9,
2001 </ref>
<ref name="xylylene"> S. Sakai, Theoretical Studies of the Electrocyclic Reaction Mechanisms of o-Xylylene to
Benzocyclobutene, J. Phys. Chem. A 2000, 104, p11615-11621 </ref>
<ref name="Butene"> B. Dinda, Essentials of Pericyclic and Photochemical Reactions,
Lecture Notes in Chemistry 93, Springer INternational Publishing Switzerland 2017, DOI 10.1007/978-3-319-45934-9_2</ref>

</references>