Third Year TS and Reactivity Lab

Transition States Exercises

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

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. 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 Molecular Reaction Dynamics computational 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 here and 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:

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.

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 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%
  • Exercise 1 (15%)
  • Exercise 2 (25%)
  • Exercise 3 (20%)
• 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: This is where you should discuss the theory behind the computational methods you have applied in this lab. Include:

• What is a potential energy surface (PES)?
• What are the mathematical definitions of minima and maxima on a PES, and how they can be related to chemical events.
• What are PM6 and DFT and how are these methods different?
• Why are we using these two methods?
  

Questions and Answers: Follow the guidelines for the 3 exercises to be completed in the wiki sections below.

Conclusion: Summarise the key concepts of the lab and your results.

• 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.

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

Tuesday 10.00 - 12.00: Sophie

Thursday 10.00 - 12.00: Sami

Friday 14.00 - 16.00:

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 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

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

2) Confirm that you have the correct TS with a frequency calculation and IRC.

3) Optimise the products at the PM6 level.

Write up and Analysis

Confirm that you have the correct reactants, products, and TS.

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 for each of the HOMO and LUMO of butadiene and ethylene, 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 sp³ and sp² 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? Is the formation of the two bonds synchronous or asynchronous (viewing the vibrational mode may help here too)?

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

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

1) Using any of the methods in the 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

Confirm that you have the correct reactants, products, and TS.

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 labeled "Sum of electronic and thermal Free Energies", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? See more detail regarding thermochemistry in Gaussian.

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 Frontier Molecular Orbital Theory has some useful information on what these secondary orbital interactions are.

Exercise 3: Diels-Alder vs Cheletropic

See the o-Xylylene-SO2 Cycloaddition section in the tutorial as a guide.

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.

Write up and Analysis

Confirm that you have the correct reactants, products, and TS.

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

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?