Rep:Mod:Yunzhang Module3 Writeup

Module3, Experiment 3: The Transition State

In this experiment, the transition state structures in larger molecules for Cope rearrangement and Diels Alder cycloaddition reactions are studies using molecular orbital-based computaional methods which solve the Schrodinger equation numerically and locate the transition state structures based on the local shape of a potential energy surface. It also gives us information about the shapes of the transition structures, the pathways in which the reaction undergoes and how big the barrier heights are.

The Cope Rearrangement Tutorial

Chemical reactivity of the Cope rearrangement of 1,5-hexadiene

Objectives: locate the low-energy minima and transition structures on the C6H10 potential energy surface and determine the preferred reaction mechanism

The [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy. Carry out the B3LYP/6-31G* optimisation using Gaussian and see how it matchees with this result.

Cope rearrangement	Chair Transition State	Boat Transition State
Cope rearrangement	Chair Transition State	Boat Transition State

Optimizing the Reactants and Products

• (a) Open GaussView -> in the Molecule window: draw 1,5-hexadiene with an "anti" linkage for the central four C atoms -> click "Clean" under the "Edit" menu.

"Calculate" -> "Gaussian" -> "Job type": optimization -> "Method": Hartree-Fock -> "Basis set": 3-21G -> "Link 0": %mem=250MB -> Submit -> save as "yun_react_anti" -> after job has finished, open the file -> Select "Yes" -> Files of type: choose *.chk -> Open "yun_react_anti" in the C:\Windows\G03\Scratch folder -> "Result": Summary -> "Edit": Symmetrize.

1,5-hexadiene with an "anti" linkage for the central four C atoms	Summary	Energy/ a.u.	Symmetry
Cyclopentasiloxane		-231.68539585	C2h

The structure is the same one as Anti3 in Appendix 1

• (b) Draw 1,5-hexadiene with a "gauche" linkage for the central four C atoms and optimize the structure at the HF/3-21G level of theory.

Would you expect this structure to have a lower or a higher energy than the anti structure you have just optimized? due to C-H pi interactions electrostatic>steric =>Gauche more stable http://en.wikipedia.org/wiki/Gauche_effect

1,5-hexadiene with a "gauche" linkage for the central four C atoms	Summary	Energy/ a.u.	Symmetry
Cyclopentasiloxane		-231.69166701	C2

The structure is the same one as Gauche 4 in Appendix 1

• (c) Based on the results above, predict the lowest energy conformation of 1,5-hexadiene and test out your hypothesis by drawing the structure and optimizing it.

The gauche conformation for 1,5-hexadiene is more stable than that of the anti conformation by 6.27116*10^(-3)a.u. due to the presence of Gauche effect. The Gauche conformation optimized above gives the same structure as the Gauche4 in Appendix 1 in which one =CH2 bond is pointing inwards whereas the other pointing outwards...... http://en.wikipedia.org/wiki/Gauche_effect

Hypothesis test:

Gauche conformer	Summary	Energy/ a.u.	Symmetry
Gauche1	Cyclopentasiloxane		-231.68771610	C2
Gauche2	Cyclopentasiloxane		-230.17405951	C2
Gauche3	Cyclopentasiloxane		-231.68085853	C1
Gauche5	Cyclopentasiloxane		-231.68961575	C1
Gauche6	Cyclopentasiloxane		-231.68916016	C1

Anti conformer	Summary	Energy/ a.u.	Symmetry
Anti1	Cyclopentasiloxane		-231.69260236	C2
Anti2	Cyclopentasiloxane		-231.69253511	Ci
Anti4	Cyclopentasiloxane		-231.69097051	C1

• (d) A table containing the low energy conformers of 1,5-hexadiene and their point groups is shown in [Appendix 1]. Compare the structures that you have optimized with those in the table and see if you can identify your structure.

• (e) Draw the Ci anti2 conformation of 1,5-hexadiene (unless you have already located it). Optimize it at the HF/3-21G level of theory and make sure it has Ci symmetry. Compare your final energy to the one given in the table.

• (f) When you are happy that your structure is the same as the one in the table, reoptimize it at the B3LYP/6-31G* level (6-31G* is equivalent to 6-31G(d) by selecting DFT under the Method menu and B3LYP from the box with the functionals on the right-hand side. Now select Link 0 and change the name of the chk file to the name of the DFT optimization that you are about to run. Note that it is always advisable to do this when re-using or modifying existing structures to ensure that the original chk file is not overwritten. Run the job and make a note of the energy. Now compare the final structures from the HF/3-21G calculation with that at the higher level of theory. How much does the overall geometry change?

Gauche conformer	Summary	Energy/ a.u.	Symmetry
Gauche1	Cyclopentasiloxane		-231.68771610	C2
Gauche2	Cyclopentasiloxane		-230.17405951	C2
Gauche3	Cyclopentasiloxane		-231.68085853	C1
Gauche4	Cyclopentasiloxane		-231.68771610	C2
Gauche5	Cyclopentasiloxane		-231.68961575	C1
Gauche6	Cyclopentasiloxane		-231.68916016	C1

Anti conformer	Summary	Energy/ a.u.	Symmetry
Anti1	Cyclopentasiloxane		-231.69260236	C2
Anti2	Cyclopentasiloxane		-231.69253511	Ci
Anti3	Cyclopentasiloxane		-231.69253511	Ci
Anti4	Cyclopentasiloxane		-231.69097051	C1

• (g) The final energies given in the output file represent the energy of the molecule on the bare potential energy surface. To be able to compare these energies with experimentally measured quantities, they need to include some additional terms, which requires a frequency calculation to be carried out. The frequency calculation can also be used to characterize the critical point, i.e. to confirm that it is a minimum in this case: that all vibrational frequencies are real and positive.

Open the optimized B3LYP/6-31G* structure -> Calculate: Gussian -> Job type: Frequency -> Method: DFT； B3LYP/6-31G（d) -> link 0: yun_freq_gau1_DFT.chk -> save -> run -> Once the job has finished, open yun_freq_gau1_DFT.log -> Results menu: Vibrations -> Check there are only real frequencies -> Spectrum.

On Results menu: View File -> find Thermochemistry -> find Vibrational temperatures: a list of energies -> Make a note of

• (i) the sum of electronic and zero-point energies,
• 　(ii) the sum of electronic and thermal energies,
• (iii) the sum of electronic and thermal enthalpies,
• (iv) the sum of electronic and thermal free energies.

The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS). It is important to make sure that you select the correct energy/enthalpy term to compare to your experimental values. Note that these corrections can also be calculated at other temperatures using the Freq=ReadIsotopes option in Gaussian, If you have time, try re-calculate these quantities at 0 K as shown in the Advanced GaussView Tutorial.

Optimizing the "Chair" and "Boat" Transition Structures

• (a) Draw a planar allyl fragment(CH2CHCH2)-> run a HF/3-21G level optimisation -> copy this structure to a new GaussView window twice and orient for them to look like the chair transition state (translate one fragment: Shift Alt keys + Left Mouse button; rotate: Alt key + Left)-> Bond distance between the terminal Cs of the CH2CHCH2 fragments ~ 2.2 Å -> Save as chair_ts_guess.

• (b) Use Hartree Fock and the default basis set 3-21G for parts (b) to (f).

File → New → Create MolGroup -> copy and paste the guess structure into the window -> Calculation: Gaussian -> Job Type: Opt+Freq; Optimization to a: TS (Berny); calculate force constants: Once; Additional keyword: Opt=NoEigen -> Submit. After the job completes, it gives an imaginary frequency -817.897cm-1 due to the Cope rearrangement.

• (c) Frozen coordinate optimization: File → New → Create MolGroup -> copy and paste the guess structure into the window -> Edit: Redundant Coord Editor -> click on Create a New Coordinate -> On GaussView window: select 2 of the terminal Cs from the CH2CHCH2 fragments which form/break a bond during the rearrangement -> On coordinate editor: select Coordination: Bond; Freeze Coordinate -> Set value: 2.2 -> click on Create a New Coordinate -> select the opposite 2 terminal Cs -> select Bond and Freeze Coordinate -> Click OK -> Submit.

• (d) Open the file after the job has finished -> Edit: Redundant Coord Editor -> create a new coordinate by clicking on Create a New Coordinate -> Select one of the bonds that was frozen before -> Coordinative: Bond; Derivative -> Repeat this procedure for the other bond -> Calculate: Gaussian -> Job type: opt+freq; optimize to a: TS(Berny); Calulate Force Constants: Never -> yun_opt_freq_redundant2 -> submit. This transition structure gives an imaginary frequency -817.947cm-1 due to the Cope rearrangement.

	Chair transition structure(Optimized under Hessian)	Chair transition structure(Optimized under Redundant)
<jmol> <jmolApplet> <title>Cyclopentasiloxane</title><color>pink</color><size>100</size> <uploadedFileContents>chair_HF_jmol.mol</uploadedFileContents> </jmolApplet>	<jmol> <jmolApplet> <title>Cyclopentasiloxane</title><color>pink</color><size>100</size> <uploadedFileContents>chair_RD_jmol.mol</uploadedFileContents> </jmolApplet>
Bond length

(e) Now we will optimize the boat transition structure. We will do this using the QST2 method. In this method, you can specify the reactants and products for a reaction and the calculation will interpolate between the two structures to try to find the transition state between them. You must make sure that your reactants and products are numbered in the same way. Therefore, although our reactants and products are both 1,5-hexadiene, we will need to manually change the numbering for the product molecule so that it corresponds to the numbering obtained if our reactant had rearranged.

e.g. Image:pic3.jpg

Open the chk file corresponding to the optimized Ci reactant molecule (anti2 in [Appendix 1]). Now open a second window and create a new MolGroup. Copy the optimized reactant molecule into the new window. In the same window, now select File → New → Add to MolGroup. The original molecule should disappear and a green circle should appear at the top left-hand corner with a 2 next to it. Clicking on the down arrow by the 2 will take you back to the original window and you will see your molecule again. This is how we read multiple geometries into GaussView. Go back to window 2, and copy and paste the reactant molecule a second time. This is going to be the product molecule and will be the molecule on which we need to change the numbering. If you now click on the icon showing two molecules side by side, then you can view both molecules simultaneously.

Now go to the View menu and select Labels so that you can see the numbering on both structures. Orient the two structures separately so they look something like the following:

Image:pic4a.jpg

Image:pic4b.jpg Reactant Product

Now click on the product structure. Go to the Edit menu and select Atom List. Starting from Atom 1 on the reactant, go through and renumber all the atoms on the Product so that they match the reactant molecule, e.g. for the numbering above you would start by changing atom 6 on the product molecule to atom 1. The other atom numbers will update as you do this so make sure you do it in the correct order. At the end, the numbering on your two molecules should correspond to each other in the following way:

Image:pic5a.jpg

Image:pic5b.jpg Reactant Product

Now we will set up the first QST2 calculation. Go to the Gaussian menu and select Job Type as Opt+Freq, and optimize to a transition state. This time you will have two options - TS (Berny) which we used in the previous calculations and TS (QST2). Select TS (QST2). Submit the job.

You will find that the job fails. To see why, open the chk file you created and view the structure. You will see that it looks a bit like the chair transition structure but more dissociated. In fact when the calculation linearly interpolated between the two structures, it simply translated the top allyl fragment and did not even consider the possibility of a rotation around the central bonds. It is clear that the QST2 method is never going to locate the boat transition structure if we start from these reactant and product structures.

Now go back to the original input file where you set up your QST2 calculation. We will now modify the reactant and product geometries so that they are closer to the boat transition structure. Click on the reactant molecule first and select the central C-C-C-C dihedral angle (i.e. C2-C3-C4-C5 for the molecule above) and change the angle to 0o. Then select the inside C-C-C (i.e. C2-C3-C4 and C3-C4-C5 for the molecule above) and reduce them to 100o. Do the same for the product molecule. Your reactant and product molecules should now look like the following:

Image:pic6a.jpg

Image:pic6b.jpg Reactant Product

Set up the QST2 calculation again, renaming both the chk file under Link 0 and the input file. Run the job again. This time it should converge to the boat transition structure. Check that there is only one imaginary frequency and visualize its motion.

The object of this exercise is to illustrate that although the QST2 method is has some advantages because it is fully automated, it can often fail if your reactants and products are not close to the transition structure. There is another method, the QST3 method, that allows you to input the geometry of a guess transition structure also and this can often be more reliable. If you have time, you can try generating a guess boat transition structure and see if you can get the calculation to converge using the original reactant and product molecules. Remember to check the atom numbers in the transition structure are in the right order.

(f) Take a look at your optimized chair and boat transition structures. Which conformers of 1,5-hexadiene do you think they connect? You will find that it is almost impossible to predict which conformer the reaction paths from the transitions structures will lead to. However, there is a method implemented in Gaussian which allows you to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface. This is called the Intrinisic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Open the chk file for one of your optimized chair transition structures. Under the Gaussian menu, select IRC under the Job Type tab. You will be presented with a number of options. The first is to decide whether to compute the reaction coordinate in one or both directions. As our reaction coordinate is symmetrical, we will only choose to compute it in the forward direction. Normally you would do both forward and reverse, either in one job or in two separate jobs. You are also given the option to calculate the force constants once, at every step along the IRC or to read them from the chk file. You would use the latter option if you have previously run a frequency calculation. In this case, to avoid confusion with chk files, we will just recompute them at the beginning of the calculation. (The IRCMax option can also be specified here. This takes a transition structure as its input, and finds the maximum energy along a specified reaction path, taking into account zero-point energy etc., and produces all the quantities needed for a variational transition state theory calculation. We will leave this unchecked for the purposes of this exercise.) The final option to consider is the number of points along the IRC. The default is 6 but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under Link 0 and submit the job. The job will take a while so now is a good time to take a coffee break...

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different. As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program FreqChk to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The FreqChk utility program can be accessed from Gaussian03W. Launch Gaussian03W. Select utilities from the menu and click on FreqChk to launch the utility program. You will be prompted for a chk file. Select your chk file from the C:\G03W\Scratch directory and follow the instructions from this web link to proceed.