Module3: Transition states and reactivity

Introduction

The Cope Rearrangement of 1,5-hexadiene

Optimizing the Reactants and Products

Drawing 1,5-hexadiene

To draw a 1,5-hexadiene molecule, first open a new file (File→ New→ Create MolGroup).
Double click on the Rings Fragment on builder window and select the cyclohexane-boat icon.
Click on the view window to make it appear.
Click the Modify Dihedral icon, then select central four Cs and change dihedral angle to 180° to make an anti-peri planar conformation, or change to 60° or -60° for an gauche conformation.
Change the dihedral angle between left four Cs or right four Cs leads to other a.p.p or gauche forms.

Optimizing the structures

We will optimize the structures (one of the a.p.p conformations (anti4),one of the gauche conformations (gauche6), one lowest energy conformation (anti1) by guessing and anti2 conformation ) using HF/3-21G level of theory. Following are the steps.

Select Gaussian calculation setup under calculate.
Job type→ optimization→ optimize to a minimum.
Method→ Method: Ground State, Hartree-Fork, Default Spin; Basis Set: 3-21G.
Leave other setting as default and Submit.
After finishing optimization. open chk file and take down the energy(Results→ Summary) and point group (Edit→Point Group).

The optimized structures and their energies and point groups are shown in the table below.

Structure

anti4

gauche6

anti1

anti2

Point Group

C₁

C₂

C_i

Energy/Hartrees HF/3-21G

-231.69097

-231.68916

-231.69260

-231.69254

Table 1. Four conformations of 1,5-hexadiene

The four structures has the same energy with the matched conformers as shown in Appendix 1. However, the lowest energy structure should be gauche 3, instead of anti1 which I was optmizing.

Reoptimizing the C_i anti2 structure

After optimizing the C_i anti2 conformation above, we then reoptimize it with a higher level method called B3LYP/6-31G*. The steps are shown below.

Select Gaussian calculation setup under calculate.
Job type→ optimization→ optimize to a minimum.
Method→ Method: Ground State, DFT..., Default Spin,B3LYP; Basis Set: 6-31G(d).
Leave other setting as default and Submit.
After finishing reoptimization. open chk file and take down the energy(Results→ Summary).

The table 2 below shows energy and structure change after reoptmization.

Before re-optimization

After re-optimization

Structure

Method

anti2 optimized with HF/3-21G

anti2 reoptimized with B3LYP/6-31G*

Energy/Hatrees

-231.69254

-234.61171

Table 2. anti2 conformation before and after reoptimization

Compare to the energy change, the geometry does not change a lot after reoptmization.

Calculating frequency

In order to compare the energy calculated above with the experimental data, we calculate frequency for taking experimental conditions into account. If the frequency calculated in this case are all positive, it is clear that we have got a local minimum. The method of frequency calculation is shown below.

Select Gaussian calculation setup under calculate.
Job type→ frequency.
Method→ Method: Ground State, DFT..., Default Spin,B3LYP; Basis Set: 6-31G(d).
Leave other setting as default and Submit.
After finishing frequency calculation. open log file and take down the energy(Results→ Vibration).

The table 3 below shows energy and structure change after reoptmization. After determining the transition state of the Cope rearrangement. We will compare the sum of electronic and zero-point energies and sum of electronic and thermal energies of anti2 as reactant and the boat and chair as transition state with experimental data.


Type of energies	Formula	Energy/Hartrees
Sum of electronic and zero-point Energies	E = E_elec + ZPE	-234.45329
Sum of electronic and thermal Energies	E = E + E_vib + E_rot + E_trans	-234.44774
Sum of electronic and thermal Enthalpie	H = E + RT	-234.44680
Sum of electronic and thermal Free Energie	G = H - TS	-234.48224

Table 3.Thermal energies calculated after calculating frequency.

Figure 3 shows the IR spectrum simulated.

Figure 2.Animation of reactant after B3LYP/6-31G* method calculation.	Figure 3. IR spectrum simulated after B3LYP/6-31G* method calculation.

Optimizing the "Chair" and "Boat" Transition Structures

The "Chair" Transition Structure

We are going to use two way to optimize the chair transition state, force field matrix (Hessian) and frozen coordinate method.

The force field matrix

The first one is optimized by computing force constant matrix at first and then update when calculation proceeds.The method is as following,

Draw and optimize an allyl fragment with HF/3-21G level of theory.
Move and rotate two optimized allyl fragments until they looks like chair TS, make sure the terminal ends are 2.2Å apart.
Select Gaussian calculation setup under calculate.
Job type→ Opt+Freq, Optimization to a TS(Berny);Calculate the force constants once.
Method→ Method: Ground State, Hatree-Fork, Default Spin; Basis Set: 3-21G.
Leave other setting as default and Submit.
After finishing TS optimising. open chk file and select Vibration under Results to get frequency and vibration.

the only imaginary frequency is -817.96cm^-1 and the same structure as in Appendix 2

Figure 5. Animation of chair TS after force constant matrix calculation.	Figure 6. IR spectrum simulated after force constant matrix calculation.

The frozen coordinate method

However, when the guess TS is too different from the real one, the force field method may fails to produce the desired output. Therefore, frozen coordinate method would be a better approach. It freezes the reaction coordinate and compute Hessian on the reaction coordinate. The transition state can then be deduced after un-freezing the reaction coordinate.

Figure 7.Animation of reactant after frozen coordinate method calculation.	Figure 8. IR spectrum simulated after frozen coordinate method calculation.

The "Boat" Transition Structure

For the boat transition state determination, we are using QST2 or QST3 method. We can specify both reactant and product and calculate the transition state by interpolating between the two structures in QST2 method. Or, in a more reliable way, we can input a guess transition state as well with QST3 method.

Figure 9. Animation of boat TS after QST2 calculation	Figure 10. IR spectrum simulated after frozen coordinate method calculation.
Figure 11. Animation of boat TS after QST3 calculation	Figure 12. IR spectrum simulated after frozen coordinate method calculation.