Mod:mj506 mod3

Module 3

Cyclohexadiene tutorial

The anti conformation of the molecule was optimized using Gaussian software using HF method with 3-21G basis set. Energy obtained was -231.68907064 a.u. Point group was C1, but after clicking on symmetrize, the point group became C_2h.
Structure was redrawn in gauche conformation, and again optimized using the same method/basis set as above. Energy obtained was -231.68771615 a.u. Point group was C1,and after symmetrizing it became C2. One would expect the energy of this conformation to be higher, as gauche conformation takes away the stabilizing hyperconjugation effect of anti-periplanar conformation, and that's what is found by the calculation.
A structure was drawn where one might expect a hyperconjugation between C-H bonding orbital and C-C antibonding orbital. Conformation was chosen anti, as it is lower in energy. Optimization performed again with HF with 3-21G basis set. But the energy found was the same as for the anti conformation above, and the structure restored to the one obtained above as well. Thus one can conclude that this is the lowest energy state of the molecule.
Comparing my structures with the ones in Appendix 1, the anti conformation I have obtained is anti3 and gauche is gauche1 from the Appendix 1. That is quite embarrasing, as there are lower energy states for these conformations in the appendix, which I have failed to find (anti1 and gauche3).
Structure anti2 was drawn and optimized twice to make sure it obtains the C_i point group. The final energy was -231.69253529 a.u., which compares perfectly with the one from the table at -231.69254 a.u.
The structure was used to re-optimize it using B3LYP method with 6-31G(d) basis set. Point group was again obtained to be C_i. The total energy was -234.61172247 a.u. Bond lengths and bond angles that differ are given in the table below:

Method	C=C bond length	-C-C- bond length	-C-C= bond length	C(sp3)-H bond length	C(sp2)-H bond length	C-C=C bond angle
B3LYP	1.33349 A	1.54794 A	1.50415 A	1.09976 A	1.08852	125.290
HF	1.31614 A	1.55287 A	1.50877 A	1.08477 A	1.07336	124.811

Thus as one can see, the bond lengths and angles differ by a slight amount, most notably the bond lengths are somewhat shorter for the B3LYP method.
Frequencies of vibrations have been performed with the B3LYP method with 6-31G(d) basis set. No negative values for frequencies were obtained, with the lowest lying frequency at 74 cm^-1. The energies obtained under the thermochemistry tab are outlined in the table below:

Sum of electronic and zero-point Energies=           -234.469162
Sum of electronic and thermal Energies=              -234.461827
Sum of electronic and thermal Enthalpies=            -234.460883
Sum of electronic and thermal Free Energies=         -234.500716

Optimizing the chair and boat transition states

Chair transition structure

Allyl fragment was optimized using HF with 3-21G basis set. Then another allyl fragment was added and positioned so it is in the chair-like transition state. Distances between terminal carbons was adjusted to be 2.2A. The optimization and frequency of this structure was performed with the following command line:

# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

Calculation finished successfully, and the terminal C-C distance was modified to 2.02A. One imaginary frequency was obtained at 818 cm^-1 and upon animating it, one can see that it corresponds to the Cope rearrangement, as the terminal carbons move as though they are about to create a bond.
The initial unoptimized structure was opened and edited with Redundant Coord Editor, making two of the terminal carbons a bond and freezing coordinates. The structure was then optimized using the following command line:

# opt=modredundant hf/3-21g geom=connectivity

Optimization finished successfully, and the transition state looks very similar to the one obtained above using opt=ts, except the terminal carbon-carbon distances were frozen at 2.2A.
Structure obtained from above was used in the redundant coord editor, to fix the two bonds which are made/broken to derivative, and optimzation of the TS was run with the below command line:

# opt=(ts,modredundant) rhf/3-21g geom=connectivity

Optimization finished successfully, and comparing the structure to one obtained with minimising the TS and calculating the force constants, it is almost exactly the same structure, as the terminal carbon-carbon distances are changed to 2.02A and the imaginary vibration is almost exactly at -818 cm^-1. Structure obtained is given on the right.

Boat transition structure

The HF optimized hexadiene anti-2 conformation was used (with point group C_i). Two molecules of the hexadiene were added, and the atoms numbered so to resemble the reactant and product, as shown below:

The optimization was then run with the following command line:

# opt=qst2 freq hf/3-21g geom=connectivity

And Gaussian crashed straight away. The reactant and product were rearranged so that C2-C3-C4-C5 dihedral angle was 0 degrees, and C3-C4-C5 and C2-C3-C4 were 100^o degrees both. Hydrogen atoms were also renumbered so no confusion will be involved, and the final molecule is shown below:

The optimization was then run with command line:

# opt=qst2 freq hf/3-21g geom=connectivity

Gaussian finished without any error. The structure obtained is indeed the boat transition structure, with the terminal carbon-carbon distance being 2.14A, and the only imaginary frequency at -839 cm^-1. It is not really possible to predict which conformer given in Appendix 1 will be formed from the boat/chair transition states. Thus, the IRC method had to be used to predict to which reactant conformation does the molecule drop to from the chair transition state, which is detailed below.

Intrinsic reaction coordinate method

The optimized chair transition state was opened, and a Gaussian file prepared by choosing the method of calculation as IRC, following IRC only to the forward reaction, force constants were chosen to be calculated once, and points to compute was changed to 50. THe overall command line looks like:

# irc=(forward,maxpoints=50,calcfc) rhf/3-21g geom=connectivity

The job was submitted to chemistry SCAN. After an hour, the calculation was finished successfully. Checkpoint file was opened, and the reaction path animated, showing the bond making in 51 steps. Unfortunately, that was not enough to obtain the final structure, and so further optimization was required. The terminal carbon atoms came close together to be in a bond length distance at around 43rd iteration. The final (51st) structure was further minimized using HF method with 3-21G basis set.

Activation energies of the Cope rearrangement

The Cope rearrangement can proceed through boat or chair conformation. Transition states of both chair and boat conformations have been optimized using B3LYP method with 6-31G(d) basis set, with the following command line:

# opt=(calcfc,ts,noeigen) freq rb3lyp/6-31g(d) geom=connectivity

Table below summarizes energy values obtained from the calculations:

Structure	Electronic energy with HF/3-21G	Electronic + zero-point energy with HF/3-21G at 0K	Electronic + thermal energies with HF/3-21G at 298K	Electronic energy with B3LYP/6-31G(d)	Electronic + zero-point energy with B3LYP/6-31G(d) at 0K	Electronic + thermal energies with B3LYP/6-31G(d) at 298K
Anti2 reactant	-231.69253529 a.u.	-231.539540 a.u.	-231.532566 a.u.	-234.61171866 a.u.	-234.469162 a.u.	-234.461827 a.u.
Chair TS	-231.61932244 a.u.	-231.466697 a.u.	-231.461338 a.u.
Boat TS	-231.60280229 a.u.	-231.450929 a.u.	-231.445300

Activation energies in a.u. and kcal/mol are given in the table below. Energies for both methods were taken from the frequency calculation from Thermochemistry section, namely the "Sum of electronic and zero-point Energies" which is at 0 K.

Structure	Energy with HF	Energy with B3LYP	Activation energy with HF	Activation energy with B3LYP
Product anti2 conformation	-231.539540 a.u.	-234.469162 a.u.	---	---
Chair transition state	-231.466697 a.u.
Boat transition state	-231.450929 a.u.