Rep:Mod:Xeon2012

Optimizing the Reactants and Products

The softwares used to calculate the optimization of molecules are Gaussian 09 and GaussView 5.0.8.

Optimizations of 1,5-hexadiene

Linkage	Anti 3	Gauche 2	Gauche 3	Anti 2
Structure
Method	HF	HF	HF	HF
Basis set	3-21G	3-21G	3-21G	3-21G
Energy/a.u.	-231.68907065	-231.69166701	-231.69266122	-231.69253528
Point group	C2h	C2	C1	Ci

It was assumed that the conformation with "anti" linkage of the center four carbon atoms would have the lowest energy as there would be less steric and electronic repulsion in this conformation. Thus the "anti 2" conformation should have had the lowest energy. However, this is not the case according to the optimizations as the "gauche 3" conformation was sligltly lower in energy. The "anti 2" conformation was reoptimized at the B3LYP/6-31G* level.

Reoptimization of "anti 2" conformation

Linkage	Anti 2
Structure
Method	B3LYP
Basis set	6-31G(d)
Energy/a.u.	-234.61170562
Point Group	Ci

From the reoptimization:

Sum of electronic and zero-point Energies=           -234.469208 a.u.
Sum of electronic and thermal Energies=              -234.461859 a.u.
Sum of electronic and thermal Enthalpies=            -234.460915 a.u.
Sum of electronic and thermal Free Energies=         -234.500785 a.u.

An IR spectrum of the optimization can be achieved. Through the different optimization method, the geometries of the molecule from different calculations didn't change.

IR spectrum of reoptimization of "anti 2" conformation.

Optimizing the "Chair" and "Boat" Transition Structures

Optimizations of fragment

Fragment
Energy/a.u.	-155.82303975

Optimization of chair transition structure

	Hessian	Freeze coordinate	Freeze coordinate (Derivative)
Structure	0
Type	Opt+Freq	Opt+Freq	Opt+Freq
Method	HF	HF	HF
Basis set	3-21G	3-21G	3-21G
Point group	C2h	C2h	C2h
Energy/a.u.	-231.61932217	-231.61424804	-231.61932243
Bond length/A	2.20	2.20	2.02

Vibration corresponding to the Cope rearrangement at an imaginary frequency of magnitude 818 cm.^-1

Failed optimizations of boat transition structure

Structure	The result of the calculation looked a bit like the chair transition structure but more dissociated. The problem with using QST2 method in this calculation is that the molecule will only be translated, but the atoms will not be rotated. The calculation result will have similar geometry as the reactant and boat transition structure will never be achieved using "anti" linkage conformation.	It can be judged from the result of the calculation that

Cis-butadiene

Cis-butadiene

Structure
Type	Optimization
Method	AM1 Semiemperical
Energy/a.u.	0.04879719
Point Group	C2v
HOMO	Antisymmetric
LUMO	Symmetric about a plane perpendicular to the nodal plane

Ethylene+cis butadiene transition structure

Ethylene+cis butadiene transition structure

Structure
Type	Optimization
Method	AM1 Semiemperical
Energy/a.u.	0.04879719
Point Group	Cs
HOMO	Antisymmetric
LUMO	Antisymmetric

The bond-lengths of the partly formed σ C-C bonds are 2.12 A. The typical sp³ bondlength is 1.53-1.55 A. The typical sp² bondlength is 1.47-1.48 A. The van der Waals radius of the C atom 170 pm.

The partly formed σ C-C bond is shorter than a typical sp³ or sp² bond, which means that the interaction between the C atoms forming the partly formed bond is weaker than a normal C-C bond. The interaction between the 2 atoms cannot be identified as a chemical bond. However, the partly formed bondlength is shorter than twice the van der Waals radius of the C atom, which means that the 2 C atoms are not too distant to interact with each other.This partly formed bond characterestic is essential to understanding the mechanisms of reactions and transition states of substances.

Vibration at an imaginary frequency of magnitude 956.19cm.^-1

Vibration at a frequency of magnitude 147.28cm.^-1

From the vibration of the transition structure at the imaginary frequency of magnitude 956.19cm.^-1 we can decide that the formation of the two bonds is synchronous, while the lowest positive frequency indicates asynchronous formation.

The HOMO of the transition structure is the combinition of two molecular orbitals, which both should ba anti-symmetric to get an anti-symmetric result. Therefore, it should be the HOMO of butadiene(which is shown above) and the LUMO of ethylene (HOMO is symmetric) that forms the HOMO of the transition structure.