Rep:Mod3:jib09

Cope Rearrangement of 1,5-Hexadiene

Optimizing the Reactants and Products

The ease of rotation about the carbon-carbon single bonds in 1,5-Hexadiene makes it possible for it to have many conformational isomers. To determine which is the most stable each of the conformers will be optimized using the Hartree-Fock method and a 3-21G basis set. This level of analysis is relatively low but it should be able to provide a guided to the potential energies of the conformers and indicate which is the most stable.

Table 1. HF/3-21G Optimization of 1,5-Hexadiene conformers

Conformation	Total Energy/ Hartrees	Relative energy/ kcal/mol	Point Group
Gauche 1	-231.68772	3.10	C2
Gauche 2	-231.69166	0.62	C2
Gauche 3	-231.69266	0.00	C1
Gauche 4	-231.69153	0.71	C2
Gauche 5	-231.68962	1.91	C1
Gauche 6	-231.68916	2.20	C1
Anti 1	-231.69260	0.04	C2
Anti 2	-231.69254	0.08	Ci
Anti 3	-231.68907	2.25	C2H
Anti 4	-231.69097	1.06	C1

• The 3DJmol structures can be viewed by following the corresponding link and the LOG files located in the references.

Prior to running the calculations it was expected that the most stable conformer would have a anti conformation, as it would have lower energy steric interactions, but as can be seen form the data the most stable conformer is gauche 3. This result could be due to the fact that a low level method of analysis was used (HF/3-21G), which is not accurate enough, or some other factor is also playing a role in determining the energy of the conformers.

To obtain more accurate calculations, the 3 most stable conformers were re-optimized using a higher level of analysis. The method used was DFT/B3YLP with a 6-31G basis set, this should yield a more accurate optimization and a better approximation to optimized geometry.

Table 2. Optimization of most stable 1,5-Hexadiene conformers using DFT/6-31G

Conformer	Total Energy/ Hartrees	Relative energy/ kcal/mol	Point group
Gauche 3	-234.55934	0.29	C1
Anti 1	-234.55978	0.00	C2
Anti 2	-234.55970	0.05	Ci

• The 3DJmol structures can be viewed by following the corresponding link and the LOG files located in the references.

The higher level of optimization resulted in both anti conformers being more stable than the gauche, which was the expected result, even though the resulting geometries for the DFT-method did not vary significantly form the Hartree-Frock method.

Frequency and Thermochemical Analysis

• Sum of Electronic and Zero-Point Energies (E = E₀ + ZPE ): The potential energy at 0K including the zero point vibrational energy.
• Sum of Electronic and Thermal Energies (E = E₀ + E_tot ): The total electronic energy + the total internal thermal energy, consisting of the vibrational, rotational and translational energy.
• Sum of electronic and Thermal Enthalpies (E = E₀ + H_corrected): The total electronic energy + the correction to enthalpy due to room temperature.
• Sum of Electronic and Thermal Free Energies (E= E₀ + G_corrected): The total electronic energy + the correction to Gibbs free energy due to internal energy.