Physical Computational Chemistry Experiment 3 - The Transition State

The Cope Rearrangement: modelling the dimer

A molecule of 1,5-hexadiene was modelled with an anti linkage about the central bond and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.69260 a.u., point group C2 and corresponds to conformer anti1 in appendix 1.

The gauche form is expected to be higher in energy in general due to increaced 1,4 strain but this depends upon the specific conformers.

A molecule of 1,5-hexadiene was then modelled with an gauche linkage about the central bond and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.69153 a.u., point group C2 and corresponds to conformer gauche4 in appendix 1.

A molecule of 1,5-hexadiene was then modelled with an anti linkage about the central bond which corresponded to conformer anti2 in appendix 1 and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.68279 a.u. and point group Ci. This is lower than the energy given in appendix 1 which, assuming the other energies are correct, makes it the lowest energy conformer.

This model was then reoptimised using the B3LYP/6-31G* method and basis set. The energy of the new model is -234.60056 a.u. and point group Ci is retained. The geometry appears to be unchanged. The vibrations were then calculated. The results showed three negative frequencies demonstrating that there was a problem with the geometry of this model. The calculations were repeated with the model reconstructed from scratch.

For the HF/3-21G calculation the new result was an energy of -231.69254 a.u. which does match that given in appendix 1. The point group was Ci. For the B3LYP/6-31G* calculation the new result was an energy of -234.61172 a.u. and point group Ci. Relative to the HF/3-21G calculated model the B3LYP/6-31G* has lengthed c=c double bonds and shortened c-c single bonds suggesting a degree of increaced delocalisation.

A vibrational analysis of this second model was performed and all frequencies produced were positive as demonstrated in the calculated IR spectrum (left). The sum of electronic and zero point energies was -234.469182. The sum of electronic and thermal energies was -234.461844. The sum of electronic and thermal enthalpies was -234.460900. The sum of electronic and thermal free energies was -234.500730.

The Cope Rearrangement: modelling the transition state

A model of the chair transition state was created by placing two delocallised allyl fragments CH₂CHCH₂ so that the terminal carbons were at a distance of 2.2A from each other. The model was then optimised to a berny transition state and the frequencies calculated using HF/3-21G. The resulting transition state (shown below) had energy -231.61932 a.u. and one imaginary frequency at -837 cm^-1 which corresponds to the cope rearrangement.

chair ts

The model was then reoptimised using the frozen coordinate method. First freezing the terminal atom spacing at 2.2 angstroms and then allowing it to vary. This new model had an energy of -231.61932 a.u. with the imaginary vibration now lying at -818 cm^-1 and the terminal atom spacing down to 2.02 angstroms from 2.14.

The boat transition structure was optimised using the QST2 method. This method generates the transition state automatically when given the reactat and product structures. The B3LYP/6-31G* anti2 model produced earlier was used for both reactant and product with atom labelling adjusted accordingly. This calculation failed since this method does not take into account the rotation around the central bond necessary to enter the transition state. The reactant and product were therefore manually manipulated to create a syn central linkage and the calculation was run again.

The resulting model had energy -231.60280 with a single imaginary frequency at -840 cm^-1.