Visualizing motion along the reaction path

· For eclipsed ethane (the transition state), looking at the atomic displacements involved for the normal mode with the imaginary frequency tells us what the reaction coordinate is like.

· This imaginary frequency corresponds to motion along the reaction path. The motion looks like a rotation of both methyl groups around the C-C bond, as expected.

So what is the barrier to rotation?

Compare the energies of the eclipsed and staggered conformations. The energies given by these calculations are the energies of the electrons in the molecule, plus the energy of interaction between the nuclei.

The calculated energies are:

E(RHF) = -79.2287550171 A.U.

(staggered)

E(RHF) = -79.2239967582 A.U.

(eclipsed)

So the barrier is 0.0047582589 Hartrees per molecule.

1 H is equivalent to 2625.5 kJ mol^–1, so the barrier is 12.49 kJ mol^–1.

This answer agrees well with experimental results for ethane.

· Eclipsed ethane is a transition state structure for a conformational change.

· Obviously we are often interested in transition states for chemical reactions.

· The same optimization procedures can be used because in both cases we are searching for a saddlepoint on the potential energy surface.

Next: optimizing a saddlepoint with the Newton-Raphson method