Simple quantum-classical reaction path dynamics

Starting with the reaction path Hamiltonian of Miller, Handy, and Adams, a set of two pairs of coupled differential equations describing the reaction dynamics is derived using a mixed quantum classical approach. The first pair of coupled equations describe the vibrational modes during the reaction and are derived quantum mechanically using time dependent perturbation in which the reaction path curvature is treated as the perturbation. The second set of coupled equations describe the motion along the reaction path and are derived classically using the mean field approximation. These two pairs of coupled equations are also coupled to each other.;Analytic equations for the reaction path potential energy, vibrational frequencies, and reaction path curvature as functions of path coordinate for the dynamics are calculated using two approaches. The first approach uses three levels of theory: HF to obtain coupling terms and vibrational frequencies, MP2 to correct the HF results, and Gaussian-2 to calculate the potential energy. This approach was used on HF and HCl elimination from their respective haloethanes, as well as HONO elimination from CH2NNO2. The second approach computes the couplings, frequencies, and potential energy at the B3LYP level of theory. By using only one level of theory, the second approach is faster and more consistent than the first. This approach was used on HF elimination from fluoroethane. Both approaches compared favorably with experiment.