Projection methods for obtaining intramolecular energy transfer rates from classical trajectory results: Application to 1,2-difluoroethane

A general method for analyzing the results of classical trajectory calculations to obtain the details of intramolecular energy transfer is described. The method is based on the determination of the time dependence of the normal mode velocities by projection of the instantaneous Cartesian velocities onto the normal mode vectors. It is shown that the method obviates the need to arbitrarily define a ‘‘bond’’ or ‘‘mode’’ energy as a means of following the energy flow. Average mode energies are computed using the virial theorem. For a given potential surface, the results are exact within the framework of the classical approximation. The method is applied to a study of intramolecular energy transfer in 1,2-difluoroethane. Decay rates and pathways of energy flow for initial excitation of each of the 18 vibrational modes are reported. The results obtained from the time variation of the normal mode velocities are used to extract a first-order, mode-to-mode energy transfer rate coefficient matrix. The mode-to-mode coefficients are shown to provide an excellent means of collating the energy transfer information. Their values yield a quantitative description of the energy transfer rates and a clear picture of the relative importance of the available pathways for energy flow in the system.