Time-dependent dynamics of electrons and nuclei

Using the time-dependent variational principle with a group theoretical coherent state defining the wave functions for electrons and nuclei, a system of coupled, first-order, nonlinear differential equations is obtained for a general molecular system. The equations form a classical Hamiltonian system within a generalized phase space that allows a systematic time-dependent study of molecular processes. The approach is general and provides a computational framework for a variety of properties such as transition and excitation probabilities in atomic and molecular collisions, and molecular spectra such as vibrational spectra with anharmonicities. The basic approximation corresponding to the choice of a single determinantal wave function for the electrons and classical nuclei is analyzed. Illustrative applications to the p+H collision process and to vibrations of the H2O molecule exhibit good agreement with experiment and with other theoretical work.