MULTIPLE TIME-SCALE QUANTUM WAVEPACKET PROPAGATION - ELECTRON-NUCLEARDYNAMICS

We have developed a multiple time scale (MTS) quantum wavepacket propa gation algorithm for the electron-nuclear dynamics in which the electr on and nuclear motions are followed simultaneously. The large mass dis parity between the electron and the nuclear degrees of freedom poses a problem when one propagates the total wavefunction using a single tim e step. The standard split operator propagation method requires a smal l time step to be used for stable propagation of the fast electronic d egrees of freedom, which leads to an unnecessarily large number of pro pagations for slow nuclear motions. A new factorization of the time ev olution operator based on the decomposition of the total Hamiltonian i nto the nuclear part and the electronic Hamiltonian is proposed. The M TS factorization allows one to choose the spatial grid size and the ti me step appropriate for each subsystem separately. The MTS algorithm i s applied to a charge-transfer model for the evaluation of optical spe ctra and thermal rate constants. It is shown that the multiple time sc ale propagation gives correct results with moderate computational time savings.