AN EFFECTIVE HAMILTONIAN-BASED METHOD FOR MIXED QUANTUM-CLASSICAL DYNAMICS ON COUPLED ELECTRONIC SURFACES

We describe an approximate method for treating the mixed quantum-class ical (QC) dynamics of many-body systems on N coupled electronic surfac es. The approach is based on calculating NXN reduced Hamiltonian matri ces for the classical and quantal degrees of freedom by partial averag ing, and then solving the appropriate equations of motion-Hamilton's e quations or the Schrodinger equation-self-consistently. The degrees of freedom requiring a quantum mechanical description are treated using a multistate Schrodinger equation with classically averaged effective time-dependent Hamiltonians and off-diagonal couplings. The classical degrees of freedom are treated by propagating N ensembles of trajector ies, one on each electronic surface, using N reduced classical Hamilto nians defined in terms of the expectation value of the full Hamiltonia n calculated using the evolving quantum wave functions. An ansatz is p roposed to approximately estimate classical off-diagonal density matri x elements required for calculating the classically averaged interacti ons that couple quantum wave functions on different electronic states. We present the theory and then test it for a simple two-dimensional a nd two-state model system. Exact quantum and multiconfiguration time-d ependent self-consistent-held (MCTDSCF) calculations are carried out t o evaluate the QC performance. Good agreement between the MCTDSCF and QC results is obtained for the model considered. (C) 1996 American Ins titute of Physics.