A SEMICLASSICAL APPROACH TO INTENSE-FIELD ABOVE-THRESHOLD DISSOCIATION IN THE LONG-WAVELENGTH LIMIT - II - CONSERVATION PRINCIPLES AND COHERENCE IN SURFACE HOPPING

This paper is a companion to our recently published semiclassical form alism for treating time-dependent Hamiltonians [J. Chem. Phys, 105, 40 94 (1996)], which was applied to study the dissociation of diatomic io ns in intense laser fields. Here two fundamental issues concerning thi s formalism are discussed in depth: conservation principles and cohere nce. For time-dependent Hamiltonians, the conservation principle to ap ply during a trajectory hop depends upon the physical origin of the el ectronic transition, with total energy conservation and nuclear moment um conservation representing the two limiting cases. It is shown that a]applying an inappropriate scheme leads to unphysical features in the kinetic energy of the dissociation products. A method is introduced t hat smoothly bridges the two limiting cases and applies the physically justified conservation scheme at all times. It is also shown that the semiclassical formalism can predict erroneous results if the electron ic amplitudes for well-separated hops are added coherently. This is a fundamental problem with the formalism which leads to unphysical resul ts if left unattended. Alternative schemes are introduced for dealing with this problem and their accuracies are assessed. Generalization of the well-known Landau-Zener formula to the time-dependent Hamiltonian case is derived, which allows one to significantly decrease the compu tational overhead involved with the numerical implementation of the se miclassical method. Finally, we show that in strong-field molecular di ssociation a trajectory can ''surf'' a moving avoided crossing. In thi s case the hopping probability is a sensitive function of the interfer ence between two closely spaced avoided crossing regions. (C) 1998 Ame rican Institute of Physics.