A multiple trajectory theory for curve crossing problems obtained by using a Gaussian wave packet representation of the nuclear motion

Abstract

This article is concerned with the time dependent quantum theory of collision of heavy particles that result in the excitation of internal degrees of freedom, such as electronic excitations or charge transfer. Attempts to treat the motion of the heavy particle classically encounter difficulties typical to all problems in which the classical degrees of freedom are strongly coupled to quantum degrees of freedom: They lack a feedback mechanism that will force the classical degree of freedom to respond to the excitation of the quantum companion. To avoid such difficulties we propose a method in which the nuclear wave function associated with each electronic state is represented by a Gaussian wave packet. Each packet is propagated by the time dependent Schrödinger equation on a different electronic energy surface in a manner that resembles classical mechanics but perserves many quantum properties such as Heisenberg uncertainty principle, quantum interference, zero point motion, and the quantum mechanical rules for computing observables. Various limiting cases are discussed in detail and compared numerically.