The classical path approximation in time-dependent quantum collision theory

Abstract

Time-dependent treatments of molecular collisions have frequently employed the combination of quantum equations for the internal degrees of freedom (i.e., vibration, rotation) with a classical description of the translational motion. In this paper, it is shown how energy-conserving classical path equations may be derived from first principles, thereby obtaining quantum correction terms of arbitrary order. These expressions have interesting implications for the question of how the classical limit is approached. If the translational degree of freedom is assumed to be described by a very narrow wave packet, the correction term to first order in fz is purely imaginary and therefore non-Hermitian. These techniques can be generalized to a classical treatment of other degrees of freedom, and the case of rotation in an atom-vibrotor collision is explicitly considered. For both the translational and rotational examples, the full series of corrections takes on an interesting and suggestive exponential form. The failure of classical path methods to satisfy microscopic reversibility is ascribed to a difficulty with the boundary conditions for the translational motion.

Semiclassical calculations on the energy dependence of the steric effect for the reaction Ca(1D)+CH3F(jkm=111)→CaF+CH3

“…[25][26][27]29,31,32,37 However, micro scopic reversibility is not obeyed., i.e., the probability of an excitation from state n to state m is not equal to the prob ability of the reverse process. Methods have been published to circumvent this problem (see, e.g., Refs.…”

Nonadiabatic Molecular Dynamics with Tight-Binding Fragment Molecular Orbitals

“…According to it, the nuclear dynamics of the overall system governs the electronic dynamics via parametric dependence of the vibronic Hamiltonian on nuclear coordinates, whereas the electronic dynamics does not affect the nuclear one. This version of the classical path approximation (CPA) had been successfully utilized in the past. − Its validity is justified by the fact that the molecular systems are sufficiently large and rigid. Specifically, nuclear forces are determined by the electronic structure of the overall system.…”

A simplified approach to optimally controlled quantum dynamics

“…The same control concepts may also be applied for semiclassical wave packet propagation [44][45][46] and mixed quantum/classical molecular dynamics. [35][36][37][38] FIGURES FIG. 1.…”