Effective Hamiltonian methods for the semiclassical treatment of molecular collisions

Abstract

Effective Hamiltonian theory has previously been applied in a quantum mechanical framework, where the computational savings resulted from the reduced number of coupled equations. The present paper shows how effective Hamiltonian theory can be combined with classical S‐matrix theory. In this case the computational difficulty is reduced by lowering the number of degrees of freedom that must be semiclassically ’’quantized’’ via root‐searching techniques. It is shown, for example, that a full classical S‐matrix calculation for collisions of two rigid diatoms would require root searches in a four‐dimensional space while an effective potential calculation would need only two‐dimensional root searches. This can represent a substantial decrease in computational effort. A modified effective potential and the centrifugal decoupling method are formulated for application to classical S‐matrix theory. Also included is a description of the rotational coordinates and momenta needed for the semiclassical treatment of an arbitrary, nonreactive bimolecular collision.