Effective Hamiltonian methods for the semiclassical treatment of molecular collisions

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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.