Close coupling-wave packet formalism for gas phase nonreactive atom–diatom collisions

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Abstract
In this paper we discuss the adaptation of the close coupling-wave packet (CCWP) method for solving the time dependent Schrödinger equation for inelastic, nonreactive gas phase atom–diatom collisions. The approach is novel in that (a) it is an initial value rather than boundary value method, (b) it can be formulated to either avoid or include the partial wave expansion normally used for gas phase atom–diatom collisions, (c) it can be formulated to determine either a single column of the differential scattering amplitude matrix or S matrix rather than the full matrix, (d) the labor involved in a single calculation scales with the number of rotor states squared rather than cubed as in standard close coupling, (e) a single calculation yields numerically exact results over the full range of energies contained in the original wave packet, and (f) results for other initial states can be obtained by means of the energy sudden (ES) or energy corrected sudden (ECS) factorization relations. The analysis for extracting the differential scattering amplitude at fixed energies is given in detail because it differs markedly from that normally given in textbook treatments of the wave packet formulation of gas phase scattering. Finally, an example approximate version of the formalism (namely the energy sudden) is given.