Quantum mechanical algebraic variational methods for inelastic and reactive molecular collisions

The quantum mechanical problem of reactive or nonreactive scattering of atoms and molecules is formulated in terms of square-integrable (ℒ²) basis sets with variational expressions for the reactance matrix. We present and test several formulations, involving expansions of the wave function (the Schwinger variational principle) or amplitude density (a generalization of the Newton variational principle), single-channel or multichannel distortion potentials, and primitive or contracted basis functions. The test results, for inelastic and reactive atom-diatom collisions, are very encouraging, and we anticipate that the methods will be very useful for a variety of collision calculations and that they will allow the accurate quantal treatment of systems for which other available methods would be prohibitively expensive.