Large-Scale Quantum Mechanical Scattering Calculations on Vector Computers

Energy transfer in molecular collisions is a very fundamental problem in chemical physics, both experimentally and theoretically. Quantitative state-to-state cross sections for energy transfer processes are important for understanding and modelling many kinds of systems, including lasers, shocked gases, planetary atmospheres, and systems containing excited reaction products of any kind. In theory these cross sections can be calculated from first principles using quantum mechanics but in practice this involves severe computational difficulties. The first step is the calculation of molecular interaction potentials, which are a consequence of the electronic structure of the interacting molecules for various geometries.There has been enormous progress in this area in the last few years, 1-3 but we shall not consider it further in this chapter. Instead we shall concentrate on the second step, the dynamical problem that yields the desired inelastic cross sections from the intermolecular potential. Only when both steps have been solved adequately will the ab initio method have reached fruition, but the techniques involved in the two steps are very specialized and to a large extent progress on these steps may occur separately and in parallel. There are two basic approaches to the dynamics problem. First, one can try to develop reliable methods based on simplifying approximations, such as using semiclassical or classical methods or low-order perturbation theory.

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