Some aspects of quantum molecular scattering in chemical dynamics

Some aspects of quantum molecular scattering in chemical dynamics 

Chemical dynamics is the link between the potential energy surface (PES) (or surfaces) and an observable chemical phenomena. In principle the PES comes from an ab initio quantum chemistry calculation (within the Born-Oppenheimer approximation) though in practice it is often constructed by some more approximate model, e.g., semiempirical quantum chemistry or totally empirical force field models. First a brief overview of the present state of the methodology and scope of applications in this area is given. We will concentrate on chemical dynamics in the gas phase, though much of the methodology of this field has carried over to the study of dynamical processes in condensed phases, gas-surface collision processes, and also dynamics in biomolecular systems. 

In the next three subsections (extracted from the work of Miller [13]) we will discuss briefly molecular collision processes (elastic, inelastic and reactive scattering), perhaps the most well-defined and rigorous approach to studying chemical dynamics. 

In the early days of chemical dynamics (the 1960 s) the study of elastic scattering was an important project, both experimentally and theoretically, for developing the tools to be used to study more interesting processes, e.g., elastic scattering of the rare gas atoms. Y.T.Lee s (1986 Nobel Prize with M. Polanyi and D. Herschbach) measurements of the differential scattering cross sections allowed the definitive determination of the intermolecular potential energy function V(r) of essentially all the rare gas atoms with each other 

The fully rigorous quantum mechanical elastic differential cross section is given by [64] 

---