Normal collision coordinates for collinear triatomic systems

Abstract

We introduce a new set of variables, called normal collision coordinates (NOCC), for the treatment of reaction dynamics in collinear triatomic systems. NOCC are a generalization of a particular set of collision coordinates introduced by Child and are equivalent in dynamical separability and coputational effort to the natural collision coordiantes (NCC) introduced by Marcus. The advantage of NOCC over NCC is primarily conceptual. In contrast to NCC, NOCC are directly expressible in terms of the relative positions of the three atoms at each stage of the reaction and allow us to regard the complicated relative motion of each nucleus as the superposition of a (in some cases, nearly uncoupled) translational and vibrational mode. This analysis leads to an interpretation of the non-adiabatic ‘bobsled effect’ in terms of the rate of change in the identity of these modes with the reaction's progress. The study of normal collision coordinates also sheds light upon the ability of NCC or NOCC to yield an ‘optimal’ separation of variables, and provides insight into the relationship between perturbed stationary state calculations and calculations based on progress-dependent collision variables. It is argued that the factorization of the wavefunction for a decomposing molecule resulting from the introduction of NOCC should make possible the calculation of photodissociation rate constants via multiphonon radiationless transition theory.