Cumulative reaction probability and reaction eigenprobabilities from time-independent quantum scattering theory - art. no. 042707

The cumulative reaction probability (CRP) is a gross characteristic of rear rangement collision processes defining the reaction rate constant. This pap er presents a complete development of the approach to the theory of CRP tha t we have recently proposed [Phys. Rev. Lett. 80, 41 (1998)]. In the core o f this approach Lies an alternative expression for CRP in terms of the outg oing wave Green's function which is formally equivalent to the Miller's def inition of this quantity in terms of the scattering matrix [J. Chem. Phys. 62, 1899 (1975)] and to the Miller-Schwartz-Tromp formula [J. Chem. Phys. 7 9, 4889 (1983)], but is direct, in contrast to the former, and mon suitable for practical calculations than the latter. Furthermore, our approach rest s on solid grounds of time-independent quantum scattering theory and provid es an appealing competitive alternative to the absorbing potential formulat ion given by Seideman and Miller [J. Chem. Phys. 96, 4412 (1992), 97, 2499 (1992)]. Ideologically, it is close to the approach considered earlier for a one-dimensional model by Manolopoulos and Light [Chem. Phys. Lett. 216, 1 8 (1993)], but is formulated from scratch for realistic systems with many d egrees of freedom. The strongest point of our approach is that its final wo rking formulas are expressed in terms of the Wigner-Eisenbud R matrix, so t hey can be easily implemented on the basis of many existing quantum scatter ing codes. All these features are discussed and illustrated by calculations of the CRP and reaction eigenprobabilities for two prototypical light atom transfer reactions in heavy-light-heavy triatomic systems in three dimensi ons for zero total angular momentum.