QUANTUM-MECHANICAL REACTION PROBABILITIES VIA A DISCRETE VARIABLE REPRESENTATION-ABSORBING BOUNDARY-CONDITION GREEN-FUNCTION

The use of a discrete variable representation (DVR) and absorbing boundary conditions (ABC) to construct the outgoing Green's function G(E+) = lim(epsilon --> 0) (E + i-epsilon - H) - 1, and its subsequent use to determine the cumulative reaction probability for a chemical reaction, bas been extended beyond our previous work [J. Chem. Phys. 96, 4412 (1992)] in several significant ways. In particular, the present paper gives a more thorough derivation and analysis of the DVR-ABC approach, shows how the same DVR-ABC Green's function can be used to obtain state-to-state (as well as cumulative) reaction probabilities, derives a DVR for the exact, multidimensional Watson Hamiltonian (referenced to a transition state), and presents illustrative calculations for the three-dimensional H + H-2 reaction with zero total angular momentum.