Quantum mechanical reaction probabilities via a discrete variable representation-absorbing boundary condition Green’s function

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Abstract
The use of a discrete variable representation (DVR) and absorbing boundary conditions (ABC) to construct the outgoing Green’s function G(E+)≡limε→0(E+iε−H)−1, and its subsequent use to determine the cumulative reaction probability for a chemical reaction, has 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+H2 reaction with zero total angular momentum.