Calculation of the cumulative reaction probability via a discrete variable representation with absorbing boundary conditions

Abstract

A new method is suggested for the calculation of the microcanonical cumulative reaction probability via flux autocorrelation relations. The Hamiltonian and the flux operators are computed in a discrete variable representation (DVR) and a well‐behaved representation for the Green’s operator, G(E⁺), is obtained by imposing absorbing boundary conditions (ABC). Applications to a one‐dimensional‐model problem and to the collinear H+H₂ reaction show that the DVR‐ABC scheme provides a very efficient method for the direct calculation of the microcanonical probability, circumventing the need to compute the state‐to‐state dynamics. Our results indicate that the cumulative reaction probability can be calculated to a high accuracy using a rather small number of DVR points, confined to the vicinity of the transition state. Only limited information regarding the potential‐energy surface is therefore required, suggesting that this method would be applicable also to higher dimensionality problems, for which the complete potential surface is often unknown.