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

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 + H ₂ 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.