Quantum mechanical reaction probabilities with a power series Green's function

We present a new method to compute the energy Green’s function with absorbing boundary conditions for use in the calculation of quantum mechanical reaction probabilities. This is an iterative technique to compute the inverse of a complex matrix which is based on Fourier transforming time-dependent dynamics. The Hamiltonian is evaluated in a sine-function based discrete variable representation, which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green’s function to the calculation of the cumulative reaction probability for the benchmark collinear H+H, system over the energy range 0.37-1.27 eV. The convergence of the power series is found to be stable at all energies and accelerated by the use of a stronger absorbing potential.