 
Summary: Quantum mechanical reaction probabilities with a power series
Green's function
Scott M. Auerbach and William H. Miller
Department of Chemistq University of California, and Chemical Sciences Division, Lawrence Berkeley
Laboratory, Berkeley, California 94720
(Received 22 October 1992; accepted 19 January 1993)
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 timedependent dynamics. The Hamiltonian is evaluated in a sinefunction
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 0.371.27 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.
I. INTRODUCTION
One of the central tasks in theoretical reaction dynam
ics is the development of computational techniques able to
predict the chemistry of large molecules. The ab initio
treatment of chemical reactions in the gas phase relies on
