 
Summary: Efficient polynomial expansion of the scattering Green's function:
Application to the D+H#= 1) rate constant
Scott M. Auerbacha) and William H. Millerb)
Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley
Laboratory, Berkeley, California 94720
(Received 13 September 1993; accepted 6 October 1993)
We apply the absorbing boundary condition (ABC) discrete variable representation (DVR)
theory of quantum reactive scattering to the initial state selected D+H,( v= 1, j) +DH+H
reaction. The ABCDVR Green's function is efficiently computed by a Newton polynomial
expansion. We compute accurate reaction probabilities for the total energies and angular mo
menta required to obtain the thermal rate constants k,= 1,j (T).At T=310K,athermalaverage
over j=(O,1,2,3) is performed to yield the final result k,,,(310 K) =1.87X lol3
cm3 molecule' sl, in quantitative agreement with the most recent experimental value (1.9
hO.2) X lol3 cm3 moleculeisi. The Jshifting approximation using accurate J=O reaction
probabilities is tested against the exact results. It reliably predicts k,= t ( T) for temperatures up
to 700 K, but individual (v= 1, j) selected rate constants are in error by as much as 41%.
I. INTRODUCTION
The past few years in chemical reaction dynamics have
seen several detailed and reliable comparisons between ex
periment and theory. `+ These comparisons have brought
