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 d...

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Bibliographic Details
Published in:The Journal of chemical physics 1993-05, Vol.98 (9), p.6917-6928
Main Authors: AUERBACH, S. M, MILLER, W. H
Format: Article
Language:English
Subjects:
661100 > Classical & Quantum Mechanics-- (1992-)
ATOM COLLISIONS
ATOM-MOLECULE COLLISIONS
Atomic and molecular collision processes and interactions
Atomic and molecular physics
BOUNDARY CONDITIONS
CALCULATION METHODS
CHEMICAL REACTION KINETICS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COLLISIONS
ELEMENTS
Exact sciences and technology
FOURIER TRANSFORMATION
FUNCTIONS
GREEN FUNCTION
HAMILTONIANS
HYDROGEN
INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
INTEGRAL TRANSFORMATIONS
ITERATIVE METHODS
KINETICS
MATHEMATICAL OPERATORS
MATRICES
MECHANICS
MOLECULE COLLISIONS
NONMETALS
Physics
POWER SERIES
QUANTUM MECHANICS
QUANTUM OPERATORS
REACTION KINETICS
Scattering of atoms, molecules and ions
SERIES EXPANSION
TIME DEPENDENCE
TRANSFORMATIONS 400201 > Chemical & Physicochemical Properties
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Description
Summary: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 sinc-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+H2 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.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.464759