Semiclassical calculation of cumulative reaction probabilities

Journal Article · Mon Jan 01 04:00:00 EST 1996 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.470878· OSTI ID:254912

Spath, B W; Miller, W H ^[1]

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1. Department of Chemistry, University of California (United States)

It is shown how the rigorous quantum mechanical expression for the cumulative reaction probability (CRP) obtained by Seideman and Miller [J. Chem. Phys. {bold 96}, 4412; {bold 97}, 2499 (1992)], {ital N}({ital E})=4tr[{epsilon}{cflx char}{sub {ital r}}{center_dot}{ital G}{cflx char}{asterisk}({ital E}){center_dot}{epsilon}{cflx char}{sub {ital p}}{center_dot}{ital G}{cflx char}({ital E})], which has been the basis for quantum calculations of the CRP for simple chemical reactions, can also be utilized with a semiclassical approximation for the Green{close_quote}s function, {ital G}{cflx char}({ital E}){identical_to}({ital E}+{ital i}{epsilon}{cflx char}-{ital H}{cflx char}){sup -1}=({ital i}{Dirac_h}){sup -1}{integral}{sup {infinity}}{sub 0} exp({ital iEt}/{Dirac_h})exp(-{ital i}({ital H}{cflx char}-{ital i}{epsilon}{cflx char}){ital t}/{Dirac_h}). Specifically, a modified Filinov transformation of an initial value representation of the semiclassical propagator has been used to approximate the Green{close_quote}s function. Numerical application of this trajectory-based semiclassical approximation to a simple one-dimensional (barrier transmission) test problem shows the approach to be an accurate description of the reaction probability, even some ways into the tunneling regime. {copyright} {ital 1996 American Institute of Physics.}

• Research Organization: Lawrence Berkeley National Laboratory
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 254912
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 1 Vol. 104; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
CHEMICAL REACTION KINETICS
DEGREES OF FREEDOM
GREEN FUNCTION
ONE-DIMENSIONAL CALCULATIONS
PROBABILISTIC ESTIMATION
SEMICLASSICAL APPROXIMATION