Cumulative reaction probability via transition state wave packets

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

DOI:https://doi.org/10.1063/1.471302· OSTI ID:279898

Zhang, D H; Light, J C ^[1]

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1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)

A new time-dependent approach to the cumulative reaction probability, {ital N}({ital E}), has been developed based on the famous formulation given by Miller and co-workers [J. Chem. Phys. {bold 79}, 4889 (1983)], {ital N}({ital E})=[(2{pi}){sup 2}/2]tr[{delta}({ital E}{minus}{ital H}){ital F}{delta}({ital E}{minus}{ital H}){ital F}]. Taking advantage of the fact that the flux operator has only two nonzero eigenvalues, we evaluate the trace efficiently in a direct product basis of the first flux operator eigenstates and the Hamiltonian eigenstates on the dividing surface (internal states). Because the microcanonical density operator, {delta}({ital E}{minus}{ital H}), will eliminate contributions to {ital N}({ital E}) from an internal state with the energy much higher than the total energy {ital E}, we can minimize the number of internal states required by choosing a dividing surface with the lowest density of internal states. If the dividing surface is located in an asymptotic region, one just needs to include all the open channels, i.e., with internal energy lower than the total energy. Utilizing the Fourier transform for {delta}({ital E}{minus}{ital H}), we can obtain the information for all the energies desired by propagating these wave packets once. Thus the present approach will be much more efficient than the initial state selected wave packet (ISSWP) approach to {ital N}({ital E}) for systems with many rotation degrees of freedom because the density of states in asymptotic region for such systems is much higher than that in the transition state region. With the present method one can also calculate the cumulative reaction probability from an initial state (or to a final state) by locating the second flux operator in the corresponding asymptotic region. This provides an alternative to the ISSWP approach which may be more efficient if the reaction probabilities from a large number of initial states are desired. (Abstract Truncated)

• DOE Contract Number: FG02-87ER13679
• OSTI ID: 279898
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 16 Vol. 104; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
CHEMICAL REACTION KINETICS
EXCITED STATES
HYDROGEN
HYDROGEN MOLECULES
POTENTIAL ENERGY SURFACES
PROBABILITY
QUANTUM MECHANICS
ROTATIONAL STATES
SCATTERING
WAVE PACKETS