Master equation analysis of intermolecular energy transfer in multiple-well, multiple-channel unimolecular reactions. II. Numerical methods and application to the mechanism of the C2H5+O2 reaction

Prasana K. Venkatesh, Anthony M. Dean, Morrel H. Cohen, Robert W. Carr

Research output: Contribution to journalArticle

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Abstract

Having elucidated a full theoretical analysis of the master equation for intermolecular and intramolecular energy transfer in multiple-well, multiple-channel chemically or thermally activated reactions [J. Chem. Phys. 107, 8904 (1997)], we now present efficient methods of numerical analysis for the computational examination of the dynamics of the master equation. We suggest the use of a Krylov-subspace method to determine the uppermost portions of the internal spectrum of the master equation kernel. Such a computation is pivotal in determining whether there exists a state of secular equilibrium for the population of the moieties and whether there exists within the possible state of secular equilibrium, a state wherein the dynamics are represented by an isolated dominating mode; for only in the state of secular equilibrium can one write rate equations for the dissociating processes that are local in time. And, if such a state is possible, we suggest the use of a Hermite-Laguerre orthogonal collocation method for obtaining highly accurate solutions to the population of the moieties. The theory and numerical analysis is then applied to study the dynamics of the chemically-activated reaction C2H5+O2. Comparison of the master equation treatment with modified strong-collision theory is also given for this system of multiple-well, multiple-channel reactions.

Original languageEnglish (US)
Pages (from-to)8313-8329
Number of pages17
JournalJournal of Chemical Physics
Volume111
Issue number18
DOIs
StatePublished - Nov 8 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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