Reaction Rate Theory

Effective-Potential Theory of Molecular Dynamics

We are using an effective-potential formulation of quantum dynamics to obtain approximate analytical expressions for the temperature dependence of rate consants and to develop a computationally inexpensive method for incorporating quantum effects into molecular dynamics simulations of chemical reactions. We expect this work to have applications in combustion chemistry, atmospheric chemistry, and materials science. Feynman and Hibbs [1] using path-integral methods showed that, within a first-order perturbation theory in 1/T, quantum statistical mechanics is equivalent to classical statistical mechanics with the potential energy replaced by a temperature-dependent effective potential that is a Gaussian average of the original potential. Subsequently, Doll [2] suggested that classical molecular dynamics on the effective potential would yield approximately the same reaction rates as quantum dynamics on the actual potential. We have modified Feynman's theory to extend the temperature range over which it is applicable, and have demonstrated [3] that the temperature-dependent activation energy, obtained from the effective potential, when substituted into the transition-state theory expression for the rate constant can give an accurate description of the reaction CH_4 + H --> CH_3 + H_2 over the entire range for which experimental measurements are available. Our goal is to construct effective potential-energy functions for use in large-scale molecular dynamics simulations of carbon-hydrogen and silicon-hydrogen reactions, which we plan to use for studies of materials processes such as chemical vapor deposition. We are developing temperature-dependent expressions for rate constants for use in modeling the kinetics of combustion and atmospheric chemistry. his project is a collaboration with Dr. Steven Valone of the Materials Science Division (MST-8) at Los Alamos National Laboratory.

[1] R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965), pp. 268-298.

[2] J. D. Doll, "Monte Carlo Fourier Path Integral Methods in Chemical Dynamics," J. Chem. Phys. 81, 3536-3541 (1984).

[3] D. Z. Goodson, D. W. Roelse, W.-T. Chiang, S. M. Valone, and J. D. Doll, " A Simple Method for Calculating Quantum Effects on the Temperature Dependence of Bimolecular Reaction Rates: Application to H_2 + H --> H + H_2 and CH_4 + H --> CH_3 + H_2," J. Am. Chem. Soc. 122, 9189 (2000).