The use of Monte Carlo simulations to evaluate kinetic data and analytic approximations

Experimental kineticists are always faced with the problem of reducing kinetic data to extract physically meaningful information. A particularly vexing problem arises when different models reproduce the data but yield different values for the physical parameters. For over forty-five years Monte Carlo simulation techniques have been used to study the statistical behavior of parameters extracted from data. Not only do these simulations provide realistic uncertainties, correlation coefficients, and confidence envelopes, but they also provide insight into the nature of the model. These insights may be obtained by viewing two-dimensional scatter plots of the fractional changes of the parameters and one-dimensional histograms of the distributions of the changes in the parameters. Monte Carlo simulations are illustrated with examples from OH+CH₄ → CH₃+H₂O and the high-pressure rate coefficient for methyl-methyl association. A more complex problem involves models for pressure-dependent rate coefficients in the falloff region. We have modeled methyl-methyl association with five of the most current analytic approximations for behavior in the falloff region. All of these reproduce the data to within their uncertainties. However, when Monte Carlo techniques are applied the correlations between the parameters and the nonlinear nature of their behavior become evident. We postulate that the statistical behavior of the parameters of a model may be used to distinguish one model from another and, thereby, identify those analytic approximations that hold promise for further investigation and utilization. Finally, the recent advent of high-speed workstations implies that Monte Carlo simulations should become a routine part of the analysis of kinetic data. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 803–817, 1997