Jp. Hessler, THE USE OF MONTE-CARLO SIMULATIONS TO EVALUATE KINETIC DATA AND ANALYTIC APPROXIMATIONS, International journal of chemical kinetics, 29(11), 1997, pp. 803-817
Experimental kineticists are always faced with the problem of reducing
kinetic data to extract physically meaningful information. A particul
arly vexing problem arises when different models reproduce the data bu
t yield different values for the physical parameters. For over forty-f
ive years Monte Carlo simulation techniques have been used to study th
e statistical behavior of parameters extracted from data. Not only do
these simulations provide realistic uncertainties, correlation coeffic
ients, and confidence envelopes, but they also provide insight into th
e nature of the model. These insights may be obtained by viewing two-d
imensional scatter plots of the fractional changes of the parameters a
nd one-dimensional histograms of the distributions of the changes in t
he parameters. Monte Carlo simulations are illustrated with examples f
rom 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 mo
deled methyl-methyl association with five of the most current analytic
approximations for behavior in the falloff region. Ail of these repro
duce the data to within their uncertainties. However, when Monte Carlo
techniques are applied the correlations between the parameters and th
e 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 analyt
ic approximations that hold promise for further investigation and util
ization. Finally, the recent advent of highspeed workstations implies
that Monte Carlo simulations should become a routine part of the analy
sis of kinetic data. (C) 1997 John Wiley & Sons, Inc.