Empirical testing of the suitability of a nonrandom integration method for classical trajectory calculations: Comparisons with Monte Carlo techniques

Abstract

A nonrandom method for approximating multidimensional integrations is compared to traditional ``random'' Monte Carlo techniques for determining reaction cross sections from quasiclassical trajectories. Reaction cross sections are calculated for the H + H2 collision system to determine the relative rates of convergence for each method as a function of the number of trajectories employed in the calculation. Estimates of the maximum probable error for the nonrandom integrations of a given number of trajectories compare favorably with the errors expected for Monte Carlo integrations and seem to imply that nonrandom integrations are more accurate than Monte Carlo calculations. However, the error of a Monte Carlo integration is easily estimated while that of a nonrandom integration is not. Thus the nonrandom method's advantage in accuracy may be overcome by other characteristics of the Monte Carlo method. For classical trajectory calculations, the nonrandom method should be considered as an alternative, but not a replacement, for the Monte Carlo method.