On the classical simulation of unimolecular reaction processes

Abstract

Abstract The numerical simulation of the internal motions of a molecule undergoing a unimolecular reaction on an assumed potential energy surface requires the step-by-step solution of a set of simultaneous differential equations. After several thousand time steps, due to differences in the handling of rounding errors in different computing systems, the situation often arises that no two computing machines will give the same result for a given trajectory, even when running the identical algorithm. Such effects are demonstrated for a simple unimolecular isomerisation reaction. In general, it is only when reliance is placed on the integration of a single trajectory, rather than on an ensemble of similar trajectories, that conclusions may be unreliable. Moreover, under certain conditions, small molecules may show signs of chaotic internal motions; conversely, but for a different reason, large molecules may exhibit non-statistical characteristics rather than RRKM behaviour. The rounding error problem, in a slightly different guise, has come to be dubbed the “butterfly effect” in popular culture, and the original proposition is re-examined using 16- and 32-decimal precision arithmetic.