First order stochastic cellular automata simulations of the lindemann mechanism

The Lindemann mechanism explains how apparent unimolecular chemical reactions arise from bimolecular collisions. In this mechanism an ingredient M activates reactants A through collisions, and the resulting activated species A* can either decay to products P or be deactivated back to A, again via collisions with M. A first-order stochastic cellular automata model described previously \Seybold, Kier, and Cheng, I Chem Inf Comput Sci 1997, 37, 3861 has been modified to simulate this mechanism. it is demonstrated that this model accurately reflects the salient features of the Lindemann mechanism, including the normal second-order kinetic behavior at low \M\ and apparent first-order kinetics at high \M\. At low \M\ the mechanism is equivalent to a rate-limited sequential process, whereas at high \M\ it becomes a preequilibrium with leakage to products. The model also allows an examination of the validity of the steady-state approximation normally employed in a deterministic analysis of this mechanism, and it is seen that this approximation is not well justified under reasonable conditions. (C) 2004 Wiley Periodicals, Inc.