Stochastic Lindemann Kinetics for Unimolecular Gas-Phase Reactions

Lindemann, almost a century ago, proposed a schematic mechanism for unimolecular gas-phase reactions. Here, we present a new semiempirical method to calculate the effective rate constant in unimolecular gas-phase kinetics through a stochastic reformulation of Lindemann kinetics. Considering the rate constants for excitation and de-excitation steps in the Lindemann mechanism as temperature dependent empirical parameters, we construct and solve a chemical master equation for unimolecular gas-phase kinetics. The effective rate constant thus obtained shows excellent agreement with experimental data in the entire concentration range in which it is reported. The extrapolated values of the effective rate constant for very low and very high concentrations of inert gas molecules are in close agreement with values obtained using the Troe semiempirical method. Stochastic Lindemann kinetics, thus, provides a simple method to construct the frill falloff curves and can be used as an alternative to the Troe semiempirical method of kinetic data analysis for unimolecular gas-phase reactions.