Investigation into the Gaussian time-dependence of the rate coefficient in dispersive kinetic models applied to simple gas-phase chemical reactions

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Abstract
Dispersive kinetic models (DKMs) based on the concept of a distribution of activation energies have shown much promise in describing complex reaction transients. In particular, DKMs exhibiting a time (t)-dependent rate coefficient, k, of approximately Gaussian functional form provide the most insight into the kinetics because they do not rely on unit-less, empirical parameters [P.J. Skrdla, J. Phys. Chem. A 113, 9329 (2009)]. The physical basis of the Gaussian behaviour is investigated using a dispersive simple harmonic oscillator (DSHO) description of Marcus-type reactions studied on the ultrafast timescale. The DSHO description is found to support the Gaussian t-dependence of k over relatively short time periods. Moreover, in cases where the transition state survives more than one vibration of the predominant reactive mode, a periodicity in k is observed that is also consistent with empirical observations.

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