Dynamics of Barrierless and Activated Chemical Reactions in a Dispersive Medium within the Fractional Diffusion Equation Approach

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• 作者：K. Seki ; B. Bagchi ; M. Tachiya
• 刊名：Journal of Physical Chemistry B
• 出版年：2008
• 出版时间：May 15, 2008
• 年：2008
• 卷：112
• 期：19
• 页码：6107 - 6113
• 全文大小：173K
• 年卷期：v.112,no.19(May 15, 2008)
• ISSN：1520-5207

文摘

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonicpotential energy surface with a position-dependent reaction sink or window located near the minimum of thesurface. This simple (but highly successful) description leads to a nonexponential survival probability only atsmall to intermediate times but exponential decay in the long-time limit. However, in several reactive eventsinvolving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law)decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierlesschemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A completeanalytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution isobtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability isa power law of the Mittag-Leffler functional form. When the barrier height is increased, the decay of thesurvival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where therate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reactionunder dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predictinga strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium.The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactionsoccurring in complex environments.