Study of the van der Zwan–Hynes model for dipole isomerization reaction rates from the viewpoint of critical phenomena

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Abstract
We study the van der Zwan–Hynes model of nonequilibrium solvation dynamics for reactions in polar solvents. In this model those authors showed the equivalence of a multidimensional reaction coordinate picture to a simple one-dimensional description. They identified several distinct regimes and successfully described these in molecular terms. They found that in the regime of long solvent response times, the reaction rate had singular aspects which could be described in terms of simple power laws. There are two sets of exponents depending on whether the solvent is underdamped or overdamped. In this paper, we show that this behavior can be readily understood by mapping this problem onto critical phenomena. We find that the two sets of exponents correspond to two types of critical behaviors. There is also a regime when both types of critical behaviors are present and one can see the crossover effects between the two by varying the parameters. Studying the resulting crossover scaling function gives new insights into this problem and reveals its rich behavior.