# Dynamic solvent effects, Kramers theory

# Dynamic solvent effects, Kramers theory

This chapter discusses dynamical solvent effects on the rate constants for chemical reactions in solution. The effect is described by stochastic dynamics, where the influence of the solvent on the reaction dynamics is included by describing the motion along the reaction coordinate as Brownian motion. Two theoretical approaches are discussed: Kramers theory with a constant time-independent solvent friction coefficient and Grote-Hynes theory, a generalization of Kramers theory, based on the generalized Langevin equation with a time-dependent solvent friction coefficient. The expressions for the rate constants have the same form as in transition-state theory, but are multiplied by transmission coefficients that incorporate the dynamical solvent effect. In the limit of fast motion along the reaction coordinate, the solvent molecules can be considered as ‘frozen’, and the predictions of the Grote–Hynes theory can differ from the Kramers theory by several orders of magnitude.

*Keywords:*
Brownian motion, stochastic dynamics, Kramers theory, transmission coefficient, generalized Langevin equation, Grote–Hynes theory

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