Barrierless isomerization dynamics in viscous liquids: Decoupling of the reaction rate from the slow frictional forces

Many important chemical and biological reactions do not face a sizable activation barrier in their motion along the reaction coordinate. As a result, these reactions often have time constants in the range of a few hundred femtoseconds (fs) only. The existing theories, on the other hand, assume only the viscous, zero frequency frictional response of the solvent, which is clearly inadequate to describe solvent viscosity effects on such ultrafast reactions. In this article, we present a theory of barrierless chemical reactions that includes the bimodal frictional response of the solvent. The generalized theory is based on a non-Markovian Smoluchowski equation, with a time (t) dependent diffusion coefficient (D(t)) to describe the reactive motion along the reaction surface; the reaction itself is described by a coordinate-dependent sink term. This description is reliable for a harmonic reaction potential energy surface. The time-dependent diffusion coefficient can be obtained from the time-dependent friction by using the known procedure. The calculated rates show that the barrierless reaction rate becomes completely decoupled from slow solvent frictional forces when the rate of the reaction is large. This is particularly true for slow viscous liquids where the fast response of the liquid is vastly separated in a time scale from the slow response. For ultrafast reactions, this theory naturally leads to a fractional viscosity (eta) dependence of the rate (k similar to eta(-alpha)), with the value of the exponent ct being close to zero at large solvent viscosities. The theory predicts excitation wavelength and temperature dependence in agreement with experiments. The results of the theory have been used to analyze and understand the experimental results of isomerization in rhodopsin, isorhodopsin, crystal violet, and several other cases.