Recent years have seen many computational studies employing several enhanced sampling techniques that attempt to map out the reaction-free energy surface in terms of several collective variables. However, less effort has been devoted to calculating the rate by quasi-analytical means on the multidimensional free energy surface. In this context, we formulate a generalized non-Markovian rate theory by explicitly considering the effect of coupling between the reactive and nonreactive modes and apply it to different models and biological systems. We explore the formalism in various cases, namely, (i) determination of the isomerization rate of stilbene molecule on a two-dimensional reaction energy surface by employing the Zwanzig-Bixon hydrodynamic theory of frequency-dependent friction, (ii) calculation of the escape rate for a Brownian particle moving on a two-dimensional periodic triangular potential, (iii) estimation of the dissociation rate of insulin dimer in aqueous solution, (iv) determination of homogeneous nucleation rate for gas to liquid transition of LJ mixtures, and (v) calculation of the heterogeneous nucleation rate for vapor to liquid nucleation of argon on a solid surface. We also explore the interplay between dimensionality and memory effects in all cases. Furthermore, we derive an exponential relation between diffusion and entropy using the basic principles of statistical mechanics, which is intriguing since it relates two seemingly unrelated properties, namely, structure and dynamics. In the absence of noise, the exponential scaling relation holds for the particle moving on a two-dimensional periodic potential surface with a crossover in some specific regions, which is attributed to the emergence of the correlated returns. However, in the presence of noise, we observe an interesting reentrance type of behavior in the plot of entropy against diffusion.

Applications of the generalized rate theory and diffusion-entropy scaling

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ACS Fall 2022

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