From Multidimensional non-Markovian Rate Theory to Diffusion-Entropy Scaling and Investigations into the validity of Hydrodynamic Stokes Law

Abstract

Multidimensional rate theory provides a theoretical framework for understanding chemical reactions that occur in systems with more than one reaction coordinate, such as isomerization reactions, protein folding, or electron transfer reactions. Although recent years have seen many computational studies employing advanced simulation techniques, like umbrella sampling and metadynamics, to construct the reaction-free energy surface in terms of several reaction coordinates, more effort needs to be directed to calculate the rate by quasi-analytical means. In this context, we formulate a non-Markovian multidimensional rate theory, explicitly considering coupling at the level of Hamiltonian and friction between reactive and non-reactive modes. The formulation is quite general, allowing recovery of other theoretical approaches, such as Langer's theory, Pollak's Hamiltonian formulation, and van der Zwan-Hynes theory, under appropriate conditions. We then use the non-Markovian theory to calculate the rate in several interesting systems, namely (i) the isomerization rate of stilbene molecule in hexane solvent, (ii) the escape rate of a particle moving on a two-dimensional periodic potential energy landscape, (iii) dissociation rate of insulin dimer in water and (iv) homogeneous gas-liquid nucleation rate in LJ system. The rate predicted by the non-Markovian theory agrees with experimental and theoretical findings. An intriguing interplay between dimensionality and memory effects was observed in rate calculations. In this context, we unveil the microscopic mechanism for the early stage of insulin dimer dissociation and the role of water molecules in explicitly facilitating the hydrophobic disentanglement.

In the second part, we derive an intriguing scaling relation between diffusion and entropy, starting from the basic principles of statistical mechanics. We explore this relation in different deterministic model systems, like two-dimensional periodic potential energy surface and periodic Lorentz gas introduced by Zwanzig. Our study reveals a noteworthy crossover in the plot of diffusion against entropy due to the correlated random walk induced by the characteristic nature of the potential energy surface. This study motivated us to investigate the non-monotonic friction dependence of diffusion in a multidimensional potential energy landscape.

In the third part, we examine the validity of Stokes' Law (SL) of hydrodynamics at molecular length scales for LJ and soft sphere systems at two different thermodynamic state points. We explain the origin of the enhanced linear regime in the absence of the attractive part of the interaction potential between the particles. We also investigate the build-up of density in front of the moving sphere and the velocity profile to understand the origin of the broad validity of Stokes Law and, thereby, of linear response theory.

In the fourth part, as reported in recent experimental studies, we discuss the analytical and simulation calculations to elucidate the rate enhancement observed in various reactions within charged microdroplets. In the fifth part, we discuss the origin of the anomalous dielectric relaxation of dipolar fluid under spherical confinement.

The thesis concludes with a brief description of ongoing and future projects.