Optically Controlled Electron-Transfer Reaction Kinetics and Solvation Dynamics: Effect of Franck-Condon States.

Experimental results for optically controlled electron-transfer reaction kinetics (ETRK) and nonequilibrium solvation dynamics (NESD) of Coumarin 480 in DMPC vesicle show their dependence on excitation wavelength λ. However, the celebrated Marcus theory and linear-response-theory-based approaches for ETRK and NESD, respectively, predict both of the processes to be independent of λ. The above said lacuna in these theories prompted us to develop a novel theory in 1D space, where the effect of innumerable Franck-Condon states is included through λ.

Projection of the Dynamics of Electron Transfer Reaction in Dual Space onto the One-Dimensional Slower Reaction Coordinate Axis.

We have derived here for the first time an exact dynamical equation within the domain of classical mechanics for the time dependent density distribution function of one-dimensional reaction coordinate (RC) in the condensed phase for electron transfer reaction by projecting the dynamics of slower modes in multidimensional Liouville space starting with a given set of coordinates of the faster modes. After the faster modes were ensemble averaged, the dynamics of the whole system solely depends on the slower RC. To simplify the complicated equation into a tractable form, benchmark approximations are employed to reduce the formally exact equation into an equation similar to the Smoluchowski equation with a delocalized sink term.

Electron transfer reactions in condensed phase: effect of reversibility.

We propose a generalized one-dimensional kinetic equation for multidimensional reversible electron transfer (ET) reaction with a nonequilibrium situation as the initial condition. The rate constant for the forward reversible ET reaction obtained here consists of the rate for the corresponding irreversible ET reaction, and an extra term due to reversibility of the ET process which includes the rates of diffusion dynamics in the reactant and product wells. In order to understand the effect of reversibility, we consider back ET reaction in a system consisting of an electron donor-acceptor pair in a solvent modeled through low frequency solvent collective coordinates (multidimensional) characterized by the orientational polarization and slowly relaxing one-dimensional vibrational mode.

Mapping the reaction dynamics in Liouville space onto a reaction coordinate space: a first-principle- based theory.

We have derived here an exact kinetic equation for the time evolution of the probability distribution for a general reaction coordinate space, starting from a multidimensional Liouville equation based on first-principles theory. To make the equation tractable we use two standard approximations, which reduce the exact equation into a Fokker-Planck-type equation with a sink term. As illustrative examples, we consider its application to two important classes of reactions, viz.

Theory of reversible electron transfer reactions in a condensed phase.

We have derived an exact analytical expression for the average forward rate of a reversible electron transfer reaction, modeled through a reaction coordinate undergoing diffusive motion in arbitrary potential wells of the reactant and the product in presence of a localized sink of arbitrary location and strength. The dynamics of diffusive motion is described by employing two coupled generalized diffusion reaction (Smoluchowski) equations with coordinate dependent diffusivity and delta sink. The average forward electron transfer rate constant obtained here for the system, with equilibrium or nonequilibrium distributions as initial condition, is determined by the forward and backward rate constants calculated based on the transition state theory and the weighted average rate for the well dynamics.

One-dimensional description of multidimensional electron transfer reactions in condensed phase.

We derive a one-dimensional energy diffusion equation for describing the dynamics of multidimensional electron transfer reactions in condensed phase, which is conceptually simpler and computationally more economic than the conventional approaches. We also obtain an analytical expression for the rate of electron transfer reactions for a general one-dimensional effective potential as well as an energy dependent diffusitivity. As an illustrative example, we consider application to electron transfer in a contact ion pair system modeled through harmonic potentials consisting of two slow classical modes and a high frequency vibrational mode for which the numerical results calculated using the proposed one-dimensional approach are shown to be in good agreement with experimental results.

A one-dimensional energy diffusion approach to multidimensional dynamical processes in the condensed phase.

We propose a generalized one-dimensional energy diffusion approach for describing the dynamics of multidimensional dynamical processes in the condensed phase. On the basis of a formalism originally due to Zwanzig, we obtain a one-dimensional kinetic equation for a properly selected relevant dynamical quantity and derive new analytical results for the dynamics of a multidimensional electron-transfer process, nonequilibrium solvation, and diffusive escape from a potential well. The calculated results for electron-transfer reactions in solvent-separated and contact ion pair systems are found to be in good agreement with the experimental results.

Mass dependence of shear viscosity in a binary fluid mixture: mode-coupling theory.

An expression for the shear viscosity of a binary fluid mixture is derived using mode-coupling theory in order to study the mass dependence. The calculated results on shear viscosity for a binary isotopic Lennard-Jones fluid mixture show good agreement with results from molecular dynamics simulation carried out over a wide range of mass ratio at different composition. Also proposed is a new generalized Stokes-Einstein relation connecting the individual diffusivities to shear viscosity.

Universal scaling laws of diffusion: application to liquid metals.

This work focuses on the universal scaling laws, which relate scaled diffusivity to excess entropy in fluids and their mixtures. The derivation of the new scaling law for diffusivity proposed recently [A. Samanta, Sk.

New universal scaling laws of diffusion and Kolmogorov-Sinai entropy in simple liquids.

A new universal scaling law relating the self-diffusivities of the components of a binary fluid mixture to their excess entropies is derived using mode coupling theory. These scaling laws yield numerical results, for a hard sphere as well as Lennard-Jones fluid mixtures, in excellent agreement with simulation results even at a low density region, where the empirical scaling laws of Dzugutov [Nature (London) 381, 137 (1996)]] and Hoyt, Asta, and Sadigh [Phys. Rev.