Concept of reaction coordinate for dynamics of optically controlled non-equilibrium processes in condensed phase

Optically controlled non-equilibrium processes in condensed phase, such as solvation of ions and electron transfer reactions, have been widely studied both experimentally and theoretically. The dynamics of these processes is investigated through the experimentally observable quantities, like non-equilibrium solvation time correlation function \( S\left( t \right) \) and the time-dependent survival probability \( P\left( t \right) \) of the reactant, respectively. On the theoretical side, although the linear response theory and Marcus theory have been widely used to predict \( S\left( t \right) \) and \( P\left( t \right) \), respectively, their main drawback is that their prediction of \( S\left( t \right) \) and \( P\left( t \right) \) does not show dependence on the initial preparation of the system, while experimental observations suggest that both these quantities depend on the initial preparation through dependence on the excitation wavelength. In this work, we address this issue and introduce the concept of a new reaction coordinate, which can take into account the effect of initial optically prepared innumerable phase space coordinates through a single parameter, viz. the optical excitation wavelength. We first project the dynamics in multi-dimensional Liouville space onto a one-dimensional reaction coordinate (RC) space, obtaining thereby a new kinetic equation for the RC. We have calculated both \( S\left( t \right) \) and \( P\left( t \right) \) by numerically solving this new equation in one-dimensional RC space for harmonic as well as anharmonic potentials and studied the effect of the initial preparation of the system by considering the excitation wavelength dependence. It is found that for solvation process, the calculated \( S\left( t \right) \) depends strongly on the initial preparation of the system (i.e. the excitation wavelength) only for anharmonic effective potentials. For electron transfer reaction, however, \( P\left( t \right) \) depends on the excitation wavelength for both harmonic and anharmonic potentials, which cannot be predicted by the Marcus theory.