Non-Markovian modification of the golden rule rate expression.

The reformulation of the standard golden rule approach considered in this paper for treating reactive tunneling reduces the computation of the reaction rate to a derivation of band shapes for energy levels of reactant and product states. This treatment is based on the assumption that the medium environment is actively involved as a partner in the energy exchange with the reactive subsystem but its reorganization effect is negligible. Starting from the quantum relaxation equation for the density matrix, the required band shapes are represented in terms of the spectral density function, exhibiting the continuum spectrum inherent to the interaction between the reactants and the medium in the total reactive system. The simplest Lorentzian spectral bands, obtained under Redfield approximation, proved to be unsatisfactory because they produced a divergent rate expression at low temperature. The problem is resolved by invoking a refined spectral band shape, which behaves as Lorentzian one at the band center but decays exponentially at its tails. The corresponding closed non-Markovian rate expression is derived and investigated taking as an example the photochemical H-transfer reaction between fluorene and acridine proceeding in the fluorene molecular crystal. The kinetics in this reactive system was thoroughly studied experimentally in a wide temperature range [B. Prass et al., Ber. Bunsenges. Phys. Chem. 102, 498 (1998)].

The model of level broadening in condensed phase.

We study a model of non-Markovian kinetics for a harmonic oscillator embedded in a harmonic heat bath. We present a new scheme for approximately solving the quantum relaxation equation for the density matrix to find a distribution of level populations. It is found to be an extended Lorentzian with the width depending on the energy. A more convenient non-Markovian distribution called square root Fourier distribution that was implemented in the preceding paper [M. V. Basilevsky et al., J. Chem. Phys. 125, 194513 (2006)] is closely related to this extended Lorentzian model. Both distributions decay exponentially far away from their centers and reproduce well standard Lorentzian widths in the vicinity of the central region. A conventional Lorentzian model with such widths results when the Redfield approximation is applied in the frame of the present procedure.

Momentum representation of the solute/bath interaction in the dynamic theory of chemical processes in condensed phase.

For the system consisting of the chemically reactive solute immersed in the oscillator bath, we consider an approach based on the solute/medium interaction expressed in terms of momenta rather than coordinates. In the adiabatic representation the medium reorganization effects are suppressed, being hidden in the solute renormalized potential and new spectral density function. The advantage proposed by the bilinear interaction in momentum representation is its spatial uniformity important for approximate dynamical treatments. The procedure of explicit transforming a standard spectral density (coordinate representation of interaction) into the spectral density in adiabatic representation (momentum representation of interaction) is the main new result of the present study. Illustrative calculations for several types of spectral functions are performed. Special discussion is devoted to clarifying the nature of the slow diffusion coordinate, to which the present approach is mainly addressed.