Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales

Abstract

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents for a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.

Effects of tunnelling and asymmetry for system-bath models of electron transfer

“…For asymmetric systems however, two different reorganization energies, λ 0 and λ 1 , are found. 71 Situations like this have been found in a number of computer simulations of molecular systems. 10,14,15 The standard Marcus theory formula, Eq.…”

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

“…While most approximate dynamics approaches, like FSSH and MFT, are capable of qualitatively capturing the famous rate turnover as a function of driving force [16,25,47,48], as shown in the bottom panel of Fig. 6, MFT fails to correctly describe the donor-acceptor product ratios for the process.…”

Surface hopping with a manifold of electronic states. I. Incorporating surface-leaking to capture lifetimes

“…where A = 0.01, B = 1.6, C = 0.005, D = 1.0, and K is a constant defined in the same manner as C in Eq. (20), and all in atomic units.…”

“…1,2,12 While the processes above have a bath of electronic states which leads to a certain amount of electronic friction and a lack of coherence, a second class of non-adiabatic processes involves only a minimal number of electronic states. These non-adiabatic problems in chemistry include most forms of photoexcited dynamics at low energies in solution, including electron transfer and electronic energy transfer, [13][14][15][16][17][18][19][20] spin relaxation, [21][22][23][24] intersystem-crossing, [25][26][27][28][29] etc. These coherent dynamics are important for understanding organic enzymes, molecular photocatalysis, and organic photoexcitations.…”