Dynamics of electron transfer in complex glassy environment modeled by the Cole–Davidson spectral density

Abstract

The dynamics of electron transfer reactions in a complex environment is investigated in the context of the spin-boson model with a bath characterized by the Cole–Davidson spectral density. Using the numerically exact multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method, the population dynamics of the two-level subsystem has been investigated in a broad physical regime. Upon changing various parameters, the simulation results exhibit either weakly damped coherent motion, incoherent decay, or localization. Transitions between these regimes are discussed in terms of several important physical parameters. Comparison of the exact ML-MCTDH simulations with the non-interacting blip approximation (NIBA) shows that the latter performs quite well in the nonadiabatic regime despite the complex multiple time scales the bath exhibits, but fails in the adiabatic and intermediate regimes where the relaxation of the bath is no longer significantly faster than the electron transfer process. In the nonadiabatic regime an interesting, semi-quantitative finding on electron transfer dynamics is discussed based on a simple relation between two parameters in the Cole–Davidson spectral density, the coupling strength and the fractional stretching exponent.