A stochastic reorganizational bath model for electronic energy transfer

Abstract

The fluctuations of optical gap induced by the environment play crucial roles in electronic energy transfer dynamics. One of the simplest approaches to incorporate such fluctuations in energy transfer dynamics is the well known Haken-Strobl-Reineker model, in which the energy-gap fluctuation is approximated as a white noise. Recently, several groups have employed molecular dynamics simulations and excited-state calculations in conjunction to take the thermal fluctuation of excitation energies into account. Here, we discuss a rigorous connection between the stochastic and the atomistic bath models. If the phonon bath is treated classically, time evolution of the exciton-phonon system can be described by Ehrenfest dynamics. To establish the relationship between the stochastic and atomistic bath models, we employ a projection operator technique to derive the generalized Langevin equations for the energy-gap fluctuations. The stochastic bath model can be obtained as an approximation of the atomistic Ehrenfest equations via the generalized Langevin approach. Based on the connection, we propose a novel scheme to correct reorganization effects within the framework of stochastic models. The proposed scheme provides a better description of the population dynamics especially in the regime of strong exciton-phonon coupling. Finally, we discuss the effect of the bath reorganization in the absorption and fluorescence spectra of ideal J-aggregates in terms of the Stokes shifts. For this purpose, we introduce a simple relationship that relates the reorganization contribution to the Stokes shifts - the reorganization shift - to three parameters: the monomer reorganization energy, the relaxation time of the optical gap, and the exciton delocalization length. This simple relationship allows one to classify the origin of the Stokes shifts in molecular aggregates

Atomistic Modeling of Two-Dimensional Electronic Spectra and Excited-State Dynamics for a Light Harvesting 2 Complex

“…Within our simulations the quantum and classical subsystems are coupled to each other in a self-consistent way using the surface-hopping method. − This method accounts for the Stokes shift and leads to a Boltzmann distribution within the quantum system in equilibrium, which is crucial when dealing with electronic systems where the energy separation between states is comparable to or larger than k B T . − Semiempirical electronic structure calculations usually assume a ground-state trajectory for the classical system and are unable to describe these effects. Some exceptions are refs and . The method presented here can readily be applied to other light harvesting systems like LH1, photosystem II, and FMO.…”

Ab Initio Study of Charge Separation Dynamics and Pump–Probe Spectroscopy in the P3HT/PCBM Blend

“…Another problem is the use of the Ehrenfest-type approach, where the equilibrium populations cannot be reproduced [33,65]. Although this deficiency would deteriorate the electron-transfer time scales, the initial coherent dynamics can be well reproduced with the present method [35].…”

“…In this study, the quantum dynamics and spectroscopy were simulated by numerically integrating the time-dependent Schrödinger equation [32][33][34][35]. The time-dependent Hamiltonian includes the time-independent and time-dependent parts as, H(t) = H e/ f + H B (t).…”

“…In the present method, the parameters for the nuclear motion are given by the λ m , T , and the inverse relaxation time (Γ). The population dynamics and optical response functions are obtained from the ensemble averages of the trajectories, which are determined by the time-dependent Schrödinger equation coupled with Langevin equation for the diagonal energy fluctuations [35].…”

Interplay of vibration- and environment-assisted energy transfer

“…The single vibration denoted by annihilation/creation operators a/a † coupled to the acceptor is a source of quantum noise and may coherently assist the excitation energy transfer [15]. The term δ(t) added to the site energy describes a classical Gaussian white noise source within the Haken-Strobl-Reinker model [20,[23][24][25], characterized by zero mean and variance σ 2 .…”