Ehrenfest and classical path dynamics with decoherence and detailed balance

Abstract

We present a semiclassical approach for nonadiabatic molecular dynamics based on the Ehrenfest method with corrections for decoherence and detailed balance. Decoherence is described via a coherence penalty functional that drives dynamics away from regions in Hilbert space characterized by large values of coherences. Detailed balance is incorporated by modification of the off-diagonal matrix elements with a quantum correction factor used in semiclassical approximations to quantum time-correlation functions. Both decoherence and detailed balance corrections introduce nonlinear terms to the Schrödinger equation. At the same time, the simplicity of fully deterministic dynamics and a single trajectory for each initial condition is preserved. In contrast, surface hopping is stochastic and requires averaging over multiple realization of the stochastic process for each initial condition. The Ehrenfest-decoherence-detailed-balance (Ehrenfest-DDB) method is adapted to the classical path approximation and ab initio time-dependent density functional theory and applied to an experimentally studied nanoscale system consisting of a fluorophore molecule and an scanning tunneling microscopy tip and undergoing current-induced charge injection, cooling, and recombination. Ehrenfest-DDB produces time scales that are similar to those obtained with decoherence induced surface hopping, which is a popular nonadiabatic molecular dynamics technique applied to condensed matter. At long times, Ehrenfest-DDB dynamics slows down considerably because the detailed balance correction makes off-diagonal elements go to zero on approach to Boltzmann equilibrium. The Ehrenfest-DDB technique provides efficient means to study quantum dynamics in large systems.

Direct Non-adiabatic Simulations of the Photoinduced Charge Transfer Dynamics

“…Despite the success of the current approach in simulating the model systems presented in this work, we acknowledge its potential limitations, including (i) the single-particle picture that could fail for the strongly coupled electron and hole dynamics, 22,36,37,41,72 (ii) the validity of the classical path approximation, 47,53,63,73 and (iii) the accuracy of the FSSH algorithms. 43,52 Encouraging progress is being made to address each of the above three challenges, enabling the possibility to obtain a more accurate description of the charge transfer dynamics in large complex systems.…”

Computational Method for Evaluating the Thermoelectric Power Factor for Organic Materials Modeled by Holstein Model: A Time-Dependent Density Matrix Renormalization Group Formalism

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