Charge transport in organic semiconductors from the mapping approach to surface hopping

TL;DR

This paper introduces the mapping approach to surface hopping (MASH), a new mixed quantum-classical method for simulating charge transport in organic semiconductors, which accurately preserves equilibrium distributions and improves mobility predictions.

Contribution

The paper presents MASH, a novel simulation method that improves upon standard surface hopping by maintaining correct equilibrium distributions in charge transport modeling.

Findings

MASH yields a long-time diffusion coefficient that plateaus correctly.

Mobility estimates from MASH are higher than relaxation time approximation results.

MASH mobility results are similar to Ehrenfest dynamics, despite differences in electronic overheating.

Abstract

We describe how to simulate charge diffusion in organic semiconductors using a recently introduced mixed quantum-classical method, the mapping approach to surface hopping (MASH). In contrast to standard fewest-switches surface hopping, this method propagates the classical degrees of freedom deterministically on the most populated adiabatic electronic state. This correctly preserves the equilibrium distribution of a quantum charge coupled to classical phonons, allowing one to time-average along trajectories to improve the statistical convergence of the calculation. We illustrate the method with an application to a standard model for the charge transport in the direction of maximum mobility in crystalline rubrene. Because of its consistency with the equilibrium distribution, the present method gives a time-dependent diffusion coefficient that plateaus correctly to a long-time limiting value. The resulting mobility is somewhat higher than that of the relaxation time approximation, which uses a phenomenological relaxation parameter to obtain a non-zero diffusion coefficient from a calculation with static phonon disorder. However, it is very similar to the mobility obtained from Ehrenfest dynamics, at least in the parameter regimes we have investigated here. This is somewhat surprising because Ehrenfest dynamics overheats the electronic subsystem and is therefore inconsistent with the equilibrium distribution.