Importance Sampling for Equilibrium Properties in Non-Adiabatic Systems: Application to Anomalous Interfacial Charge Transfer

Interfacial charge transfer plays a significant role in the performance of optoelectronic devices. Compared with real-time non-adiabatic dynamics simulations, statistical mechanics could obtain the equilibrium properties directly. We here present an importance sampling approach to calculate the electron distribution at general interfaces. The configuration distribution based on a series of reference potential energy surfaces is utilized to reweight the properties of interest. The high accuracy, precision, and efficiency of the new method are verified by comparing the results of different sampling approaches and non-adiabatic dynamics simulations. We find that numbers of states, electronic couplings, reorganization energies, and energetic disorders all have strong impacts on the anomalous interfacial charge transfer across a high energy barrier. In addition, based on the data computed by importance sampling in relatively small but diverse systems, we propose an effective machine learning approach to train artificial neural networks, which could predict the interfacial charge transfer in extremely large systems. Due to its high performance, our importance sampling method is promising for the statistical study of equilibrium properties in general non-adiabatic systems.