Semi-classical generalized Langevin equation for equilibrium and nonequilibrium molecular dynamics simulation

Molecular dynamics (MD) simulation based on Langevin equation has been widely used in the study of structural, thermal properties of matter in different phases. Normally, the atomic dynamics are described by classical equations of motion and the effect of the environment is taken into account through the fluctuating and frictional forces. Generally, the nuclear quantum effects and their coupling to other degrees of freedom are difficult to include in an efficient way. This could be a serious limitation on its application to the study of dynamical properties of materials made from light elements, in the presence of external driving electrical or thermal fields. One example of such system is single molecule dynamics on metal surface, an important system that has received intense study in surface science. In this review, we summarize recent effort in extending the Langevin MD to include nuclear quantum effect and their coupling to flowing electrical current. We discuss its applications in the study of adsorbate dynamics on metal surface, current-induced dynamics in molecular junctions, and quantum thermal transport between different reservoirs.