Dissipative electronic nonadiabatic dynamics within the framework of the Schrödinger–Langevin equation

A two-state version of the Schrodinger–Langevin equation is developed to describe dissipative effects on electronic nonadiabatic dynamics. This equation is obtained by including the dissipative potential on each potential surface into the coupled time-dependent Schrodinger equations for a two-state system in the diabatic representation. The hydrodynamic equations of motion for dissipative Bohmian trajectories evolving on each potential surface are derived using the quantum trajectory formulation. Several important properties associated with the two-state Schrodinger–Langevin equation are derived as well. The frictional effects on nonadiabatic transitions are studied for two model systems. Computational results are presented and analyzed, including the evolution of the probability densities, the dynamics of quantum trajectories, and the evolution of population transfer between two surfaces. This study demonstrates that the two-state Schrodinger–Langevin equation provides a phenomenological description for dissipative electronic nonadiabatic dynamics.