Complex-valued derivative propagation method with adaptive moving grids for electronic nonadiabatic dynamics

Abstract

The coupled complex quantum Hamilton–Jacobi equations in the diabatic representation are solved on adaptive moving grids for electronic nonadiabatic dynamics. Substitution of the wave functions in exponential form into the coupled time-dependent Schrödinger equations yields the coupled complex quantum Hamilton–Jacobi equations. Analytic equations of motion are derived for the spatial derivatives of the complex action functions for both surfaces. The equations of motion for the complex actions and their spatial derivatives are converted into the arbitrary Lagrangian–Eulerian frame, allowing us to have many ways to choose the velocities for the moving points. The grid points can be specified to move along with the probability fluid. In contrast, choosing the boundary grid points to follow Lagrangian trajectories and forcing the internal grid points to be equally spaced at each time step, we obtain a moving structured grid of uniform spacing during the wave packet evolution. Several examples are presented to illustrate main features of the adaptive grid method, including a single avoided crossing system, a dual avoided crossing system, an ultrashort laser pulse excitation system, and a three-dimensional nonadiabatic system. Accurate computational results demonstrate that the adaptive grid method provides an alternative way to study electronic nonadiabatic dynamics.