Moving boundary truncated grid method for electronic nonadiabatic dynamics

The moving boundary truncated grid method is developed to study the wave packet dynamics of electronic nonadiabatic transitions between a pair of diabatic potential energy surfaces. The coupled time-dependent Schrödinger equations (TDSEs) in the diabatic representation are integrated using adaptive truncated grids for both the surfaces. As time evolves, a variable number of grid points fixed in space are activated and deactivated without any advance information of the wave packet dynamics. Essential features of the truncated grid method are first illustrated through applications to three one-dimensional model problems, including the systems of single avoided crossing, dual avoided crossing, and extended coupling region with reflection. As a demonstration for chemical applications, the truncated grid method is then employed to study the dynamics of photoisomerization of retinal in rhodopsin described by a two-electronic-state two-dimensional model. To demonstrate the capability of the truncated grid method to deal with the electronic nonadiabatic problem in high dimensionality, we consider a multidimensional electronic nonadiabatic system in two, three, and four dimensions. The results indicate that the correct grid points are automatically activated to capture the growth and decay of the wave packets on both of the surfaces. Therefore, the truncated grid method greatly decreases the computational effort to integrate the coupled TDSEs for multidimensional electronic nonadiabatic systems.