Moving adaptive grid methods for numerical solution of the time-dependent molecular Schrodinger equation in laser fields

We present a moving adaptive grid method for solving the time-dependent Sch rodinger equation, TDSE, for molecules in intense laser fields, applicable in the nonperturbative nonlinear regime where dissociation ionization occur s. The method is based on a Lagrangian, moving coordinate system. In this r epresentation, the reference system is moving with the laser pulse so that the classical movement of free particles in the field, i.e., in the asympto tic region where electron-molecule potentials are negligible but the laser field is still present, is exactly described. As a consequence, the asympto tic quantum wave functions are exact in presence of a laser pulse. We have tested several discrete propagator methods for the TDSE in different gauges in a Born-Oppenheimer simulation of H-2(+) in a short, intense laser pulse . Our comparison of convergence between the same discretization methods for different gauges have demonstrated the superiority of the present Lagrangi an adaptive grid method to treat the response of molecules to intense time- dependent electromagnetic fields. (C) 2001 American Institute of Physics.