Parallel solver for the three-dimensional Cartesian-grid-based time-dependent Schrodinger equation and its applications in laser-H2+ interaction studies

A parallelized three-dimensional Cartesian-grid-based time-dependent Schrodinger equation (TDSE) solver for molecules with a single electron, assuming the motion of the nucleus is frozen, is presented in this paper. An explicit stagger-time algorithm is employed for time integration of the TDSE, in which the real and imaginary parts of the wave function are defined at alternate times, while a cell-centered finite-volume method is utilized for spatial discretization of the TDSE on Cartesian grids. The TDSE solver is then parallelized using the domain decomposition method on distributed memory machines by applying a multilevel graph-partitioning technique. The solver is validated using a H-2(+) molecule system, both by observing the total electron probability and total energy conservation without laser interaction, and by comparing the ionization rates with previous two-dimensional axisymmetric simulation results with an aligned incident laser pulse. The parallel efficiency of this TDSE solver is presented and discussed; the parallel efficiency can be as high as 75% using 128 processors. Finally, examples of the temporal evolution of the probability distribution of laser incidence onto a H-2(+) molecule at inter-nuclear distance of 9 a.u. (chi=0 degrees and 90 degrees) and the spectral intensities of harmonic generation at internuclear distance of 2 a.u. (chi=0 degrees, 30 degrees, 60 degrees, and 90 degrees) are presented to demonstrate the powerful capability of the current TDSE solver. Future possible extensions of the present method are also outlined at the end of this paper.