A parallelized three-dimensional Cartesian-grid-based time-dependent Schrödinger 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 H2+ 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 H2+ molecule at inter-nuclear distance of 9 a.u. (χ=0° and 90°) and the spectral intensities of harmonic generation at internuclear distance of 2 a.u. (χ=0°, 30°, 60°, and 90°) 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.
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|State||Published - 31 Jan 2008|