AN ASYMPTOTIC WAVE-FUNCTION SPLITTING PROCEDURE FOR PROPAGATING SPATIALLY EXTENDED WAVE-FUNCTIONS - APPLICATION TO INTENSE FIELD PHOTODISSSOCIATION OF H-2+

We describe an efficient procedure for propagation a spatially extended wavefunction evaluated on a small grid. The procedure involves the repeated splitting of the wavefunction into a part residing mainly in the interaction region (small fragment separation) and parts residing solely in the asymptotic region (large fragment separation), and propagation each part separately. The splitting is done by multiplying the wavefunction by the functions f(R) and 1 - f(R), where R is the internuclear separation of an unbound degree of freedom and f(R) equals one in the interaction region and falls to zero in the asymptotic region. Each asymptotic piece of the wavefunction is propagated to some final time, in the momentum representation where it does not spread or translate, by a single application of a free-particle propagator. Unlike the use of an absorbing boundary, the total wavefunction can be reassembled at a later time by adding the individual asymptotic pieces, propagated to a common final time with a free-particle propagator, to the part of the wavefunction remaining in the interaction region. This procedure is well suited to propagation methods that evaluate the wavefunction on a spatial grid, because the amount of asymptotic region included in the grid, and therefore the computational effort, can be minimized (the smaller the asymptotic region, the more frequent the splitting). The propagation method is demonstrated in the calculation of the fragment kinetic energy distribution produced by the intense field photodissociation of H2+. This example illustrates the propagation method for a system whose wavefunction becomes very extended with time due to multiphoton bound-continuum and continuum-continuum transitions.