Asymptotic analysis in time-dependent calculations with divergent coupling

An efficient time-dependent method is presented to obtain, at any time, the nuclear wave functions corresponding to the intense field photodissociation of homonuclear ions, which possess a divergent electronic transition moment, as the internuclear separation increases. It consists of splitting the wave functions into two parts, one part corresponding to the internal region and the second to the asymptotic part. The propagation of the wave packet's asymptotic part is done analytically even during the field interaction. The advantage of the method presented here is that the extension of the grid, needed to represent the wave packets, is fixed once and for all. Therefore, the numerical effort is reduced to the propagation in a previously fixed region of space, regardless of the duration of the field. The method is applied to calculate the proton kinetic energy spectrum in the photodissociation of the H₂⁺ molecule.