Ionization and dissociation using B-splines: photoionization of the hydrogen molecule

One of the most significant developments in modern computational physics has been the introduction of B-spline basis sets to evaluate continuum states of atoms and molecules. B-splines were first used in the early 1970s to describe the hydrogen atom and, since then, most applications have focused on atomic systems. Very recently, B-splines have emerged as powerful tools to describe the molecular continuum as well. Ionization and dissociation can now be studied with an accuracy comparable to that achieved in recent experiments. In this paper, we review the theoretical tools needed for the description of the molecular continuum with B-splines and discuss what is probably the most successful application up to date: the photoionization of H 2 , including resonant effects and simultaneous dissociation. Recent progress for more complicated molecules is also reviewed.