Hybrid Gaussian–discrete-variable representation for describing molecular double-ionization events

Abstract

A hybrid method that combines Gaussian basis functions typically used in bound-state molecular electronic structure calculations with a grid-based discrete-variable representation with finite elements suitable for a general electronic continuum representation is used to fully describe the double ionization of molecular ${\mathrm{H}}_{2}$ by a single photoabsorption. This work expands the hybrid method, previously applied to single-ionization events, to double photoionization. Constructing the full two-electron operator encoding the electron correlation necessary to doubly ionize the target via the action of a single photon requires all classes of mixed integrals between combinations of the different basis-function types. Comparison of the present results with benchmark theoretical calculations and experimental results shows excellent agreement for both molecular ${\mathrm{H}}_{2}$ and its united-atom limit, atomic helium; the triply differential cross sections that relate the angular distribution and energy sharing of all of the particles in the frame of the molecule are compared. The two-electron results computed using this hybrid basis hint at application of this general descriptive scheme beyond this simplest molecular target towards describing double ionization in more complicated and experimentally relevant molecules.