Convergence strategies for equivalent core hole states in photoionization calculations

When photoionization leads to degenerate ion states, coupling between those channels is expected to be large.  As a consequence, the single-channel static-exchange approximation fails to describe the physics of inner-shell photoionization when using delocalized orbitals to represent the core-hole states. We have recently shown [PRA 102, 012815 (2020)] that by using localized core orbitals, coupling between core-hole channels is negligible and independent single-channel calculations can achieve results nearly equivalent to those obtained in fully coupled calculations. However, for molecules that involve second-row atoms, additional numerical difficulties are encountered in attempting to converge core photoionization amplitudes with basis set variational methods.  The origin of these difficulties lies in the inability of standard contracted Gaussian basis sets to accurately describe core-hole ionization wavefunctions in the region spanned by the core hole. We present a strategy that successfully overcomes these deficiencies.  Comparisons of theory and experiment for total cross sections and molecular frame photoelectron angular distributions for inner-shell ionization of the chlorine 2p orbitals in CCl₄ are presented.