Symmetry breaking and hole localization in multiple core electron ionization

Motivated by recent opportunitites to study hollow molecules with multiple core holes offered by X-ray free electron lasers, we revisit the core-hole localization and symmetry breaking problem, now studying ionization of more than one core electron. It is shown, using a N₂ molecule with one, two, three, and four core holes, for example, that in a multiconfigurational determination of the core ionization potentials employing a molecular point group with broken inversion symmetry, one particular configuration is sufficient to account for the symmetry breaking relaxation energy in an independent particle approximation in the case of one or three holes, whereas the choice of point group symmetry is unessential for two and four holes. The relaxation energy follows a quadratic dependence on the number of holes in both representations.