Multi-reference approach to the computation of double core-hole spectra

Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K⁻²) are obtained for H₂O, N₂, CO, and C₂H_2n (n = 1–3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K⁻² shake-up spectra of H₂O and C₂H₂n molecules are here completely characterized for the first time.