Extended Configuration-Interaction Singles Method with Core/Valence Separation (XCIS-CVS): Core-Level Spectra of Open-Shell Molecules

Spectroscopic core-to-valence transitions serve as reporters on the valence virtual orbitals, which is especially informative for molecules and materials with open-shell ground states that feature (quasi-)degenerate frontier molecular orbitals. Excited states of open-shell molecules are difficult to model using methods based on single excitations only, a category that includes time-dependent density functional theory, due to severe spin contamination (in both ground and excited states) when a spin-unrestricted reference determinant is used. Extended configuration-interaction singles (XCIS) is a simple, variational, and size-consistent wave function ansatz that augments the usual CIS excitation space with a limited set of doubly substituted determinants in order to recover spin-pure excited states starting from a restricted open-shell Hartree-Fock (ROHF) ground state. XCIS eliminates spin contamination and offers better accuracy as compared to ROHF-based CIS. Here, we report an implementation of XCIS based on the core/valence separation (CVS) approximation, which restricts the orbital active space to a few occupied orbitals so that core-to-valence transitions can be simulated efficiently. In applications of XCIS-CVS to X-ray transitions in a variety of open-shell systems, including 3d transition metal complexes, we find that both K-edge and pre-edge orbital splittings are reproduced semiquantitatively as compared to experiment.