Computing L- and M-edge spectra using the DFT/CIS method with spin-orbit coupling

Modeling L-edge spectra at X-ray wavelengths requires consideration of spin-orbit splitting of the 2p orbitals. We introduce a low-cost tool to compute core-level spectra that combines a spin-orbit mean-field description of the Breit-Pauli Hamiltonian with nonrelativistic excited states computed using the semi-empirical density-functional theory configuration-interaction singles (DFT/CIS) method, within the state-interaction approach. Our version of DFT/CIS was introduced recently for K-edge spectra and includes a semi-empirical correction to the core orbital energies, significantly reducing ad hoc shifts that are typically required when time-dependent (TD-)DFT is applied to core-level excitations. In combination with the core/valence separation approximation and spin-orbit couplings, the DFT/CIS method affords semiquantitative L-edge spectra at CIS cost. Spin-orbit coupling has a qualitative effect on the spectra, as demonstrated for a variety of 3d transition metal systems and main-group compounds. The use of different active orbital spaces helps to facilitate spectral assignments. We find that spin-orbit splitting has a negligible effect on M-edge spectra for 3d transition metal species.