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

Modeling L- and M-edge spectra at x-ray and extreme ultraviolet wavelengths requires consideration of spin-orbit splitting within the 2p and 3p orbital manifolds. 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) approach. The latter was previously introduced for K-edge spectra and includes a semi-empirical correction to the core orbital energies, significantly reducing the 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- and M-edge spectra at TD-DFT cost, as demonstrated here for a variety of 3d transition metal systems and main-group compounds. The use of different active orbital spaces to make spectral assignments is also discussed.