Theory of $L$-edge spectroscopy of strongly correlated systems

X-ray absorption spectroscopy measured at the $L$-edge of transition metals (TMs) is a powerful element-selective tool providing direct information about the correlation effects in the $3d$ states. The theoretical modeling of the $2p\rightarrow3d$ excitation processes remains to be challenging for contemporary \textit{ab initio} electronic structure techniques, due to strong core-hole and multiplet effects influencing the spectra. In this work we present a realization of the method combining the density-functional theory with multiplet ligand field theory, proposed in Haverkort et al. (https://link.aps.org/doi/10.1103/PhysRevB.85.165113), Phys. Rev. B 85, 165113 (2012). In this approach a single-impurity Anderson model (SIAM) is constructed, with almost all parameters obtained from first principles, and then solved to obtain the spectra. In our implementation we adopt the language of the dynamical mean-field theory and utilize the local density of states and the hybridization function, projected onto TM $3d$ states, in order to construct the SIAM. The developed computational scheme is applied to calculate the $L$-edge spectra for several TM monoxides. A very good agreement between the theory and experiment is found for all studied systems. The effect of core-hole relaxation, hybridization discretization, possible extensions of the method as well as its limitations are discussed.