This presentation reports the theoretical study of 3d core-electron excitation in lanthanide compounds in terms of electronic structure effects and optical properties. The calculations are done at the Density-Functional Theory (DFT) level complemented with an effective Hamiltonian based on ligand-field theory. The strategy consists of obtaining from DFT a totally symmetric density, where an active subspace is set up that forms the basis of the fivefold 3d and sevenfold 4f atomic orbitals of the lanthanide ion. This active subspace is defined with the fractional occupation of electrons, which represents open-shell species with the composite configuration 3d94fn+1. Based on the ligand-field analysis of the DFT results, the multiplet energies and ligand-field effects associated with the configuration 3d94fn+1 are evaluated; and the X-ray absorption spectra are simulated in terms of the intra-atomic 4fn → 3d94fn+1 electron transitions within the electric-dipole approximation. Examples for application are proposed taking into consideration the isolated trivalent lanthanides ions and compounds Cs2NaPrX6, with X = F, Cl, and Br. The results are compared with available experimental data, where a good agreement is qualitatively achieved. Also, the screening of the inter-electron repulsion and spin-orbit coupling interaction is numerically obtained that allows one to establish a fully non-empirical treatment of the 3d core-electron excitation, which can be valuable in the characterization and modeling of the spectral profiles of lanthanide M4,5-edge X-ray absorption spectroscopy. The enclosed theoretical model, which is being implemented in the Amsterdam Density Functional (ADF) suite of programs, is computationally economic and can be applied to any lanthanide system without limitations in terms of the size of the matrix elements of the effective Hamiltonian or the coordination symmetry of the lanthanide center.