On the calculation of multiplet energies of three-open-shell 4f135fn6d1 electron configuration by LFDFT: modeling the optical spectra of 4f core-electron excitation in actinide compounds

Abstract

Methodological concepts are reported for the calculation, without empirical parameters, of multiplet energy levels and ligand-field effects associated with three-open-shell 4f¹³5fⁿ6d¹ electron configurations, and for the modeling of X-ray absorption spectra in relation to intra-atomic 5fⁿ → 4f¹³5fⁿ6d¹ electron transitions. A density functional theory (DFT) method is used for the determination of the electronic structure. An effective ligand-field Hamiltonian is also used to incorporate many body effects and corrections via the configuration interaction algorithm within the active space of Kohn–Sham orbitals with dominant actinide 4f, 5f and 6d characters. The theoretical method ensures a parameter-free ligand-field model, which will be implemented in the Amsterdam density functional (ADF) program package as part of the available and automated ligand-field density functional theory (LFDFT) routine. The theoretical method is illustrated with examples for applications: U⁴⁺ in the free ion and U⁴⁺ in bulk UO₂ by means of the molecular (UO₈)¹²⁻ cluster. The DFT calculations are performed at different levels of the DFT functional, from which the LFDFT parameters such as Slater–Condon integrals, spin–orbit coupling constants and ligand-field potential (represented within the Wybourne formalism) are emulated. The comparison with available experimental data is good. Therefore, a non-empirical ligand-field treatment of the 4f¹³5fⁿ6d¹ configuration is established illustrating the spectroscopic details of the 4f core-electron excitation, which can be valuable for further understanding and prediction of the spectral profiles of actinide N_6,7-edge X-ray absorption spectroscopy.