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Using a recently developed method combining a nonspherical self-interactioncorrected LDA+$U$ scheme and an on-site multi-body Hamiltonian [Phys.\ Rev.\ B83, 085106 (2011)], we calculate the crystal field parameters and crystal field(CF) excitation levels of $f$-element dioxides in the fluorite structure with$f^{n}$ electronic configurations, including $n=1$ (PaO$_{2}$, PrO$_{2}$),$n=2$ (UO$_{2}$), $n=3$ (NpO$_{2}$), and $n=4$ (PuO$_{2}$). It is shown thatgood agreement with experimental data (within approximately 10 to 20 meV) canbe obtained in all cases. The properties of the multi-electron CF ground statesare analyzed.

Self-consistent density functional calculations of the crystal field levels in lanthanide and actinide dioxides