Crystal field and magnetic structure of UO$_{2}$: a computational probe of the multi-determinantal ground and excited states

The properties of UO$_{2}$ is the result of complex $f$-electron physics, characterized by localization of orbitals, strong electronic interactions and spin-orbit effects, crystal field potential, magnetic and electron-lattice couplings. We present a comprehensive theoretical study of the electronic structure of UO$_{2}$ with combined applications of a newly improved density functional method and a model Hamiltonian. The model, unambiguously parametrized with DFT calculations, predict the excitation energies of the $f^{2}$ states, including the whole spectrum with different $L,S,J$ as well as the low energy crystal field excitations $\Gamma_{5} \rightarrow \Gamma_{3,4,1}$, with good agreement to experiment. The $\Gamma_{5}$ triplet is confirmed as the lowest multiplet. We also investigated different non-collinear magnetic structures, in particular the 3-k ground state, of UO$_{2}$.