Fig. 1

Energy levels of the 4f ¹ orbital of Ce³⁺. Ce³⁺ splits initially by spin-orbit coupling (SOC) and subsequently by cubic crystal field (CF) of the the fluorite structure. The spin-orbit splitting between J = 5/2 and J = 7/2 is about 0.28 eV^{29, 49}. The color gradient (see color bar) indicates the probability distribution at 1900 K, given by exp(−E _i /k_B T), and numbers in parentheses stand for the degeneracy of the electronic states. The first predicted Γ₈ → Γ₇ excitation for CeO₂ is 0.12 eV. Predictions for the higher CF levels of J = 7/2 are 0.25, 0.32, 0.46 respectively