Quantitative Evidence for Lanthanide-Oxygen Orbital Mixing in CeO₂, PrO₂, and TbO₂

Understanding the nature of covalent (band-like) vs ionic (atomic-like) electrons in metal oxides continues to be at the forefront of research in the physical sciences. In particular, the development of a coherent and quantitative model of bonding and electronic structure for the lanthanide dioxides, LnO₂ (Ln = Ce, Pr, and Tb), has remained a considerable challenge for both experiment and theory. Herein, relative changes in mixing between the O 2p orbitals and the Ln 4f and 5d orbitals in LnO₂ are evaluated quantitatively using O K-edge X-ray absorption spectroscopy (XAS) obtained with a scanning transmission X-ray microscope and density functional theory (DFT) calculations. For each LnO₂, the results reveal significant amounts of Ln 5d and O 2p mixing in the orbitals of t_2g (σ-bonding) and e_g (π-bonding) symmetry. The remarkable agreement between experiment and theory also shows that significant mixing with the O 2p orbitals occurs in a band derived from the 4f orbitals of a_2u symmetry (σ-bonding) for each compound. However, a large increase in orbital mixing is observed for PrO₂ that is ascribed to a unique interaction derived from the 4f orbitals of t_1u symmetry (σ- and π-bonding). O K-edge XAS and DFT results are compared with complementary L₃-edge and M_5,4-edge XAS measurements and configuration interaction calculations, which shows that each spectroscopic approach provides evidence for ground state O 2p and Ln 4f orbital mixing despite inducing very different core-hole potentials in the final state.