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Bringing oxygen atoms from infinite, passing equilibrium until short enough distances, we aim to reveal the 4 f 5 d  electron bonding property and its relevance to the peculiar physical properties within PrO 2  based on both accounting for electron Coulomb repulsion and spin-orbit coupling effects in combination with Wannier function methods. The microscopic mechanism of static Janh-Teller distortions and the physical insight into the dynamic Jahn-Teller effects are clarified. Peculiarly, the magnetic coupling is suggested to be via 4 f -5 d -O2 p -5 d -4 f  pathway in PrO 2 , and the coupling between spin and orbital ordering of 4 f  electrons is for the first time disclosed. The 5 d  orbitals, hybridized with 4 f  electrons, are found to play important roles in these processes.

Strong-correlated behavior of 4f electrons and 4f5d hybridization in PrO2