In order to clarify, from the electronic structure, the origin of the appearance of the tri-valent Ce state in irradiated cerium dioxide with swift heavy ions, we performed comprehensive first-principles calculations on various defective structures in cerium dioxide. The calculated results show that an oxygen mono-vacancy or an oxygen Frenkel pair can induce two tri-valent Ce states neighboring the oxygen vacancy. The calculation of the oxygen Frenkel pair further reveals that an interstitial oxygen atom that moves from the lattice position and an oxygen atom on the lattice can form a dimer that behaves as an oxygen molecule of negative di-valence. This bonding state can also produce excess electrons and the tri-valent Ce state in cerium dioxide.
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