The effects of M ͑M =Mn,Pr,Sn,Zr͒ doping on the redox thermodynamics of CeO 2 have been investigated using first-principles density-functional theory calculations with the on-site Coulomb interaction taken into account. Two different mechanisms for the O-vacancy formation in doped CeO 2 have been clarified. Compared with the case of pure CeO 2 , the decrease in the O-vacancy formation energy for the Zr-doped CeO 2 is mostly caused by the structural distortion, whereas the decrease for Mn-, Pr-, or Sn-doped CeO 2 originates from the electronic modification as well as from the structural distortion. It is found that the electronic modification occurs in those dopants whose uttermost atomic orbitals are half or fully occupied by the filling of the excess electrons left by the formation of the O vacancy. Two effects also contribute to concentration dependence of the O-vacancy formation energies for different dopant species.
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