Acceptor-bound holes in oxides often localize asymmetrically at one out of several equivalent oxygen ligands. Whereas Hartree-Fock (HF) theory overly favors such symmetry-broken polaronic hole localization in oxides, standard local-density (LD) calculations suffer from spurious delocalization among several oxygen sites. These opposite biases originate from the opposite curvatures of the energy as a function of the fractional occupation number $n$, i.e., $d^{2}E/d{n}^2<0$ in HF and $d^{2}E/d{n}^2>0$ in LD. We recover the correct linear behavior, $d^{2}E/d{n}^2=0$, that removes the (de)localization bias by formulating a generalized Koopmans condition. The correct description of oxygen hole localization reveals that the cation-site nominal single acceptors in ZnO, ${\text{In}}_2{\text{O}}_3$, and ${\text{SnO}}_2$ can bind multiple holes.

• Received 17 February 2009

DOI:https://doi.org/10.1103/PhysRevB.80.085202