By substituting a Ti atom in anatase $\text{TiO}_2$ lattice with a Al atom, an oxygen hole $\text{O}^-$ will be created considering a formal charge of +4 for Ti, -2 for O and +3 for Al .
In this paper "Intrinsic Oxygen Vacancy and Extrinsic Aluminum Dopant Interplay: A Route to the Restoration of Defective TiO2", the authors applied the method of DFT+U to investigate the energy level of such oxygen hole. By increasing the U value, the energy level of oxygen hole was gradually raised from the top of the valance band of $\text{TiO}_2$ to somewhere near the bottom of the conduction band. The authors stated that the reason to increase the U value is for localizing the oxygen hole (displaying a rather localized charge density in real space).
My confusion is: Why it is necessary for the oxygen hole to be localized?
