Fig. 1: Enforcement of the piecewise linearity.

Energy levels \({\epsilon }_{{{{\rm{p}}}}}^{U}(+1)\) and \({\epsilon }_{{{{\rm{p}}}}}^{U}(0)\) as a function of U for the self-trapped hole in MgO. The defect levels are identified by their respective charge. The value Uk is found such that \({\epsilon }_{{{{\rm{p}}}}}^{{U}_{{{{\rm{k}}}}}}(+1)={\epsilon }_{{{{\rm{p}}}}}^{{U}_{{{{\rm{k}}}}}}(0)\).