One-Shot Approach for Enforcing Piecewise Linearity on HybridFunctionals: Application to Band Gap Predictions br

We present an efficient procedure for constructing nonempirical hybrid functionals toaccurately predict band gaps of extended systems. We determine mixing parameters by enforcing thegeneralized Koopmans'condition on localized electron states, which are achieved by inserting anoptimized potential probe. Application of this scheme to a large set of materials yields band gapswith a mean error of 0.30 eV with respect to experiment. Next, we consider a perturbative one-shotapproach in which the single-particle eigenvalues are calculated with the wave functions obtained atthe semilocal level. In this way, the computational cost is reduced by similar to 85% without loss of accuracy.The scheme is found to be robust upon consideration of different defect species and functionalforms.