Reliability of Hybrid Functionals in Predicting Band Gaps

We show that orbital energies from existing hybrid functionals do not give reliable band gaps. Even if a functional yields a good bulk gap, it in general does not provide accurate gaps in different structural configurations, e. g., surfaces or nanostructures. For example, none of the popular hybrid functionals adequately describe the surface-state gap of the Si(111)-(2 x 1) surface. For graphene nanoribbons, some hybrid functionals give good optical gaps (neglecting strong excitonic effects), but not quasiparticle gaps. In both cases, there are strong variations from different hybrid functionals.