Band gaps, ionization potentials, and electron affinities of periodic electron systems via the adiabatic-connection fluctuation-dissipation theorem

Abstract

An approach to calculate fundamental band gaps, ionization energies, and electron affinities of periodic electron systems is explored. Starting from total energies obtained with the help of the adiabatic-connection fluctuation-dissipation (ACFD) theorem, these physical observables are calculated according to their basic definition by differences of the total energies of the $N$-, $(N\ensuremath{-}1)$-, and $(N+1)$-electron system. The response functions entering the ACFD theorem are approximated here by the direct random phase approximation (dRPA). For a set of prototypical semiconductors and insulators it is shown that even with this quite drastic approximation the resulting band gaps are very close to experiment and of a similar quality to those from the computationally more involved $GW$ approximation. By going beyond the dRPA in the future the accuracy of the calculated band gaps may be significantly improved further.