koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals

Abstract

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional formulation. These functionals address two fundamental issues with density functional theory (DFT). First, while Kohn-Sham eigenvalues can loosely mirror experimental quasiparticle energies, they are not meant to reproduce excitation energies and there is formally no connection between the two (except for the HOMO for the exact functional). Second, (semi-)local DFT deviates from the expected piecewise linear behavior of the energy as a function of the total number of electrons. This can make eigenvalues an even poorer proxy for quasiparticle energies and, together with the absence of the exchange-correlation derivative discontinuity, contributes to DFT's underestimation of band gaps. By enforcing a generalized piecewise linearity condition to the entire electronic manifold, Koopmans functionals yield molecular orbital energies and solid-state band structures with comparable accuracy to many-body perturbation theory but at greatly reduced computational cost and preserving a functional formulation. This paper introduces koopmans, an open-source package that contains all of the code and workflows needed to perform Koopmans functional calculations without requiring expert knowledge. The theory and algorithms behind Koopmans functionals are summarized, and it is shown how one can easily use the koopmans package to obtain reliable spectral properties of molecules and materials.