Continuous corrections to the molecular Kohn-Sham gap and virtual orbitals

TL;DR

This paper introduces a projector-based correction to the Kohn-Sham Hamiltonian in density functional theory, improving virtual orbitals and energy gaps to better match quasiparticle predictions and experimental results.

Contribution

It proposes a novel scissors-like operator correction that adjusts virtual orbitals and energy gaps in DFT, aligning them more closely with quasiparticle theory and experiments.

Findings

Good agreement of corrected gaps with experimental data

The correction captures electrostatic contributions to the band gap

Improves virtual orbitals, making them more similar to Hartree-Fock orbitals

Abstract

We use projector operators to correct the Kohn-Sham Hamiltonian of density functional theory (KS-DFT) so that the resulting mean-field scheme yields, in finite systems, virtual orbitals and energy gaps in better agreement with those predicted by quasiparticle theory. The proposed correction term is a scissors-like operator of the form $(\hat{I}-\hat{\rho})\delta \hat{H}(\hat{I}-\hat{\rho})$, where $\hat{I}$ is the identity operator, $\hat{\rho}$ the density matrix of the N-particle system and $\delta \hat{H}$ is either the difference between the N+1- and N-particle Kohn-Sham Hamiltonians or a non-self-consistent approximation to it. Such a term replaces the Kohn-Sham virtual orbitals of the $N$-particle system by the HOMO and virtual orbitals of the system with $N+1$ particles in an attempt to mimic a true quasiparticle spectrum. Using a local density approximation (LDA) we compute the gaps of a variety of small molecules finding good agreement with experiment and computationally more demanding methods. For these systems we examine the physical origin of this gap correction and show that so-called band gap discontinuity, $\Delta_{xc}$, contains electrostatic contributions that do not originate from the discontinuity in the exchange-correlation potential. The similarity between the corrected and Hartree-Fock virtual orbitals is illustrated and the extent to which the bare LDA virtual orbitals are improved is considered. The lack of band-gap discontinuity and the presence of self-interaction errors in the proposed correction are also discussed.