Using Kohn-Sham density functional theory to describe charged excitations in finite systems

We use projector operators to correct the Kohn-Sham Hamiltonian of density functional theory (KS-DFT) so that, in finite systems, the resulting mean-field scheme yields virtual orbitals and energy gaps in better agreement with those predicted by quasiparticle theory. The proposed correction term is a scissorslike operator of the form $({ ̂ \^{}{}}{I}{-}{ ̂ \^{}{}}{{ρ}}){δ}{ ̂ \^{}{}}{H}({ ̂ \^{}{}}{I}{-}{ ̂ \^{}{}}{{ρ}})$, where ${ ̂ \^{}{}}{I}$ is the identity operator, ${ ̂ \^{}{}}{{ρ}}$ is the $N$-particle KS-DFT density matrix, and ${δ}{ ̂ \^{}{}}{H}$ is the difference between the $N+1$- and $N$-particle Kohn-Sham Hamiltonians. Such a term replaces the Kohn-Sham virtual orbitals of the $N$-particle system by the highest occupied molecular orbital and virtual orbitals of the system with $N+1$ particles in an attempt to mimic a true quasiparticle spectrum. The physical origin of the proposed correction is discussed and illustrated by considering a system of interacting electrons---the Moshinsky atom---where the gap can be computed exactly. A local-density approximation (LDA) is then used to evaluate δ ̂ \^H in order to compute the gaps and orbitals of a variety of small molecules to find that the approximation improves the agreement with both experiment and computationally more demanding methods. 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.