Variational generalized Kohn-Sham approach combining the random-phase-approximation and Green's-function methods

摘要

A generalized Kohn-Sham (GKS) scheme which variationally minimizes the random phase approximation (RPA) ground-state energy with respect to the GKS one-particle density matrix is put forward. We introduce the notion of functional self-consistent schemes, which vary the one-particle Kohn-Sham (KS) potential entering an explicitly potential-dependent exchange-correlation (XC) energy functional for a given density, and distinguish them from orbital-self-consistent (OSC) schemes, which vary the density, or the orbitals, density matrix, or KS potential generating the density. It is shown that, for explicitly potential-dependent XC functionals, existing OSC schemes such as the optimized effective potential method violate the Hellmann-Feynman theorem for the density, producing a spurious discrepancy between the KS density and the correct Hellmann-Feynman density for approximate functionals. A functional self-consistency condition is derived which resolves this discrepancy by requiring the XC energy to be stationary with respect to the KS potential at fixed density. We approximately impose functional self-consistency by semicanonical projection (sp) of the Perdew, Burke, and Ernzerhof KS Hamiltonian. Variational OSC minimization of the resulting GKS-spRPA energy functional leads to a nonlocal correlation potential whose off-diagonal blocks correspond to orbital rotation gradients, while its diagonal blocks are related to the RPA self-energy at a real frequency. Quasiparticle GW energies are a first-order perturbative limit of the GKS-spRPA orbital energies; the lowest-order change of the total energy captures the renormalized singles excitation correction to RPA. GKS-spRPA orbital energies are found to approximate ionization potentials and fundamental gaps of atoms and molecules more accurately than semilocal density functional approximations (SL DFAs) or G_0W_0 and correct the spurious behavior of SL DFAs for negative ions. GKS-spRPA energy differences are uniformly more a