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

Abstract

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 introduced. We introduce the notion of functional-selfconsistent (FSC) schemes, which vary the oneparticle Kohn-Sham (KS) potential entering an explicitly potential-dependent exchange-correlation (XC) energy functional for a given density, and distinguish them from orbital-selfconsistent (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 selfconsistency 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 selfconsistency by by semicanonical projection (sp) of the PBE 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 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 G0W0 and correct the spurious behavior of SL DFAs for negative ions. GKS-spRPA energy differences are uniformly more accurate than the SL-RPA ones; improvements are modest for covalent bonds but substantial for weakly bound systems. GKS-spRPA energy minimization also removes the spurious maximum in the SL-RPA potential energy curve of Be2, and produces a single Coulson-Fischer point at ∼ 2.7 times the equilibrium bond length in H2. GKS-spRPA thus corrects most density-driven errors of SL-RPA, enhances the accuracy of RPA energy differences for electron-pair conserving processes, and provides an intuitive one-electron GKS picture yielding ionization potentials energies and gaps of GW quality.

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules

“…If MP2 results are nevertheless desired, diagnostic α PT2 c values should be used to gauge their reliability. Similarly, the present results support the use of RPA calculations to calibrate dispersion-corrected DFA results.RPA calculations of NIs benefit from variational optimization of the reference,148 but the improvement appears to be most pronounced for small systems such as rare gas dimers and diminish with increasing monomer size. With average interaction energy errors consistently in the 5-10% range, RPA is accurate enough for a wide range of applications, irrespective of system size, gap size, or empirical training sets.…”

Assessment of Density Functional Theory in Predicting Interaction Energies between Water and Polycyclic Aromatic Hydrocarbons: from Water on Benzene to Water on Graphene

“…Explorative selfconsistent spRPA calculations 60 suggested that residual density-driven errors are small. All interaction energies are counterpoise-corrected for BSSE as discussed above, and all core-orbitals were frozen in RPA correlation energy calculations.…”

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules

“…Taken together with the superior accuracy of RPA for large and polarizable systems without RPA calculations of NIs benefit from variational optimization of the reference, 148 but the improvement appears to be most pronounced for small systems such as rare gas dimers and diminish with increasing monomer size. With average interaction energy errors consistently in the 5-10% range, RPA is accurate enough for a wide range of applications, irrespective of system size, gap size, or empirical training sets.…”

“…The present results cast further doubt on the validity of empirical 1/R 6 corrections for very large and polarizable monomers -even though some dispersion-corrected DFAs admittedly perform remarkably well for large systems. An accurate description of NIs for such systems may require methods Similarly, the present results support the use of RPA calculations to calibrate dispersion-corrected DFA results.RPA calculations of NIs benefit from variational optimization of the reference,148 but the improvement appears to be most pronounced for small systems such as rare gas dimers and diminish with increasing monomer size. With average interaction energy errors consistently in the 5-10% range, RPA is accurate enough for a wide range of applications, irrespective…”