Comment on "Total energy method from many-body formulation"

Improved One-Shot Total Energies from the Linearized GW Density Matrix

The linearized GW density matrix (γ^GW) is an efficient method to improve the static portion of the self-energy compared to that of ordinary perturbative GW while keeping the single-shot simplicity of the calculation. Previous work has shown that γ^GW gives an improved Fock operator and total energy components that approach the self-consistent GW quality. Here, we test γ^GW for dimer dissociation for the first time by studying N₂, LiH, and Be₂. We also calculate a set of self-consistent GW results in identical basis sets for a direct and consistent comparison. γ^GW approaches self-consistent GW total energies for a starting point based on a high amount of exact exchange. We also compare the accuracy of different total energy functionals, which differ when evaluated with a non-self-consistent density or density matrix. While the errors in total energies among different functionals and starting points are small, the individual energy components show noticeable errors when compared to reference data. The energy component errors of γ^GW are smaller than functionals of the density and we suggest that the linearized GW density matrix is a route to improving total energy evaluations in the adiabatic connection framework.

First-principles study of relative stability of rutile and anatase TiO2 using the random phase approximation

By considering high-order correlations using the random phase approximation, rutile is correctly predicted to be more stable than anatase.

Ab initio calculation of van der Waals bonded molecular crystals

Intermolecular interactions in the van der Waals bonded benzene crystal are studied from first principles, by combining exact exchange energies with correlation energies defined by the adiabatic connection fluctuation-dissipation theorem, within the random phase approximation. Correlation energies are evaluated using an iterative procedure to compute the eigenvalues of dielectric matrices, which eliminates the computation of unoccupied electronic states. Our results for the structural and binding properties of solid benzene are in very good agreement with experimental results and show that the framework adopted here is a very promising one to investigate molecular crystals and other condensed systems bound by dispersion forces.

First-principles description of correlation effects in layered materials

We present a first-principles description of anisotropic materials characterized by having both weak (dispersionlike) and strong covalent bonds, based on the adiabatic-connection fluctuation-dissipation theorem with density functional theory. For hexagonal boron nitride the in-plane and out-of-plane bonding as well as vibrational dynamics are well described both at equilibrium and when the layers are pulled apart. Bonding in covalent and ionic solids is also described. The formalism allows us to ping down the deficiencies of common exchange-correlation functionals and provides insight toward the inclusion of dispersion interactions into the correlation functional.

Describing static correlation in bond dissociation by Kohn–Sham density functional theory

We show that density functional theory within the RPA (random phase approximation for the exchange-correlation energy) provides a correct description of bond dissociation in H(2) in a spin-restricted Kohn-Sham formalism, i.e., without artificial symmetry breaking. We present accurate adiabatic connection curves both at equilibrium and beyond the Coulson-Fisher point. The strong curvature at large bond length implies important static (left-right) correlation, justifying modern hybrid functional constructions but also demonstrating their limitations. Although exact at infinite separation and accurate near the equilibrium bond length, the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths. Going beyond the RPA by including the exact exchange kernel (RPA+X), we find a similar repulsion. We argue that this deficiency is due to the absence of double excitations in adiabatic linear response theory. Further analyzing the H(2) dissociation limit we show that the RPA+X is not size consistent, in contrast to the RPA.

Lack of Hohenberg-Kohn theorem for excited states

For a given excited state there exist densities that arise from more than one external potential. This is due to a qualitatively different energy-density relationship from that of the ground state and is related to positive eigenvalues in the nonlocal susceptibility for excited states. Resulting problems with the generalization of the density functional methodology to excited states are discussed.