In past decades the scientific community has been looking for a reliable first-principles method to predict the electronic structure of solids with high accuracy. Here we present an approach which we call the quasiparticle self-consistent approximation. It is based on a kind of self-consistent perturbation theory, where the self-consistency is constructed to minimize the perturbation. We apply it to selections from different classes of materials, including alkali metals, semiconductors, wide band gap insulators, transition metals, transition metal oxides, magnetic insulators, and rare earth compounds. Apart from some mild exceptions, the properties are very well described, particularly in weakly correlated cases. Self-consistency dramatically improves agreement with experiment, and is sometimes essential. Discrepancies with experiment are systematic, and can be explained in terms of approximations made.

We have developed a new type of self-consistent scheme within the GW approximation, which we call quasiparticle self-consistent GW (QSGW ). We have shown that QSGW describes energy bands for a wide-range of materials rather well, including many where the local-density approximation fails. QSGW contains physical effects found in other theories such as LDA+U , SIC and GW in a satisfactory manner without many of their drawbacks (partitioning of itinerant and localized electrons, adjustable parameters, ambiguities in double-counting, etc.). We present some theoretical discussion concerning the formulation of QSGW , including a prescription for calculating the total energy. We also address several key methodological points needed for implementation. We then show convergence checks and some representative results in a variety of materials.

We present a new kind self-consistent GW approximation (scGW) based on the all-electron, fullpotential LMTO method. By iterating the eigenfunctions of the GW Hamiltonian, self-consistency in both the charge density and the quasiparticle spectrum is achieved. We explain why this form of self-consistency should be preferred to the conventional one. Then some results for Si are shown as a representative semiconductor, to establish agreement with a prior scGW calculation. Finally we consider many details in the electronic structure of the antiferromagnetic insulators MnO and NiO. Excellent agreement with experiment is shown for many properties, suggesting that a Landau quasiparticle (energy band) picture of MnO and NiO provides a reasonable description of electronic structure even in these correlated materials. The GW approximation (GWA) of Hedin[1] is generally believed to accurately predict excited-state properties, and in particular improve on the local density approximation (LDA), whose limitations are well known, e.g. to underestimate bandgaps semiconductors and insulators. Usually GWA is computed as 1-shot calculation starting from the LDA eigenfunctions and eigenvalues; the self-energy Σ is approximated as Σ = iG LDA W LDA , where G LDA is a bare Green function constructed from LDA eigenfunctions, and W LDA is the screened Coulomb interaction constructed from G LDA in the random phase approximation (RPA). However, establishing the validity of the 1-shot approach has been seriously hampered by the fact that nearly all calculations to date make further approximations, e.g. computing Σ from valence electrons only; the plasmon-pole approximations; and the pseudopotential (PP) approximation to deal with the core. Only recently when reliable all-electron implementations have begun to appear, has it been shown that the 1-shot GWA with PP leads to systematic errors [2,3,4]. There is general agreement among the all-electron calculations (see Table I) that the Γ-X transition in Si is underestimated when Σ = iG LDA W LDA . And we have shown previously[2] that the tendency for Σ = iG LDA W LDA to underestimate gaps is almost universal in semiconductors. This is reasonable because W LDA overestimates the screening owing to the LDA small band gaps. G constructed from quasiparticles (QP) with a wider gap (e.g. a self-consistent G) reduces the screening, and therefore generates GW with a wider gap. However, there are many possible ways to achieve selfconsistency. The theoretically simplest (and internally consistent) is the fully self-consistent scheme (scGW), which is derived through the Luttinger-Ward functional with the exchange-correlation energy approximated as the sum of RPA ring diagrams. Then W is evaluated as W = v(1 − vP ) −1 with the proper part of the polarization function P = −iG × G. However, such a construction may not give reasonable W [5], resulting in a poor G, for the following reason. If Σ is ω-dependent, G can be partitioned into a QP part and a residual satellite part. The QP part consists of terms whos...

Following the usual procedure of the GW approximation (GW A) within the first-principles framework, we calculate the self energy from eigenfunctions and eigenvalues generated by the local-density approximation (LDA). We analyze several possible sources of error in the theory and its implementation, using a recently development all-electron method approach based on the fullpotential linear muffin-tin orbital (LMTO) method. First we present some analysis of convergence in some quasiparticle energies with respect to the number of bands, and also their dependence on different basis sets within the LMTO method. We next present a new analysis of core contributions.Then we apply the GW A to a variety of materials systems, to test its range of validity. For simple sp semiconductors, GW A always underestimates bandgaps. Better agreement with experiment is obtained when the renormalization (Z) factor is not included, and we propose a justification for it. We close with some analysis of difficulties in the usual GW A procedure.

We present a new all-electron, augmented-wave implementation of the GW approximation using eigenfunctions generated by a recent variant of the full-potential LMTO method. The dynamically screened Coulomb interaction W is expanded in a mixed basis set which consists of two contributions, local atom-centered functions confined to muffin-tin spheres, and plane waves with the overlap to the local functions projected out. The former can include any of the core states; thus the core and valence states can be treated on an equal footing. Systematic studies of semiconductors and insulators show that the GW fundamental bandgaps consistently fall low in comparison to experiment, and also the quasiparticle levels differ significantly from other, approximate methods, in particular those that approximate the core with a pseudopotential. 71.15.Qe ,71.15.Mb The GW approximation (GWA) of Hedin [1] has been applied to many kinds of materials [2,3]. In customary ab initio implementations, the self-energy Σ is generated from eigenvalues and eigenfunctions calculated within the self-consistent local-density approximation (LDA). It has been shown that quasiparticle energies computed in this way are in significantly better agreement with experiment that are the LDA eigenvalues.The various implementations of GWA by may classified by what kinds of basis sets are used in the expansion of the LDA eigenfunctions, and the expansion of the bare and screened Coulomb interactions v and W . The most common implementations make an additional pseudopotential approximation for the core, which makes it possible to expand all these quantities in plane waves. However, a plane-wave basis is poorly suited to localized orbitals such as d-or f -states. Moreover, as we show here, it appears that the pseudopotential approximation is somewhat inadequate when used in conjunction with the GW approximation. Two other GW implementations that do not use pseudopotentials have also been published [4,5]. In both of these methods, v and W are expanded in plane waves; owing to the difficulty in a plane-wave expansion of localized orbitals they did not take into account core contributions. Aryasetiawan and collaborators implemented a method that expands v and W in a linear combination of augmented wave function products (product basis) and has applied it to several kind of materials, including NiO [7], with reasonable results. However this implementation requires the atomic spheres approximation (ASA) for the LDA, which approximates space by a superposition of atom-centered ("muffin-tin") spheres, neglecting the interstitial. Thus, its reliability is uncertain.We present a new GW implementation which uses a mixed-basis expansion for v and W . v and W are expanded in Aryasetiawan's product-basis in the muffin-tin (MT) spheres, and the interstitial plane waves (IPW) in the interstitial region. An IPW is a plane wave with the MT contributions projected out. This basis can be an efficient one applicable for the localized electrons and cores. Together with the rather...