All-electron GW approximation with the mixed basis expansion based on the full-potential LMTO method

Abstract

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...

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

“…1. As found in numerous previous LDA/GGA calculations [57][58][59][60][61][62] the filled Zn-3d shells form a narrow band at 6 eV below the valence band edge. This 3d band is also observed in valence photoemission experiments, but at a larger binding energy of 9 eV [63,64].…”

Ab‐initio theory of semiconductor band structures: New developments and progress

“…For silicon, the QP gaps calculated upon the LDA or HSE03 starting point bracket the experimental values G W values slightly underestimate the gaps. This corresponds to the general trend of gap underestimation in the LDA + 0 0 G W and/or GGA + 0 0 G W approach using also fullpotential methods recently established by different groups [20,49]. For the gKS starting point, the calculated gaps are slightly larger than the experimental ones.…”

“…The use of a gKS functional is found to yield the correct ordering of the 1c Γ and 15v Γ states at the zone center, in contrast to LDA findings which give a negative sp gap [48]. This is essential for the QP description, since a correct energetic ordering of the single-particle states is an inevitable prerequisite for a perturbative treatment of the GW corrections [10,49]. The solution of the QP equation (8) with an XC potential XC ( ) V , ¢ x x also allows for a generalization to spinors and inclusion of non-collinear spins.…”

Exciting prospects for solids: Exact‐exchange based functionals meet quasiparticle energy calculations

“…Fig. 1), that even subsequent all-electron 0 0 G W calculations only open the gap to 0.02-0.05 eV [94,99]. Here the importance of removing the self-interaction from the ground state calculation has been demonstrated before by combining SIC-LDA calculations with 0 0 G W calculations (albeit in a rather approximate way by adjusting the pd repulsion and combining calculations with and without the 4d-electrons in the core of the In pseudopotential) [100,101].…”

“…Table 3). The only way to remedy this problem within LDA + 0 0 G W is to free the electrons in question by performing all-electron 0 0 G W calculations [94] or by using pseudopotentials that include the entire shell as valence electrons [48,91,92], which in the latter case introduces formidably high plane-wave cutoffs. If, on the other hand, OEPx or OEPx(cLDA) is used for the ground state calculation, then the exchange self-energy already acts on the semicore s-and p-states in the generation of the pseudopotential.…”