GWwith linearized augmented plane waves extended by high-energy local orbitals

Abstract

Many-body perturbation theory in the GW approximation is currently the most accurate and robust firstprinciples approach to determine the electronic band structure of weakly correlated insulating materials without any empirical input. Recent GW results for ZnO with more careful investigation of the convergence with respect to the number of unoccupied states have led to heated debates regarding the numerical accuracy of previously reported GW results using either pseudopotential plane waves or all-electron linearized augmented plane waves (LAPWs). The latter has been arguably regarded as the most accurate scheme for electronic-structure theory for solids. This work aims to solve the ZnO puzzle via a systematic investigation of the effects of including high-energy local orbitals (HLOs) in the LAPW-based GW calculations of semiconductors. Using ZnO as the prototypical example, it is shown that the inclusion of HLOs has two main effects: it improves the description of high-lying unoccupied states by reducing the linearization errors of the standard LAPW basis, and in addition it provides an efficient way to achieve the completeness in the summation of states in GW calculations. By investigating the convergence of GW band gaps with respect to the number of HLOs for several other typical examples, it was found that the effects of HLOs are highly system-dependent, and in most cases the inclusion of HLOs changes the band gap by less than 0.2 eV. Compared to its effects on the band gap, the consideration of HLOs has even stronger effects on the GW correction to the valence-band maximum, which is of great significance for the GW prediction of the ionization potentials of semiconductors. By considering an extended set of semiconductors with relatively wellestablished experimental band gaps, it was found that in general using a HLO-enhanced LAPW basis significantly improves the agreement with experiment for both the band gap and the ionization potential, and overall the partially self-consistent GW 0 approach based on the generalized gradient approximation gives an optimal performance.

Electronic band structure of cuprous and silver halides: An all-electronGWstudy

“…41 Obviously, by using LAPW+HLOs, PBE-based GW 0 can well predict fundamental band gaps of CuX and AgX with an mean absolute error (MAE) of about 0.15 eV, which is comparable to the errors of the same approach to typical sp semiconductors. 41 The MAE of the G 0 W 0 band gaps is 0.5 eV, which is still significantly smaller than those in previous reported results. Our investigation clearly indicates that physically CuX and AgX can still be regarded as "simple", i.e.…”

“…We term this extended basis as LAPW+HLOs. 41 The quality of LAPW+HLOs is controlled by two parameters, besides those of the standard LAPW basis, namely the additional number of nodes in the radial function of highest energy local orbitals with respect to that of the LAPW basis with the same angular quantum number, denoted as n LO , and the maximum angular quantum number of local orbitals, denoted as l max characterize the radial and angular variation of local orbitals within the muffin-tin sphere, respectively. We denote the default LAPW basis by n LO = 0 in the recent version of WIEN2K, 59 which is actually a mixture of the APW+lo basis 60 for the valence states, the ordinary LAPW basis for higher l channels up to l max = 10 and additional local orbitals (LOs) for semi-core states if present.…”

“…the summation of the changes in the band gap with HLOs added to each element separately is nearly equal to the change with HLOs added to all elements simultaneously. 41 According to this observation, we perform the calculations with HLOs added only to either Cu or Cl atom, and the results are shown in Fig. 2.…”

“…n LO = 0) is used at this stage, since the effects of including HLOs in SCF calculations are negligible, as we have shown in a previous study. 41 A similar interpolation technique as described previously is employed to obtain the band structure along a particular k-path for comparison with GW . Considering that the systems investigated in this work are composed of heavy elements, we also consider the effects of spinorbit coupling (SOC) on electronic band structure by using the second variational approach 67 at the PBE level.…”

Challenges for Theory and Computation

“…Recently, a careful discussion about the band gaps of solids was presented combining fundamental concepts (generalized Kohn-Sham theory) with applications for selected systems [12]. If DFT single particle theory is not sufficient, one can use the DFT orbitals as input for many-body perturbation theories, such as the GW approximation [13] for better quasiparticle energies, in which the self-energy ∑ is expanded in terms of the single particle Green's function G and the screened Coulomb interaction W. Another scheme is the Bethe-Salpeter equation (BSE) approach [14,15] to account for excitonic effects. Recently, the combination of TDDFT and excitons was presented in [16].…”