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

Abstract

1 Introduction Density functional theory (DFT) has contributed significantly to our present understanding of a wide range of materials and their properties. As quantummechanical theory of the density and the total energy, it provides an atomistic description from first principles and is, in the local-density or generalized gradient approximation (LDA and GGA), applicable to polyatomic systems containing up to several thousand atoms. However, a combination of three factors limits the applicability of LDA and GGA to a range of important materials and interesting phenomena. They are approximate (jellium-based) exchange-correlation functionals, which suffer from incomplete cancellation of artificial self-interaction and lack the discontinuity of the exchange-correlation potential with respect to the number of electrons. As a consequence the Kohn-Sham (KS) single-particle eigenvalue band gap for semiconductors and insulators underestimates the quasiparticle band gap as measured by the difference of ionisation energy (via photoemission spectroscopy (PES)) and electron affinity (via inverse PES (IPES)). This reduces the predictive power for materials whose band gap is not know from experiment and poses a problem for calculations

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

“…Applied in the standard way as perturbation to an LDA ground state ͑G 0 W 0 @ LDA͒ the GW calculation suffers from the pathologies of the LDA starting point. [14][15][16][17][18]20,21,[24][25][26]29,[31][32][33][34][35] Following our previous work for f-electron systems, 29 we demonstrate in this paper that applying Hubbard U corrections to the LDA calculations ͑LDA+ U͒ provides an insightful way to systematically analyze the problem. We investigate examples from three common classes of semiconductors: empty d states ͑ScN͒, fully filled semicore d states ͑ZnS͒, and partially filled d states ͑transition-metal oxides NiO, MnO, FeO, and CoO͒.…”

“…The actual reason is still a matter of debate but it is likely that it is associated to the absence of strong short-range correlations in the GW approximation. 35,42,63,[105][106][107][108][109][110] The error in the band gap can be considerable and the binding energies of semicore d electrons ͑⑀ d ͒ are significantly underestimated. Miyake et al 47 have recently studied ZnS in G 0 W 0 @ LDA+ U with a particular emphasis on the d-band position.…”

“…However, the omission of the vertex function that would introduce higher order interactions with every iteration makes a self-consistent solution inconsistent and worsens the spectral properties of the Green's function. 6,35 In practical calcula-tions, a "best G best W" strategy is therefore adopted, where the GW quasiparticle energies are expressed as a first-order correction to a reference single-particle Hamiltonian H 0 . Both G and W are calculated using eigenenergies and eigenfunctions of H 0 , hence the abbreviation G 0 W 0 .…”

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

“…Since EXX-OEP is self-interaction-free, band gaps usually increase compared to LDA/GGA and compare well with QP energies. A recent review article covers this approach [28].…”

Unified description of ground and excited states of finite systems: The self-consistentGWapproach

“…6 Predominantly, GW calculations are still performed perturbatively (one-shot G 0 W 0 ) on a set of singleparticle orbitals and eigenvalues obtained from a preceding density-functional theory 9 (DFT) or Hartree-Fock (HF) calculation. This procedure introduces a considerable starting-point dependence, [10][11][12] which can be eliminated by iterating the Dyson equation to self-consistency. [6][7][8]13 The resulting selfconsistent GW (sc-GW ) framework is a conserving approximation in the sense of Baym and Kadanoff 14 (i.e., it satisfies momentum, energy, and particle number conservation laws).…”