The GW approximation: content, successes and limitations

Abstract

Many observables such as the density, total energy, or electric current, can be expressed explicitly in terms of the one‐body Green's function, which describes electron addition or removal to or from a system. An efficient way to determine such a Green's function is to introduce a self‐energy, which is a nonlocal and dynamic effective potential that influences the propagation of particles in an interacting system. The state‐of‐the art approximation for the self‐energy is the GW approximation, where the system to (or from) which the electron is added (or removed) is described as a polarizable, screening, medium. This is expressed by the name of the approximation: ‘GW’ stands for the one‐body Green's function G and for W, the dynamically screened Coulomb interaction. The GW approximation is very popular for the calculation of band structures in solids, and increasingly used also to describe nanostructures, clusters, and molecules. As compared to static mean‐field approximations for the effective potential, the dynamical screening of the Coulomb interaction in GW leads to a renormalization of energies, to broadening and/or to the observation of additional excitations. An analysis of the approximations that lead to the GW self‐energy, and of the underlying picture, explains the successes and the limitations of the approach. This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Structure and Mechanism > Computational Materials Science

Atomic structures and orbital energies of 61,489 crystal-forming organic molecules

“…In two subsets, randomly drawn to span more than half (31k) and more than 5000 (5k) of the molecular structures, we provide additional computational results: the influence of solvation -in this case implicit water -on the energy levels is addressed on the PBE0 level for a subset of 30,876 molecules. For the second subset of 5,239 molecules, we computed the quasi-particle energies with many-body perturbation theory in the G 0 W 0 approximation [11,14,42] and extrapolated to the complete basis set (CBS) limit. Figure 2 gives a schematic overview of the dataset nesting in OE62 while Table 1 lists computational settings and computed properties.…”

Quasiparticle and Optical Properties of Hydrogen Titanate and Its Defective Systems: An Investigation by Density Functional Theory with Hubbard Correction, Many‐Body Perturbation Theory, and Bethe–Salpeter Equation

“…Starting with the perfect hydrogen titanate system both of the band structures show an indirect bandgap semiconductor with a value of 3.2 eV for the DFT+ U (the highest occupied level is at L = 0.00 eV and the lowest unoccupied level is at Γ = 3.22 eV) and 5.6 eV for the G o W o (the highest occupied level is at X = −0.07 eV and the lowest unoccupied level is at Γ = 5.59 eV). As expected from the effect of the G o W o correction, an expansion occurred compared with DFT and DFT+ U band structures in which the bottom of the CB moved upward by around 2.4 eV, whereas there is a small change regarding the top of the VB (moved by about 0.1 eV).…”

“…Many‐body perturbation GW approximation (GWA) was used to calculate quasiparticle (QP) excitations in solids, as measured by direct and inverse photoemission experiments . For the optical spectrum, the Bethe–Salpeter equation (BSE) was solved to include the effects of electron–hole interactions …”

“…[22] Many-body perturbation GW approximation (GWA) was used to calculate quasiparticle (QP) excitations in solids, as measured by direct and inverse photoemission experiments. [23] For the optical spectrum, the Bethe-Salpeter equation (BSE) was solved to include the effects of electron-hole interactions. [20,24,26] In this work, we investigate the origin of changes in the structural, electronic, and optical properties of H 2 Ti 3 O 7 in terms of the neutral oxygen, hydroxyl, and hydrogen vacancies, including a rigorous description of the optical spectra, the spatial distribution of exciton wave-functions, and the optical transitions of the excitons by means of spin-polarized DFTþU, GWA, and BSE.…”

Density-Based Basis-Set Incompleteness Correction for GW Methods

“…[2][3][4] The so-called GW approximation is the workhorse of MBPT and has a long and successful history in the calculation of the electronic structure of solids. [2][3][4] GW is getting increasingly popular in molecular systems [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] thanks to efficient implementation relying on plane waves [21][22][23] or local basis functions. 5,9,[24][25][26][27][28][29][30][31][32] The GW approximation stems from the acclaimed Hedin's equations 33 G(12) = G 0 (12) + G 0 (13)Σ(34)G (42) which connects the Green function G, its non-interacting version G 0 , the irreducible vertex function Γ, the irreducible polarizability P, the dynamically-screened Coulomb interaction W and the self-energy Σ, where is the bare Coulomb interaction, δ(12) is the Dirac delta function 34 and 1 is a composite coordinate gathering space, spin, and time variables (r 1 , σ 1 , t 1 ).…”