Implementation and performance of the frequency-dependentGWmethod within the PAW framework

Abstract

Algorithmic details and results of fully frequency-dependent G 0 W 0 calculations are presented. The implementation relies on the spectral representation of the involved matrices and their Hilbert or Kramers-Kronig transforms to obtain the polarizability and self-energy matrices at each frequency. Using this approach, the computational time for the calculation of polarizability matrices and quasiparticle energies is twice as that for a single frequency, plus Hilbert transforms. In addition, the implementation relies on the PAW method, which allows to treat d-states with relatively modest effort and permits the reevaluation of the core-valence interaction on the level of the Hartree-Fock approximation. Tests performed on an sp material ͑Si͒ and materials with d electrons ͑GaAs and CdS͒ yield quasiparticle energies that are very close to previous all-electron pseudopotential and all-electron full-potential linear muffin-tin-orbital calculations.

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

“…The collection of experimental gap and d-binding energy values are taken from the collections in Refs. [20,62]. For the III-V compounds the 0 0 G W QP gap values approach the experimental values while the improved ones (with self-consistency of the eigenvalues) tend to overestimate slightly the experimental values.…”

Toward a realistic description of multilayer black phosphorus: FromGWapproximation to large-scale tight-binding simulations

“…[32] adopt a non-self-consistent G 0 W 0 scheme, where the screened Coulomb interaction W 0 is calculated within the general plasmon pole model [39] and report a band gap of 0.3 eV for bulk BP, which is within the range of available experimental data. However, the use of a more reliable random phase approximation (RPA) [40] within the G 0 W 0 scheme yields a smaller value of 0.1 eV [20]. More accurate band gap values are supposed to be obtained within the RPA in terms of a partially self-consistent GW 0 scheme.…”

“…In the notation of different methods, G0 and W0 imply that the Green's function and screened Coulomb repulsion in the GW approach are calculated non-self-consistently on the basis of wave functions derived from density functional (GGA) or hybrid functional (HSE) calculations, whereas G means a self-consistent calculation of the Green's function. W ′ 0 and W0 denote that the screened Coulomb interaction is calculated by using the general plasmon pole model [39] and RPA [40], respectively. …”

“…The Green's functions (G) were first calculated by using the Kohn-Sham eigenvalues and eigenstates and then iterated four times, which proved to be sufficient to achieve numerical convergence [44]. The screened Coulomb interaction (W 0 ) is calculated on the basis of the frequencydependent dielectric function, W 0 = ǫ −1 0 v, which, in turn, is computed at the RPA level [40] as ǫ 0 = 1 − vχ 0 , where v is the bare Coulomb interaction and χ 0 is the independent particle polarizability. The latter is evaluated by using the DFT-GGA [45] eigenvalues and eigenstates in the spectral representation.…”

Electronic structure of InN studied using soft x-ray emission, soft x-ray absorption, and quasiparticle band structure calculations

“…In the GW calculations, the Coulomb potential was screened fully dynamical using the RPA dielectric function based on the HSE eigenvalues and functions. 15 This approach to the QP band structure circumvents the problems related to the negative band gap of InN in DFT-LDA and was found to give reliable results for a large variety of semiconductors and insulators, especially those with shallow d-electrons. 16 The present approach goes beyond previously reported calculations since it is independent of the experimental d-band binding energy and provides access to the d-states DOS.…”