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 (Si) and materials with $d$ electrons (GaAs and CdS) yield quasiparticle energies that are very close to previous all-electron pseudopotential and all-electron full-potential linear muffin-tin-orbital calculations.