Enhanced static approximation to the electron self-energy operator for efficient calculation of quasiparticle energies

Abstract

An enhanced static approximation for the electron self-energy operator is proposed for efficient calculation of quasiparticle energies. Analysis of the static Coulomb-hole screened-exchange ͑COHSEX͒ approximation originally proposed by Hedin shows that most of the error derives from the short-wavelength contributions of the assumed adiabatic accumulation of the Coulomb hole. A wave-vector-dependent correction factor can be incorporated as the basis for a new static approximation. This factor can be approximated by a single scaling function, determined from the homogeneous electron-gas model. The local field effect in real materials is captured by a simple ansatz based on symmetry consideration. As inherited from the COHSEX approximation, the new approximation presents a Hermitian self-energy operator and the summation over empty states is eliminated from the evaluation of the self-energy operator. Tests were conducted comparing the new approximation to GW calculations for diverse materials ranging from crystals, molecules, atoms and a carbon nanotube. The accuracy for the minimum gap is about 10% or better. Like in the COHSEX approximation, the occupied bandwidth is overestimated.

Speeding up GW Calculations to Meet the Challenge of Large Scale Quasiparticle Predictions

“…One direction is to introduce better (optimized) bases for representing the dielectric matrix and/or the self-energy operator beyond plane waves and KS eigen states192021. The second direction is to reduce the number of conduction bands N c by replacing the summation over high-energy states with computationally tractable terms78112223, or completely removing the necessity of summing over unoccupied states242526. Other efforts include applications of the Lanczos algorithm for calculating the dielectric functions2728, the development of the stochastic GW approach29, and the separation of the dynamical and nonlocal correlations30 in dynamical mean field theory (DMFT) calculations which may also be applied to GW calculations.…”

Quasiparticle GW calculations for solids, molecules, and two-dimensional materials

“…We mention that a detailed discussion of the drawbacks of COHSEX and how to correct its main deficiencies can be found in Ref. 52 the quasiparticle gap increases by 0.4 eV. One well-known problematic case for the GW approximation is ZnO (both in the zincblende and the wurtzite structure).…”

Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators

“…The local-field and dynamic effects are thus neglected in the screened exchange, akin to the static diagonal-COHSEX method [94]. Nonetheless, these effects are insignificant for homogeneous systems and the resulting screened exchange is sufficiently accurate for bulk solids [175]. The other contribution, namely the Coulomb hole, is effectively accounted for by a fraction of semilocal PBE exchange [cf.…”