Enhanced Static Approximation to the Electron Self-Energy Operator for Efficient Calculation of Quasiparticle Energies

TL;DR

This paper introduces an improved static approximation for the electron self-energy operator that enhances the efficiency and accuracy of quasiparticle energy calculations by incorporating a wavevector-dependent correction based on the homogeneous electron gas model.

Contribution

The authors develop a new static approximation that corrects the COHSEX method using a wavevector-dependent factor, eliminating the need for empty state summations and improving accuracy.

Findings

Achieves about 10% accuracy for minimum gap calculations.

Maintains Hermitian self-energy operator, simplifying computations.

Overestimates occupied bandwidth similar to COHSEX.

Abstract

An enhanced static approximation for the electron self energy operator is proposed for efficient calculation of quasiparticle energies. Analysis of the static COHSEX 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 wavevector 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 and nanotubes. The accuracy for the minimum gap is about 10% or better. Like in the COHSEX approximation, the occupied bandwidth is overestimated.