Benchmark of $\boldsymbol{GW}$ Methods for Core-Level Binding Energies

TL;DR

This paper benchmarks various $GW$ methods for calculating core-level binding energies, identifying the most accurate approaches with mean errors below 0.2 eV compared to experimental data.

Contribution

It provides a comprehensive comparison of different $GW$ schemes for core-level energies, highlighting the most accurate methods for molecular inner-shell excitations.

Findings

Three $GW$ schemes outperform others with 0.3 eV MAE.

Eigenvalue self-consistency and Hedin shift yield errors <0.2 eV.

All methods produce consistent relative binding energies.

Abstract

The $GW$ approximation has recently gained increasing attention as a viable method for the computation of deep core-level binding energies as measured by X-ray photoelectron spectroscopy (XPS). We present a comprehensive benchmark study of different $GW$ methodologies (starting-point optimized, partial and full eigenvalue-self-consistent, Hedin shift and renormalized singles) for molecular inner-shell excitations. We demonstrate that all methods yield a unique solution and apply them to the CORE65 benchmark set and ethyl trifluoroacetate. Three $GW$ schemes clearly outperform the other methods for absolute core-level energies with a mean absolute error of 0.3 eV with respect to experiment. These are partial eigenvalue self-consistency, in which the eigenvalues are only updated in the Green's function, single-shot $GW$ calculations based on an optimized hybrid functional starting point and a Hedin shift in the Green's function. While all methods reproduce the experimental relative binding energies well, the eigenvalue self-consistent schemes and the Hedin shift yield with mean errors $<0.2$ eV the best results.