Accurate absolute and relative core-level binding energies from $GW$

TL;DR

This paper introduces an improved $GW$ method for accurately calculating core-level binding energies in X-ray photoelectron spectra, addressing limitations of previous density functional theory approaches.

Contribution

It demonstrates that partial self-consistent $GW$ schemes or hybrid functionals with high exact exchange are necessary for accurate core-level calculations, providing a benchmark for 65 molecular excitations.

Findings

Absolute $GW$ core-level energies agree within 0.3 eV with experiments.

Relative $GW$ core-level energies agree within 0.2 eV with experiments.

Single-shot $G_0W_0$ fails for core levels, causing spectral weight transfer.

Abstract

We present an accurate approach to compute X-ray photoelectron spectra based on the $GW$ Green's function method, that overcomes shortcomings of common density functional theory approaches. $GW$ has become a popular tool to compute valence excitations for a wide range of materials. However, core-level spectroscopy is thus far almost uncharted in $GW$. We show that single-shot perturbation calculations in the $G_0W_0$ approximation, which are routinely used for valence states, cannot be applied for core levels and suffer from an extreme, erroneous transfer of spectral weight to the satellite spectrum. The correct behavior can be restored by partial self-consistent $GW$ schemes or by using hybrid functionals with almost 50% of exact exchange as starting point for $G_0W_0$. We include also relativistic corrections and present a benchmark study for 65 molecular 1s excitations. Our absolute and relative $GW$ core-level binding energies agree within 0.3 and 0.2 eV with experiment, respectively.