Core-Level Binding Energies from GW: An Efficient Full-Frequency Approach within a Localized Basis

Abstract

The GW method is routinely used to predict charged valence excitations in molecules and solids. However, the numerical techniques employed in the most efficient GW algorithms break down when computing core excitations as measured by X-ray photoelectron spectroscopy (XPS). We present a full-frequency approach on the real axis using a localized basis to enable the treatment of core levels in GW. Our scheme is based on the contour deformation technique and allows for a precise and efficient calculation of the self-energy, which has a complicated pole structure for core states. The accuracy of our method is validated by comparing to a fully analytic GW algorithm. Furthermore, we report the obtained core-level binding energies and their deviations from experiment for a set of small molecules and large polycyclic hydrocarbons. The core-level excitations computed with our GW approach deviate by less than 0.5 eV from the experimental reference. For comparison, we also report core-level binding energies calculated by density functional theory (DFT)-based approaches such as the popular delta self-consistent field (ΔSCF) method. Our implementation is optimized for massively parallel execution, enabling the computation of systems up to 100 atoms.

Calculation of core‐level electron spectra of ionic liquids

“…In this study, we have applied for the first time the delta Kohn–Sham (ΔKS) method for obtaining the BEs of ion pairs. Despite doubts regarding charge transfer in ILs modeled with the core hole, [ 36 ] this study demonstrates a good agreement between the available experimental XPS data and the calculated ΔKS BEs. Furthermore, we present and discuss the correlations found between the ΔKS BE values, 1s KS orbital energies, and atomic charges.…”

“…Recently, Golze et al hypothesized that the negative charge at an anion could displace to neutralize the core hole at a cation atom in the excited ion pair. [ 36 ] As can be seen in Figure 3, there is no notable partial charge transfer between the BF 4 − anion and the EMIm + cation; a small redistribution of the electron density occurs only in the vicinity of the carbon atom with a full core hole.…”

“…For instance, the most recent implementation of the GW method for massively parallel execution applies to systems up to 100 atoms. [ 36,71 ] The ΔKS method can be applied to extensive systems, but it requires additional calculations for each BE value, making it substantially more resource‐demanding than the ε(1s) method. Therefore, the use of the ε(1s) method is justified for large systems, for example, complex interface models calculated with DFT (with or without periodic boundary conditions) or simulated with DFT‐based molecular dynamics, discussed in refs.…”

“…Still, the final‐state method is computationally less expensive than the alternatives such as the third‐order algebraic diagrammatic construction (ADC(3)) method and the GW approximation. [ 36,40,41 ] For comparison, the GW method, applied to small molecules, gives MAEs below 0.1 eV. [ 42 ]…”

Robust Analytic-Continuation Approach to Many-Body GW Calculations

“…Finally, in the contour deformation technique, 4,13,[50][51][52][53] the integral along the real-axis is transformed into an integral along the imaginary axis. This integral must be complemented however by the contribution of the residues of W at the poles of the Green's function G that are shifted into the first/third quadrant by the energy at which the self-energy is required (see Fig.…”