Relativistic correction scheme for core-level binding energies from GW.

Levi Keller,Dorothea Golze,Patrick Rinke,Volker Blum

doi:10.1063/5.0018231

Levi Keller, Dorothea Golze + Show 2 more

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https://doi.org/10.1063/5.0018231

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Abstract

We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the GW approximation, which does not add computational overhead. An element-specific corrective term is derived as the difference between the 1s eigenvalues obtained from the self-consistent solutions to the non- or scalar-relativistic Kohn-Sham equations and the four-component Dirac-Kohn-Sham equations for a free neutral atom. We examine the dependence of this corrective term on the molecular environment and the amount of exact exchange in hybrid exchange-correlation functionals. This corrective term is then added as a perturbation to the quasiparticle energies from partially self-consistent and single-shot GW calculations. We show that this element-specific relativistic correction, when applied to a previously reported benchmark set of 65 core-state excitations [D. Golze et al., J. Phys. Chem. Lett. 11, 1840-1847 (2020)], reduces the mean absolute error (MAE) with respect to the experiment from 0.55 eV to 0.30 eV and eliminates the species dependence of the MAE, which otherwise increases with the atomic number. The relativistic corrections also reduce the species dependence for the optimal amount of exact exchange in the hybrid functional used as a starting point for the single-shot G0W0 calculations. Our correction scheme can be transferred to other methods, which we demonstrate for the delta self-consistent field (ΔSCF) approach based on density functional theory.

Highlights

Core-level binding energies (BEs), measured by x-ray photoemission spectroscopy (XPS), are element-specific and depend on the local chemical environment and afford access to information about the chemical bonding, oxidation state, and coordination of a given element in a sample.1–3 The energetic differences between atomic species of the same type can be smaller than 0.5 eV for second row elements and can be as low as 0.1 eV for carbon 1s excitations.4 The interpretation of an XPS spectrum can be very difficult due to overlapping features or the lack of well-defined reference data.5,6 Highly accurate theoretical tools for the prediction of relative and absolute BEs are, necessary to guide the experiment and its interpretation
For GW, we have developed three simple correction schemes to account for relativistic effects: (I) Atomic relativistic corrections are added to the QP energies. (II) The atomic ZORA scheme (aZORA) Hamiltonian is used for the underlying DFT calculation, and the obtained KS eigenvalues and molecular orbitals (MOs) are used as a starting point for GW. (III) aZORA is used as in II, and atomic relativistic corrections are added to the QP energies
We proceed with a discussion of non-relativistic results for the CORE65 benchmark set and demonstrate how our simple correction schemes, based on these atomic corrections, improve the agreement of the computed absolute 1s BEs to the experiment

Summary

Introduction

Core-level binding energies (BEs), measured by x-ray photoemission spectroscopy (XPS), are element-specific and depend on the local chemical environment and afford access to information about the chemical bonding, oxidation state, and coordination of a given element in a sample. The energetic differences (chemical shifts) between atomic species of the same type can be smaller than 0.5 eV for second row elements and can be as low as 0.1 eV for carbon 1s excitations. The interpretation of an XPS spectrum can be very difficult due to overlapping features or the lack of well-defined reference data. Highly accurate theoretical tools for the prediction of relative and absolute BEs are, necessary to guide the experiment and its interpretation. Accurate theoretical tools for the prediction of relative and absolute BEs are, necessary to guide the experiment and its interpretation. The reliable computation of absolute core-level energies is generally more challenging than the calculation of energy shifts and is the focus of this work. The most common approach to calculating core-level BEs is the delta self-consistent field (ΔSCF) method, wherein one computes the total energy difference between the ground and core-ionized states using Kohn–Sham density functional theory (KS-DFT). The best absolute core-level BEs have been obtained with meta-generalized gradient approximation (meta-GGA) functionals, yielding mean deviations of ≈0.2 eV with respect to the experiment for small molecules.. A similar accuracy has been obtained with high-level wavefunction-based delta coupled cluster methods, albeit at much higher computational cost. The introduction of occupation constraints and the explicit generation of a charged system in Δ-based approaches lead to a plethora of problems. Most importantly, the application to periodic systems requires further approximations, e.g., neutralizing the unit or supercell.

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