Finite-size effects and energy alignment in molecular XANES under periodic boundary conditions: A systematic comparison of core-hole treatments

TL;DR

This study systematically compares core-hole treatments in molecular XANES calculations under periodic boundary conditions, revealing how finite-size effects influence energy alignment and proposing correction methods for improved accuracy.

Contribution

It introduces a comprehensive analysis of core-hole approximations in PBC-DFT XANES, proposing correction schemes to enhance energy alignment and chemical-shift reproducibility.

Findings

XCH converges rapidly with supercell size, unlike FCH.

Makov-Payne and EF/2 corrections effectively mitigate finite-size effects.

XCH and FCH+EF/2 accurately reproduce experimental chemical shifts.

Abstract

X-ray absorption near-edge structure (XANES) provides element-specific insight into local electronic and structural environments, but quantitative interpretation of molecular XANES under periodic boundary conditions (PBC) remains challenging due to finite-size effects and core-hole treatments. In this work, we systematically investigate how core-hole approximations and charge compensation schemes affect transition energies, energy alignment, and chemical-shift reproducibility in PBC-DFT-based molecular XANES calculations. Using ethane as a model system, we show that the full core-hole (FCH) approach exhibits pronounced supercell-size dependence originating from interactions between background charge and charged molecules, with transition energies largely changed by leading-order finite-size terms. In contrast, the excited core-hole (XCH) method rapidly converges owing to its neutral final state. We further demonstrate that most finite-size effects in FCH can be removed by Makov-Payne corrections based on multipole expansion of the electrostatic energy of charged supercells under PBC. Furthermore, we propose a simple Fermi-level-based energy correction (EF/2) that provides comparable improvement using only a single supercell. Extending the analysis to an n-alkane series reveals that while intrinsic electronic-structure changes govern peak shifts for small molecules, systematic energy drifts persist in FCH for larger molecules, whereas XCH and FCH+EF/2 remain stable. Finally, for small molecules at the C and N K-edges, XCH and FCH+EF/2 accurately reproduce experimental chemical shifts, whereas uncorrected FCH fails. These results provide practical guidelines for reliable energy alignment and chemical-shift analysis in molecular XANES under PBC, supporting robust applications to molecular, adsorption, and interfacial systems.