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

Abstract

X-ray absorption near-edge structure (XANES) provides element-specific insights 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-density functional theory-based molecular XANES calculations. Using ethane as a model system, we show that the full core-hole (FCH) approach exhibits a 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.