Theoretical calculation of finite-temperature X-ray absorption fine structure: application to sodium K-edge in NaCl

TL;DR

This work addresses the challenge of accurately predicting finite-temperature X-ray absorption fine structure ($XAFS$), including both near-edge ($XANES$) and extended ($EXAFS$) features, for chemically specific systems. It introduces a computational pipeline that integrates time-dependent density-functional perturbation theory for core excitations with ab initio molecular dynamics sampling, together with GW2X$^*$ corrections, to produce temperature-averaged spectra. The approach is demonstrated on the Na K-edge in NaCl, achieving good agreement with thin-film transmission measurements and enabling decomposition into bulk, defect, and surface contributions. This methodology provides a robust route to generate chemically specific XAFS cross sections for challenging species, aiding materials design and analysis in energy and catalysis contexts.

Abstract

We present a comprehensive computational framework for reproducing the full X-ray absorption fine structure (XAFS) through quantum-chemical simulations. The near-edge region is accurately captured using an efficient implementation of time-dependent density-functional perturbation theory applied to core excitations, while ab initio molecular dynamics provides essential sampling of core-excitation energies and interatomic distance distributions for interpreting extended X-ray absorption fine structure (EXAFS) features. Owing to the efficiency of the approach, the total spectrum can be decomposed into contributions from bulk, defective, and surface environments, which commonly coexist in experimental systems. The methodology is demonstrated for sodium at the Na K-edge in NaCl, where the predicted spectra show good agreement with experimental measurements on thin film samples. This strategy offers a practical route to generating chemically specific XAFS cross-section data for elements and species that remain challenging to characterize experimentally, thereby enabling deeper insights into materials of technological importance.

Figures (5)

• Figure 1: AIMD snapshots of the structures representing (a) NaCl bulk structure, and (b) NaCl (100) surface together with their respective unit cells considered here. Purple and green spheres denote sodium and chlorine atoms, respectively.
• Figure 2: Computed XANES of bulk NaCl perfect crystal at $T=300$ K (black) and $T=400$ K (red), as well as defective sample (blue) and NaCl (100) surface (green), both at $T=300$ K.
• Figure 3: Calculated XANES for the perfect NaCl crystal (orange), defective crystal (green), and NaCl (100) surface (red). Experimental spectrum measured for a thin film sample is also shown (blue). Purple curve represents a linear combination of the computed spectra with equal weights. The spectra were shifted vertically for clarity.
• Figure 4: Radial distribution functions (upper panels) of Na-Cl (left), Na-Na (middle), and Na-all (right) in different systems, namely perfect crystal at $T=300$K (black), perfect crystal at $T=400$K (red), defective crystal (blue), and NaCl (100) surface (green). Please note the different normalization factors for $g(r)$ in each system. The panels on the lower row show the corresponding number of neighboring atoms from a typical sodium atom.
• Figure 5: (a) EXAFS data (black) together with used Hanning windows (green). (b) Magnitude of the non-phase-shift-corrected FFT of the EXAFS data (light gray) together with the same FFT data rigidly shifted by $\sim$0.3 eV (red). Also shown in black is a scaled radial distribution function, $g_{\rm Na-all} (r)$ obtained from the AIMD simulations on the defective crystal system (Fig. \ref{['fig4']}). For a better comparison, the rigid shift and the scaling factor were chosen so that the first peaks in the red and black curve coincide in both position and intensity.