Improving sensitivity of XANES structural fit to the bridged metal-metal coordination

Abstract

Hard X-ray absorption spectroscopy is a valuable in situ probe for non-destructive diagnostics of metal sites. The low-energy interval of a spectrum (XANES) contains information about the metal oxidation state, ligand type, symmetry and distances in the first coordination shell but shows almost no dependency on the bridged metal-metal bond length. The higher-energy interval (EXAFS), on the contrary, is more sensitive to the coordination numbers and can decouple the contribution from distances in different coordination shells. Supervised machine-learning methods can combine information from different intervals of a spectrum; however, computational approaches for the near-edge region of the spectrum and higher energies are different. This work aims to keep all benefits of XANES and extend its sensitivity towards the interatomic distances in the first and second coordination shells. Using a binuclear bridged copper complex as a case study and cross-validation analysis as a quantitative tool it is shown that the first 170 eV above the edge are already sufficient to balance the contributions of Cu-O/N scattering and Cu-Cu scattering. As a more general outcome this work highlights the trivial but often overlooked importance of using `longer' energy intervals of XANES for structural refinement and machine-learning predictions. The first 200 eV above the absorption edge still do not require parametrization of Debye-Waller damping and can be calculated within full multiple scattering or finite difference approximations with only moderately increased computational costs.

Keywords: EXAFS; XANES; improved hypercube sampling; machine learning; radial basis functions; vibrational spectroscopy.

Figure 1

The whole structure of the studied copper complex (left) and splitting into fragments for deformations (right). The arrows show the direction of shift for each fragment.

Figure 2

Sensitivity of spectra to structural deformations. Panels (a) and (b) show changes in μ(E) and χ(k) for varying p ₁ parameter (Cu–Cu distance only); panels (c) and (d) show spectral changes when all p ₁,…, p ₅ deformations are considered.

Figure 3

Best fits using the first 70 eV above the absorption edge (a) and 170 eV converted to k ²χ(k) (b).

Figure 4

Variation of the R-factor in the proximity of the best fit. Panels (a) and (c) show the R-factor calculated for the XANES region (first 70 eV of the spectrum). Panels (b) and (d) show the R-factor calculated for the extended XANES region [first 170 eV and converted into k ²χ(k)]. The fit is shown in the space of two parameters: Cu–O and Cu–Cu bonds [panels (a) and (b)] or two distances in the first coordination shell [panels (c) and (d)].

Figure 5

Estimation of the RMSE from the cross-validation scheme for average Cu–O/N (a) and Cu–Cu (b) distances by using a theoretical training set and limiting χ(k) to the [1.5…k] or [k…6.5] interval (relative to the baseline accuracy of the full range; closer to the baseline is better). Red curves show the variation of the uncertainty in the interatomic distance prediction when the left border of the interval is varied [meaning extension of χ(k) to lower k-values]. Black curves show the variation of the uncertainty when the right border of the interval is varied (i.e. extension of XANES to higher k-values).

Figure 6

Spectral changes for a binuclear complex with longer equilibrium Cu–Cu distance. (a) Low sensitivity to the Cu–Cu distance of k ²-weighted χ(k) in the range 1.5–6.5 Å⁻¹. (b) Variation of the C—H bending frequency of tri­ethyl­amine ligands as a function of Cu–Cu distance. The C—H bending mode is denoted with dashed orange arrows.