Accurate modeling of the X-ray absorption near-edge spectra (XANES) is required to unravel the local structure of metal sites in complex systems and their structural changes upon chemical or light stimuli. Two relevant examples are reported here concerning the following: (i) the effect of molecular adsorption on 3d metals hosted inside metal-organic frameworks and (ii) light induced dynamics of spin crossover in metal-organic complexes. In both cases, the amount of structural models for simulation can reach a hundred, depending on the number of structural parameters. Thus, the choice of an accurate but computationally demanding finite difference method for the ab initio X-ray absorption simulations severely restricts the range of molecular systems that can be analyzed by personal computers. Employing the FDMNES code [Phys. Rev. B, 2001, 63, 125120] we show that this problem can be handled if a proper diagonalization scheme is applied. Due to the use of dedicated solvers for sparse matrices, the calculation time was reduced by more than 1 order of magnitude compared to the standard Gaussian method, while the amount of required RAM was halved. Ni K-edge XANES simulations performed by the accelerated version of the code allowed analyzing the coordination geometry of CO and NO on the Ni active sites in CPO-27-Ni MOF. The Ni-CO configuration was found to be linear, while Ni-NO was bent by almost 90°. Modeling of the Fe K-edge XANES of photoexcited aqueous [Fe(bpy)3](2+) with a 100 ps delay we identified the Fe-N distance elongation and bipyridine rotation upon transition from the initial low-spin to the final high-spin state. Subsequently, the X-ray absorption spectrum for the intermediate triplet state with expected 100 fs lifetime was theoretically predicted.

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Unveiling the nature and the distribution of surface sites in heterogeneous catalysts, and for the Phillips catalyst (CrO3/SiO2) in particular, is still a grand challenge despite more than 60 years of research. Commonly used references in Cr K-edge XANES spectral analysis rely on bulk materials (Cr-foil, Cr2O3) or molecules (CrCl3) that significantly differ from actual surface sites. In this work, we built a library of Cr K-edge XANES spectra for a series of tailored molecular Cr complexes, varying in oxidation state, local coordination environment, and ligand strength. Quantitative analysis of the pre-edge region revealed the origin of the pre-edge shape and intensity distribution. In particular, the characteristic pre-edge splitting observed for Cr­(III) and Cr­(IV) molecular complexes is directly related to the electronic exchange interactions in the frontier orbitals (spin-up and -down transitions). The series of experimental references was extended by theoretical spectra for potential active site structures and used for training the Extra Trees machine learning algorithm. The most informative features of the spectra (descriptors) were selected for the prediction of Cr oxidation states, mean interatomic distances in the first coordination sphere, and type of ligands. This set of descriptors was applied to uncover the site distribution in the Phillips catalyst at three different stages of the process. The freshly calcined catalyst consists of mainly Cr­(VI) sites. The CO-exposed catalyst contains mainly Cr­(II) silicates with a minor fraction of Cr­(III) sites. The Phillips catalyst exposed to ethylene contains mainly highly coordinated Cr­(III) silicates along with unreduced Cr­(VI) sites.

X-ray absorption near-edge structure (XANES) spectra are the fingerprint of the local atomic and electronic structures around the absorbing atom. However, the quantitative analysis of these spectra is not straightforward. Even with the most recent advances in this area, for a given spectrum, it is not clear a priori which structural parameters can be refined and how uncertainties should be estimated. Here, we present an alternative concept for the analysis of XANES spectra, which is based on machine learning algorithms and establishes the relationship between intuitive descriptors of spectra, such as edge position, intensities, positions, and curvatures of minima and maxima on the one hand, and those related to the local atomic and electronic structure which are the coordination numbers, bond distances and angles and oxidation state on the other hand. This approach overcoms the problem of the systematic difference between theoretical and experimental spectra. Furthermore, the numerical relations can be expressed in analytical formulas providing a simple and fast tool to extract structural parameters based on the spectral shape. The methodology was successfully applied to experimental data for the multicomponent Fe:SiO2 system and reference iron compounds, demonstrating the high prediction quality for both the theoretical validation sets and experimental data.