Abstract
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:SiO
2
system and reference iron compounds, demonstrating the high prediction quality for both the theoretical validation sets and experimental data.
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)32+ 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.
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•Different theoretical methods in the simulation of the XANES spectra are discussed.•An extended list of available codes for XANES spectra simulation is provided.•The potential of ...operando XANES in catalysis is described with relevant examples.•Chemometric methods in the treatment of operando XANES spectra is discussed.•Machine learning approaches are used to provide structural determination from XANES.
In the last decade the appearance of progressively more sophisticated codes, together with the increased computational capabilities, has made XANES a spectroscopic technique able to quantitatively confirm (or discard) a structural model, thus becoming a new fundamental diagnostic tool in catalysis, where the active species are often diluted metal centers supported on a matrix. After providing a brief historical introduction and the basic insights on the technique, in this review article, we provide a selection of four examples where operando XANES technique has been able to provide capital information on the structure of the active site in catalysts of industrial relevance: (i) Phillips catalyst for ethylene polymerization reaction; (ii) TS-1 catalyst for selective hydrogenation reactions; (iii) carbon supported Pd nanoparticles for hydrogenation reactions; (iv) Cu-CHA zeolite for NH3-assisted selective reduction of NOx and for partial oxidation of methane to methanol. The last example testifies how the multivariate curve resolution supported by the alternating least-squares algorithm applied to a high number of XANES spectra collected under operando conditions allows to quantitatively determine different species in mutual transformation. This approach is particularly powerful in the analysis of experiments where a large number of spectra has been collected, typical of time- or space-resolved experiments. Finally, machine learning approaches (both indirect and direct) have been applied to determine, from the XANES spectra, the structure of CO, CO2 and NO adsorbed on Ni2+ sites of activated CPO-27-Ni metal-organic framework.
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A novel approach for the analysis of extended X-ray absorption fine structure (EXAFS) spectra is developed exploiting an inverse machine learning-based algorithm. Through this approach, it is ...possible to explore and account for, in a precise way, the nonlinear geometry dependence of the photoelectron backscattering phases and amplitudes of single and multiple scattering paths. In addition, the determined parameters are directly related to the 3D atomic structure, without the need to use complex parametrization as in the classical fitting approach. The applicability of the approach, its potential and the advantages over the classical fit were demonstrated by fitting the EXAFS data of two molecular systems, namely, the KAu (CN)2 and the RuCl2(CO)32 complexes.
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Modern synchrotron radiation sources and free electron laser made X-ray absorption spectroscopy (XAS) an analytical tool for the structural analysis of materials under
in situ
or
operando
conditions. ...Fourier approach applied to the extended region of the XAS spectrum (EXAFS) allows the estimation of the number of structural and non-structural parameters which can be refined through a fitting procedure. The near edge region of the XAS spectrum (XANES) is also sensitive to the coordinates of all the atoms in the local cluster around the absorbing atom. However, in contrast to EXAFS, the existing approaches of quantitative analysis provide no estimation for the number of structural parameters that can be evaluated for a given XANES spectrum. This problem exists both for the classical gradient descent approaches and for modern machine learning methods based on neural networks. We developed a new approach for rational fit based on principal component descriptors of the spectrum. In this work the principal component analysis (PCA) is applied to a dataset of theoretical spectra calculated
a priori
on a grid of variable structural parameters of a molecule or cluster. Each principal component of the dataset is related then to a combined variation of several structural parameters, similar to the vibrational normal mode. Orthogonal principal components determine orthogonal deformations that can be extracted independently upon the analysis of the XANES spectrum. Applying statistical criteria, the PCA-based fit of the XANES determines the accessible structural information in the spectrum for a given system.
A novel PCA based XANES fit is introduced. This approach selects those combinations of structural parameters affecting more the variation of a XANES spectrum and determines the amount of accessible structural information.
X-ray absorption near-edge spectroscopy (XANES) is becoming an extremely popular tool for material science thanks to the development of new synchrotron radiation light sources. It provides ...information about charge state and local geometry around atoms of interest in operando and extreme conditions. However, in contrast to X-ray diffraction, a quantitative analysis of XANES spectra is rarely performed in the research papers. The reason must be found in the larger amount of time required for the calculation of a single spectrum compared to a diffractogram. For such time-consuming calculations, in the space of several structural parameters, we developed an interpolation approach proposed originally by Smolentsev and Soldatov (2007). The current version of this software, named PyFitIt, is a major upgrade version of FitIt and it is based on machine learning algorithms. We have chosen Jupyter Notebook framework to be friendly for users and at the same time being available for remastering. The analytical work is divided into two steps. First, the series of experimental spectra are analyzed statistically and decomposed into principal components. Second, pure spectral profiles, recovered by principal components, are fitted by theoretical interpolated spectra. We implemented different schemes of choice of nodes for approximation and learning algorithms including Gradient Boosting of Random Trees, Radial Basis Functions and Neural Networks. The fitting procedure can be performed both for a XANES spectrum or for a difference spectrum, thus minimizing the systematic errors of theoretical simulations. The problem of several local minima is addressed in the framework of direct and indirect approaches.
Program title: PyFitIt.
Program Files doi:http://dx.doi.org/10.17632/ydkgfdc38t.1
Licensing provisions: GNU General Public License 3.
Programming language: Python, Jupyter Notebook framework.
Nature of problem: Quantitative structural refinements of the X-ray absorption near-edge structure spectra (XANES). Identification of the pure spectral and concentration profiles associated with an experimental XANES dataset.
Solution method: The fitting procedure of the experimental XANES spectra or of their differences is realized by means of the inverse and direct approaches based on the training set and approximation machine learning algorithms. The spectral resolution method is based on the PCA technique involving the usage of a target transformation matrix.
Additional comments including restrictions and unusual features: The current version is compatible with the free FDMNES program package for XANES simulations. However, users can prepare their own matrices of spectra calculated by an arbitrary software and the corresponding structural parameters to perform the fitting procedure in PyFitIt. The complete set of examples is distributed along with the program.
References: PyFitIt web page: http://hpc.nano.sfedu.ru/pyfitit/
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In this work we have applied machine learning methods (Extra Trees, Ridge Regression and Neural Networks) to predict structural parameters of the system based on its XANES spectrum. We used two ML ...approaches: direct one, i.e. when ML model is trained to predict the structural parameters directly from the XANES spectrum and inverse one when ML model is used to approximate spectrum as a function of structural parameters. We show the applicability of several ML approaches to predict the geometry of CO2 molecule adsorbed on Ni2+ surface sites hosted in the channels of CPO-27-Ni metal-organic framework. Quantitative fitting is based on difference XANES spectra and we discuss advantages and disadvantages of the two ML approaches and critically examine the overfitting phenomenon, caused by systematic differences of experimental data and learning dataset.
•Machine learning methods were applied for quantitative analysis of XANES spectra.•Distance and bond angle in molecular adsoprtion were predicted.•Direct and inverse mashine learning methods have been proposed.•Extra Trees, Neural Network and Ridge Regression methods were compared.•Extra Trees method showed best agreement with experimental data.
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This review deals with key methods of synthesis and characterization of metal-organic frameworks (MOFs). The modular structure affords a wide variety of MOFs with different active metal sites and ...organic linkers. These compounds represent a new stage of development of porous materials in which the pore size and the active site structure can be modified within wide limits. The set of experimental methods considered in this review is sufficient for studying the short-range and long-range order of the MOF crystal structure, determining the morphology of samples and elucidating the processes that occur at the active metal site in the course of chemical reactions. The interest in metal-organic frameworks results, first of all, from their numerous possible applications, ranging from gas separation and storage to chemical reactions within the pores. The bibliography includes 362 references.
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.
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