X-ray Wavefunction Refinement Research Articles

X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review.

The X-ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X-ray diffraction data is reviewed. The two-center probability distribution model used to perform nuclear-position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87-100] is carefully distinguished from the newer one-center probability distribution model. In the one-center model, Hirshfeld atoms are used, and the Hirshfeld atom based X-ray constrained wavefunction (HA-XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X-ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method - the procedure by which one determines when overfitting has occurred - is named and work on it reviewed.

π-Hole bonding in a new co-crystal hydrate of gallic acid and pyrazine: static and dynamic charge density analysis.

A new cocrystal hydrate of gallic acid with pyrazine (4GA, Py, 4H2O; GA4PyW4) was obtained and characterized by single crystal X-ray diffraction. In addition to structure determination, experimental charge density analysis was carried out in terms of Multipole Modelling (MP), X-ray wavefunction refinement (XWR) and maximum entropy method (MEM). As a part of XWR, the structural refinement via Hirshfeld atom refinement was carried out and resulted in O-H bond lengths close to values from neutron diffraction. A systematic comparison of molecular conformations and aromatic interactions in this new cocrystal hydrate was performed with other existing polymorphs of gallic acid. In GA4PyW4, the two symmetry-independent gallic acid molecules have a syn COOH orientation and form the common (COOH)2 dimeric synthon. The carboxyl C atom displays the characteristics of π-holes with electropositive regions above and below the molecular plane and engages in acceptor-donor interactions with oxygen atoms of acidic O-H groups and phenol groups of neighbouring gallic acid molecules. The signature of the π-hole was identified from experimental charge density analysis, both in static density maps in MP and XWR as well as dynamic density in MEM, but it cannot be pinned down to a specific atom-atom interaction. This study presents the first comparison between an XWR and a MEM experimental electron-density determination.

X-ray wavefunction refinement and comprehensive structural studies on bromo-substituted analogues of 2-deoxy-d-glucose in solid state and solution.

The structural studies on two bromo-substituted derivatives of 2-deoxy-d-glucose (2-DG), namely 2-deoxy-2-bromo-d-glucose (2-BG) and 2-deoxy-2-bromo-d-mannose (2-BM) are described. 2-DG itself is an inhibitor of hexokinase, the first enzyme in the glycolysis process, playing a vital role in both cancer cell metabolism and viral replication in host cells. Because of that, 2-DG derivatives are considered as potential anti-cancer and anti-viral drugs. An X-ray quantum crystallography approach allowed us to obtain more accurate positions of hydrogen atoms by applying Hirshfeld atom refinement, providing a better description of hydrogen bonding even in the case of data from routine X-ray experiments. Obtained structures showed that the introduction of bromine at the C2 position in the pyranose ring has a minor influence on its conformation but still, it has a noticeable effect on the crystal structure. Bromine imposes the formation of a layered supramolecular landscape containing hydrogen bonds, which involves the bromine atom. Periodic DFT calculations of cohesive and interaction energies (at the B3LYP level of theory) have supported these findings and highlighted energetic changes upon bromine substitution. Based on molecular wavefunction from the refinement, we calculated the electrostatic potential, Laplacian, and ELI-D, and applied them to charge-density studies, which confirmed the geometry of hydrogen bonding and involvement of the bromine atom with these intermolecular interactions. NMR studies in the solution show that both compounds do not display significant differences in their anomeric equilibria compared to 2-DG, and the pyranose ring puckering is similar in both aqueous and solid state.

The influence of refinement strategies on the wavefunctions derived from an experiment

The synergy between theory and experiment found in X-ray wavefunction refinement (XWR) makes it one of the most compelling techniques available for chemical physics. The foremost benefit of XWR – obtaining wavefunctions constrained to experimental data – is at the same time its Achilles heel, because of the dependence of the results on the quality of both empirical and theoretical data. The purpose of this work is to answer the following: What is the effect of the refinement strategy and manipulation of input data on the physical properties obtained from XWR? With that in mind, cutoffs based on data resolution and F/σ(F) ratios were applied for both steps of XWR, the Hirshfeld atom refinement (HAR) and the X-ray constrained wavefunction fitting (XCW), for four selected systems: sulfur dioxide, urea, carbamazepine and oxalic acid. The effects of changing the weighting scheme or the method to transform σ(F 2) to σ(F) were also analysed. The results show that while HAR always reaches the same result, XCW is extremely sensitive to crystallographic data manipulation. This is a result of the variability of the experimental uncertainties for different resolution shells, and of not having proper standard uncertainties. Therefore, the use of distinct constraints for each resolution interval in XCW is proposed to fix this instability.

The advanced treatment of hydrogen bonding in quantum crystallography.

Although hydrogen bonding is one of the most important motifs in chemistry and biology, H-atom parameters are especially problematic to refine against X-ray diffraction data. New developments in quantum crystallography offer a remedy. This article reports how hydrogen bonds are treated in three different quantum-crystallographic methods: Hirshfeld atom refinement (HAR), HAR coupled to extremely localized molecular orbitals and X-ray wavefunction refinement. Three different compound classes that form strong intra- or intermolecular hydrogen bonds are used as test cases: hydrogen maleates, the tripeptide l-alanyl-glycyl-l-alanine co-crystallized with water, and xylitol. The differences in the quantum-mechanical electron densities underlying all the used methods are analysed, as well as how these differences impact on the refinement results.

Comparison of X-ray wavefunction refinement and multipole refinement based on the energetic analysis of the crystal structures of 2-hydroxo-8-X-quinoline derivatives (X = Cl, Br, I, S-Ph)

Comparison of X-ray wavefunction refinement and multipole refinement based on the energetic analysis of the crystal structures of 2-hydroxo-8-<i>X</i>-quinoline derivatives (<i>X</i> = Cl, Br, I, S-Ph)

Energetics of interactions in the solid state of 2-hydroxy-8-X-quinoline derivatives (X = Cl, Br, I, S-Ph): comparison of Hirshfeld atom, X-ray wavefunction and multipole refinements.

In this work, two methods of high-resolution X-ray data refinement: multipole refinement (MM) and Hirshfeld atom refinement (HAR) - together with X-ray wavefunction refinement (XWR) - are applied to investigate the refinement of positions and anisotropic thermal motion of hydrogen atoms, experiment-based reconstruction of electron density, refinement of anharmonic thermal vibrations, as well as the effects of excluding the weakest reflections in the refinement. The study is based on X-ray data sets of varying quality collected for the crystals of four quinoline derivatives with Cl, Br, I atoms and the -S-Ph group as substituents. Energetic investigations are performed, comprising the calculation of the energy of intermolecular interactions, cohesive and geometrical relaxation energy. The results obtained for experimentally derived structures are verified against the values calculated for structures optimized using dispersion-corrected periodic density functional theory. For the high-quality data sets (the Cl and -S-Ph compounds), both MM and XWR could be successfully used to refine the atomic displacement parameters and the positions of hydrogen atoms; however, the bond lengths obtained with XWR were more precise and closer to the theoretical values. In the application to the more challenging data sets (the Br and I compounds), only XWR enabled free refinement of hydrogen atom geometrical parameters, nevertheless, the results clearly showed poor data quality. For both refinement methods, the energy values (intermolecular interactions, cohesive and relaxation) calculated for the experimental structures were in similar agreement with the values associated with the optimized structures - the most significant divergences were observed when experimental geometries were biased by poor data quality. XWR was found to be more robust in avoiding incorrect distortions of the reconstructed electron density as a result of data quality issues. Based on the problem of anharmonic thermal motion refinement, this study reveals that for the most correct interpretation of the obtained results, it is necessary to use the complete data set, including the weak reflections in order to draw conclusions.

Chemical Bonding in Polarised Push-Pull Ethylenes.

1,1-Diamino-2,2-bis(triflyl)ethylenes with both twisted and planar structures around the partial "C=C" bond were synthesised. Bonding properties in these compounds were analysed by an experimental approach using high-resolution X-ray diffraction data treated with X-ray wavefunction refinement (XWR). In the twisted compound, a dominant contribution of the charge-separated resonance structure was revealed. On the contrary, the nearly planar compound still showed π-bonding character, however, with a considerable contribution of the charge-separated resonance structure.

Chemical Bonding in Polarised Push–Pull Ethylenes

Abstract1,1‐Diamino‐2,2‐bis(triflyl)ethylenes with both twisted and planar structures around the partial “C=C” bond were synthesised. Bonding properties in these compounds were analysed by an experimental approach using high‐resolution X‐ray diffraction data treated with X‐ray wavefunction refinement (XWR). In the twisted compound, a dominant contribution of the charge‐separated resonance structure was revealed. On the contrary, the nearly planar compound still showed π‐bonding character, however, with a considerable contribution of the charge‐separated resonance structure.

Validation of X‐ray Wavefunction Refinement

AbstractThe front cover artwork is provided by the group of Prof. Krzysztof Woźniak, Dr. Paulina M. Dominiak, and Dr. Magdalena Woińska. The image shows X‐ray wavefunction refinement as a method of electron density reconstruction (symbolized by a jigsaw puzzle), which allows to obtain accurate and precise molecular geometries as well as properties of electron density, and to perform data quality evaluations. Read the full text of the article at 10.1002/cphc.201700810.

Validation of X-ray Wavefunction Refinement.

In this work, the quality of the electron density in crystals reconstructed by the multipolar model (MM) and by X-ray wavefunction refinement (XWR) is tested on a set of high-resolution X-ray diffraction data sets of four amino acids and six tripeptides. It results in the first thorough validation of XWR. Agreement statistics, figures of merit, residual- and deformation-density maps, as well as atomic displacement parameters are used to measure the quality of the reconstruction relative to the measured structure factors. Topological analysis of the reconstructed density is carried out to obtain atomic and bond-topological properties, which are subsequently compared to the values derived from benchmarking periodic DFT geometry optimizations. XWR is simultaneously in better agreement than the MM with both benchmarking theory and the measured diffraction pattern. In particular, the obvious problems with the description of polar bonds in the MM are significantly reduced by using XWR. Similarly, modeling of electron density in the vicinity of hydrogen atoms with XWR is visibly improved.

Tuning the Electronic Properties of the Dative N-B Bond with Associated O-B Interaction: Electron Localizability Indicator from X-Ray Wavefunction Refinement.

Despite the immense growth in interest in difluoroborate dyes, the nature of the interactions of the boron atom within the N-BF2 -O kernel is not yet fully understood. Herein, a set of real-space bonding indicators is used to quantify the electronic characteristics of the dative N-B bond in difluoroborate derivatives. The atoms-in-molecules (AIM) partitioning scheme is complemented by the electron localizability indicator (ELI-D) approach, and both were applied to experimental and theoretical electron-density distributions (X-ray constrained wavefunction fitting vs. DFT calculations). Additionally, Fermi orbital analysis was introduced for small DFT models to support and extend the findings for structures that contain BF2 .

New Look on 3-Hydroxyiminoflavanone and Its Palladium(II) Complex: Crystallographic and Spectroscopic Studies, Theoretical Calculations and Cytotoxic Activity.

This work presents the synthesis, spectroscopic properties and single-crystal X-ray examination of the structure of 3-hydroxyiminoflavanone and its palladium complex. It presents the results of NMR (Nuclear Magnetic Resonance) spectroscopy, electron-density studies based on X-ray wavefunction refinement and theoretical calculations combined with QTAIM (Quantum Theory of Atoms in Molecules) and ELI-D (Electron Localizability Indicator) analyses. These offer an interesting new insight into the structures and behavior of flavanone and its complex, in solid state and in solution. The study also examines the cytotoxicity of the ligand and its complex against three human ovarian and lung cancer cell lines.

S⋯O chalcogen bonding in sulfa drugs: insights from multipole charge density and X-ray wavefunction of acetazolamide

Experimental charge density analysis combined with the quantum crystallographic technique of X-ray wavefunction refinement (XWR) provides quantitative insights into the intra- and intermolecular interactions formed by acetazolamide, a diuretic drug. Firstly, the analysis of charge density topology at the intermolecular level shows the presence of exceptionally strong interaction motifs such as a DDAA-AADD (D-donor, A-acceptor) type quadruple hydrogen bond motif and a sulfonamide dimer synthon. The nature and strength of intra-molecular S···O chalcogen bonding have been characterized using descriptors from the multipole model (MM) and XWR. Although pure geometrical criteria suggest the possibility of two intra-molecular S···O chalcogen bonded ring motifs, only one of them satisfies the "orbital geometry" so as to exhibit an interaction in terms of an electron density bond path and a bond critical point. The presence of 'σ-holes' on the sulfur atom leading to the S···O chalcogen bond has been visualized on the electrostatic potential surface and Laplacian isosurfaces close to the 'reactive surface'. The electron localizability indicator (ELI) and Roby bond orders derived from the 'experimental wave function' provide insights into the nature of S···O chalcogen bonding.

Applications of X-ray Wavefunction Refinement

X-ray wavefunction refinement (XWR) is a way of modeling the total aspherical electron density from an X-ray diffraction experiment on a single crystal of a molecular compound. It is a combination of existing quantum-crystallographical techniques: In the first step, geometry is determined using Hirshfeld atom refinement,[1] which is based on a stockholder partitioning of quantum-mechanical aspherical electron densities. In the second step, the same wavefunction is fitted to the experimental data to reproduce the diffraction pattern and simultaneously minimize the molecular energy.[2] The XWR protocol involves embedding the molecule into a field of point charges and dipoles as well as termination strategies to avoid overfitting.[3] Results from an X-ray wavefunction refinement are not restricted to the analysis of electron density: the full reconstructed density matrix is available. Therefore, chemical problems can be tackled with suitable tools for any given question including, e.g., experimentally derived bond orders, electron-pair localisation information, or energetics. We will present first applications of this protocol for a selection of organic (hydrogen maleate salts, sulfur-containing protease inhibitors) and inorganic (siloxanes, sulfur dioxide) compounds, for which we measured high-resolution low-temperature X-ray diffraction data at various synchrotron facilities. We will show geometry improvements, anisotropic displacement parameters for hydrogens, anharmonic motion parameters for sulfur and chlorine atoms, and improved total electron-density distributions in comparison to results from multipole modeling. Moreover, we will discuss the contribution of the experimental data to the final constrained wavefunction (defect density) and demonstrate how the experimentally derived orbital-based descriptors assist in solving fundamental chemical problems.

Treatment of anharmonic motion in X-ray wavefunction refinement (XWR)

Treatment of anharmonic motion in X-ray wavefunction refinement (XWR)

A comparison of electron density from Hirshfeld-atom refinement, X-ray wavefunction refinement and multipole refinement on three urea derivatives

Electron density distributions of three urea derivatives N-methylurea, N-phenylurea and N,N′-diphenylurea were determined by single-crystal X-ray diffraction. High-resolution data were measured with synchrotron radiation. Data were subjected to a multipole refinement using the Hansen–Coppens multipole model, to Hirshfeld-atom refinement with and without a surrounding cluster of point charges/dipoles and to X-ray wavefunction refinement. Electron density distributions were evaluated in terms of deformation and residual electron density plots as well as bond critical points, atomic volumes and charges as defined in Bader's Theory of Atoms In Molecules. Given a sufficiently extended basis-set Hirshfeld-atom refinement yields results superior to multipole model refinements; best figures of merit were achieved by X-ray wavefunction refinement. Results indicate how conventional crystallographic studies can be systematically improved.