Probing the accuracy and precision of Hirshfeld atom refinement with HARt interfaced with Olex2

Unusually Short H⋅⋅⋅H Contacts in Intramolecularly Cyclized Helically Fused Anthracenes

The intramolecular coupling of dichloro-substituted helically fused anthracenes using the Yamamoto coupling yielded cyclized products with sterically congested molecular structures. The X-ray analysis and DFT calculations showed that the aromatic framework adopted a nonplanar structure with a twisted conformation about the newly formed single bond, which acts as a chiral axis. Interestingly, the X-ray structure obtained through the Hirshfeld atom refinement revealed short interatomic distances between the inner hydrogen atoms (1.648-1.692 Å), much shorter than the sum of their van der Waals radii. Owing to these unusually short contacts, the 1H NMR spectrum exhibited a significant deshielding (12.5 ppm) and a large nuclear Overhauser effect (44 %). Additionally, the IR spectrum displayed a high-frequency shift of the C-H stretching vibration. These observations, along with the noncovalent interaction plot indicative of a characteristic steric environment, strongly support the presence of steric hindrance. Moreover, dynamic NMR measurement of the mesityl-substituted derivative yielded a barrier to helical inversion of 84 kJ mol-1. The optical properties and crystal packing of the cyclized products are also reported.

Dynamic Covalent Bonds in the Ebselen Class of Antioxidants Probed by X-ray Quantum Crystallography

Dynamic bonds are essential structural ingredients of dynamic covalent chemistry that involve reversible cleavage and formation of bonds. Herein, we explore the electronic characteristics of Se-N bonds in the organo-selenium antioxidant ebselen and its derivatives for their propensity to function as dynamic covalent bonds by employing high-resolution X-ray quantum crystallography and complementary computational studies. An analysis of the experimentally reconstructed X-ray wavefunctions reveals the salient electronic features of the Se-N bonds with very low electron density localized at the bonding region and a positive Laplacian value at the bond critical point. Bond orders and percentage covalency and ionicity estimated from the X-ray wavefunctions, along with localized orbital locator (LOL) and electron localization function (ELF) analyses show that the Se-N bond is unique in its closed shell-like features, despite being a covalent bond. Time-dependent DFT calculations simulate the cleavage of Se-N bonds in ebselen in the excited state, further substantiating their nature as dynamic bonds.

Transferable Hirshfeld atom model for rapid evaluation of aspherical atomic form factors

Form factors based on aspherical models of atomic electron density have brought great improvement in the accuracies of hydrogen atom parameters derived from X-ray crystal structure refinement. Today, two main groups of such models are available, the banks of transferable atomic densities parametrized using the Hansen-Coppens multipole model which allows for rapid evaluation of atomic form factors and Hirshfeld atom refinement (HAR)-related methods which are usually more accurate but also slower. In this work, a model that combines the ideas utilized in the two approaches is tested. It uses atomic electron densities based on Hirshfeld partitions of electron densities, which are precalculated and stored in a databank. This model was also applied during the refinement of the structures of five small molecules. A comparison of the resulting hydrogen atom parameters with those derived from neutron diffraction data indicates that they are more accurate than those obtained with the Hansen-Coppens based databank, and only slightly less accurate than those obtained with a version of HAR that neglects the crystal environment. The advantage of using HAR becomes more noticeable when the effects of the environment are included. To speed up calculations, atomic densities were represented by multipole expansion with spherical harmonics up to l = 7, which used numerical radial functions (a different approach to that applied in the Hansen-Coppens model). Calculations of atomic form factors for the small protein crambin (at 0.73 Å resolution) took only 68 s using 12 CPU cores.

In data we trust: X-ray diffraction experiments for charge density investigations

A short commentary is given on the paper by Vosegaard et al. [Acta Cryst. (2023), 79, 380-391], which compares charge density models derived from four datasets measured on conventional diffractometers with the results of a high-quality dataset from SPring-8.

Comparative study of conventional and synchrotron X-ray electron densities on molecular crystals

Five different electron density datasets obtained from conventional and synchrotron single crystal X-ray diffraction experiments are compared. The general aim of the study is to investigate the quality of data for electron density analysis from current state-of-the-art conventional sources, and to see how the data perform in comparison with high-quality synchrotron data. A molecular crystal of melamine was selected as the test compound due to its ability to form excellent single crystals, the light atom content, and an advantageous suitability factor of 3.6 for electron density modeling. These features make melamine an optimal system for conventional X-ray diffractometers since the inherent advantages of synchrotron sources such as short wavelength and high intensity are less critical in this case. Data were obtained at 100 K from new in-house diffractometers Rigaku Synergy-S (Mo and Ag source, HyPix100 detector) and Stoe Stadivari (Mo source, EIGER2 1M CdTe detector), and an older Oxford Diffraction Supernova (Mo source, Atlas CCD detector). The synchrotron data were obtained at 25 K from BL02B1 beamline at SPring-8 in Japan (λ = 0.2480 Å, Pilatus3 X 1M CdTe detector). The five datasets were compared on general quality parameters such as resolution, ⟨I/σ⟩, redundancy and R factors, as well as the more model specific fractal dimension plot and residual density maps. Comparison of the extracted electron densities reveals that all datasets can provide reliable multipole models, which overall convey similar chemical information. However, the new laboratory X-ray diffractometers with advanced pixel detector technology clearly measure data with significantly less noise and much higher reliability giving densities of higher quality, compared to the older instrument. The synchrotron data have higher resolution and lower measurement temperature, and they allow for finer details to be modeled (e.g. hydrogen κ parameters).

Hydrogen atoms in supramolecular chemistry: a structural perspective. Where are they, and why does it matter?

Hydrogen bonding interactions are ubiquitous across the biochemical and chemical sciences, and are of particular interest to supramolecular chemists. They have been used to assemble hydrogen bonded polymers, cages and frameworks, and are the functional motif in many host-guest systems. Single crystal X-ray diffraction studies are often used as a key support for proposed structures, although this presents challenges as hydrogen atoms interact only weakly with X-rays. In this Tutorial Review, we discuss the information that can be gleaned about hydrogen bonding interactions through crystallographic experiments, key limitations of the data, and emerging techniques to overcome these limitations.

Hirshfeld Atom Refinement of Metal-Organic Complexes: Treatment of Hydrogen Atoms Bonded to Transition Metals

Hydrogen positions in hydrides play a key role in hydrogen storage materials and high-temperature superconductors. Our recently published study of five crystal structures of transition-metal-bound hydride complexes showed that using aspherical atomic scattering factors for Hirshfeld atom refinement (HAR) resulted in a systematic elongation of metal-hydrogen bonds compared to using spherical scattering factors with the Independent Atom Model (IAM). Even though only standard-resolution X-ray data was used, for the highest-quality data, we obtained excellent agreement between the X-ray and the neutron-derived bond lengths. We present an extended version of this study including 10 crystal structures of metal-organic complexes containing hydrogen atoms bonded to transition-metal atoms for which both X-ray and neutron data are available. The neutron structures were used as a benchmark, and the X-ray structures were refined by applying Hirshfeld atom refinement using various basis sets and DFT functionals in order to investigate the influence of the technical aspects on the length of metal-hydrogen bonds. The result of including relativistic effects in the Hamiltonian and using a cluster of multipoles simulating interactions with a crystal environment during wave function calculations was examined. The effect of the data quality on the final result was also evaluated. The study confirms that a high quality of experimental data is the key factor allowing us to obtain significant improvement in transition metal (TM)-hydrogen bond lengths from HAR in comparison with the IAM. Individual adjustments and better choices of the basis set can improve hydrogen positions. Average differences between TM-H bond lengths obtained with various DFT functionals upon including relativistic effects or between double-ζ and triple-ζ basis sets were not statistically significant. However, if all bonds formed by H atoms were considered, significant differences caused by different refinement strategies were observed. Finally, we examined the refinement of atomic thermal motions. Anisotropic refinement of hydrogen thermal motions with HAR was feasible only in some cases, and isotropically refined hydrogen thermal motions were in similar agreement with neutron values whether obtained with HAR or with the IAM.

Influence of modelling disorder on Hirshfeld atom refinement results of an organo-gold(I) compound

Details of the validation of disorder modelling with Hirshfeld atom refinement (HAR) for a previously investigated organo-gold(I) compound are presented here. The impact of refining disorder on HAR results is discussed using an analysis of the differences of dynamic structure factors. These dynamic structure factor differences are calculated from thermally smeared quantum mechanical electron densities based on wavefunctions that include or exclude electron correlation and relativistic effects. When disorder is modelled, the electron densities stem from a weighted superposition of two (or more) different conformers. Here this is shown to impact the relative importance of electron correlation and relativistic effect estimates expressed by the structure factor magnitudes. The role of disorder modelling is also compared with the effect of the treatment of hydrogen anisotropic displacement parameter (ADP) values and atomic anharmonicity of the gold atom. The analysis of ADP values of gold and disordered carbon atoms showed that the effect of disorder significantly altered carbon ADP values and did not influence those of the gold atom.

2,3,5-Tri-O-benzyl-d-xylofuranose

The synthesis and crystallization of 2,3,5-tri-O-benzyl-d-xylofuranose permitted us to isolate the alpha anomer with a small contamination of the beta form (ca 10%), whose first crystallographic structure obtained in the P212121 space group was determined at 100 K up to a resolution of sin θmax/λ = 0.71 Å−1 and refined to an R1 value of 0.0171 with a Hirshfeld atom refinement (HAR) approach.

X-ray constrained wavefunctions based on Hirshfeld atoms. II. Reproducibility of electron densities in crystals of α-oxalic acid dihydrate

The Hirshfeld atom-based X-ray constrained wavefunction fitting (HA-XCW) procedure is tested for its reproducibility, and the information content of the fitted wavefunction is critically assessed. Fourteen different α-oxalic acid dihydrate data sets are used for this purpose, and the first joint fitting to 12 of these data sets is reported. There are systematic features in the electron density obtained from all data sets which agree with higher level benchmark calculations, but there are also many other strong systematic features which disagree with the reference calculations, most notably those associated with the electron density near the nuclei. To enhance reproducibility, three new protocols are described and tested to address the halting problem of XCW fitting, namely: an empirical power-function method, which is useful for estimating the accuracy of the structure factor uncertainties; an asymptotic extrapolation method based on ideas from density functional theory; and a `conservative method' whereby the smallest value of the regularization parameter is chosen from a series of data sets, or subsets.

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.

Fragmentation and transferability in Hirshfeld atom refinement

Hirshfeld atom refinement (HAR) is one of the most effective methods for obtaining accurate structural parameters for hydrogen atoms from X-ray diffraction data. Unfortunately, it is also relatively computationally expensive, especially for larger molecules due to wavefunction calculations. Here, a fragmentation approach has been tested as a remedy for this problem. It gives an order of magnitude improvement in computation time for larger organic systems and is a few times faster for metal-organic systems at the cost of only minor differences in the calculated structural parameters when compared with the original HAR calculations. Fragmentation was also applied to polymeric and disordered systems where it provides a natural solution to problems that arise when HAR is applied. The concept of fragmentation is closely related to the transferable aspherical atom model (TAAM) and allows insight into possible ways to improve TAAM. Hybrid approaches combining fragmentation with the transfer of atomic densities between chemically similar atoms have been tested. An efficient handling of intermolecular interactions was also introduced for calculations involving fragmentation. When applied in fragHAR (a fragmentation approach for polypeptides) as a replacement for the original approach, it allowed for more efficient calculations. All of the calculations were performed with a locally modified version of Olex2 combined with a development version of discamb2tsc and ORCA. Care was taken to efficiently use the power of multicore processors by simple implementation of load-balancing, which was found to be very important for lowering computational time.

Hirshfeld atom refinement based on projector augmented wave densities with periodic boundary conditions

Hirshfeld atom refinement (HAR) is an X-ray diffraction refinement method that, in numerous publications, has been shown to give H-atom bond lengths in close agreement with neutron diffraction derived values. Presented here is a first evaluation of an approach using densities derived from projector augmented wave (PAW) densities with three-dimensional periodic boundary conditions for HAR. The results show an improvement over refinements that neglect the crystal environment or treat it classically, while being on a par with non-periodic approximations for treating the solid-state environment quantum mechanically. A suite of functionals were evaluated for this purpose, showing that the SCAN and revSCAN functionals are most suited to these types of calculation.

Crystal structure and Hirshfeld surface analysis of (S)-N-methyl-1-phenylethan-1-aminium chloride

Ammonium chlorides, such as the title compound (S)-N-methyl-1-phenyl­ethan-1-amnonium chloride (1), usually represent by-products in amination processes of chloro­silanes. Hirshfeld surface analysis and Hirshfeld atom refinement (HAR) were performed to obtain detailed information about the crystal packing and the exact position of the hydrogen atoms of compound 1.

The title compound C₉H₁₄N⁺·Cl⁻, (1), can be synthesized starting from (S)-N-methyl-1-phenyl­ethan-1-amine (2). Compound 2 upon addition of HCl·Et₂O leads to crystallization of compound 1 as colorless blocks. The configuration of compound 1 is stable as well as preserved in space group P2₁2₁2₁. Ammonium chlorides, like the title compound, are often observed as undesirable by-products in amino­silylation of chloro­silanes. Additionally, these by-products are usually soluble in selected organic solvents, which require difficult separation steps. Therefore, detailed studies on structural features and inter­molecular inter­actions performed by Hirshfeld atom refinement (HAR) using NoSpherA2 [Kleemiss et al. (2021 ▸). Chem. Sci.12, 1675–1692] and Hirshfeld surface analysis were used to address structural issues on that separation problem.

Insights into Proton Dynamics in a Photofunctional Salt-Cocrystal Continuum: Single-Crystal X-ray, Neutron Diffraction, and Hirshfeld Atom Refinement

X-ray diffraction, neutron diffraction, and theoretical calculations were used to investigate the relationship between the optical properties and degree of protonation in acid-base complexes. We prepared five acid-base complexes by using a pyridine-modified pyrrolopyrrole derivative and salicylic acid. Two of the prepared acid-base complexes were polymorphs of guest-free crystals with green emission; the other three were guest-inclusion crystals with yellow emission containing CH₂ Cl₂ , CH₂ Br₂ , or C₂ H₄ Cl₂ . The presence or absence of guests caused the emission to change color, altering the hydrogen bond strength between the acid-base complexes. Accurate N⋅⋅⋅H distances between the pyridyl moiety and the carboxy group over the temperature range 123 to 273 K were 1.40 Å for the guest-free crystals and 1.25 Å for the guest-inclusion crystals. Our findings contribute to a better understanding of the complex relationship between photofunction and proton dynamics in acid-base complexes.

H-Atom Assignment and Sb-O Bonding of [Mes3SbOH][O3SPh] Confirmed by Neutron Diffraction, Multipole Modeling, and Hirshfeld Atom Refinement

Neutron wavelength-resolved Laue diffraction experiments permit accurate refinement of the H-atom positions and anisotropic displacement parameters of [Mes₃SbOH][O₃SPh]. A multipole-based charge density refinement and a topological analysis of the refined electron density were also performed. Hirshfeld atom refinement (HAR) recovers the neutron-determined H-atom parameters, and the quantum-mechanical electron density used in HAR recovers the electron density topology from the refined multipole model. These results confirm that [Mes₃SbOH][O₃SPh] does indeed feature a hydroxystibonium cation with a nominal Sb-O single bond and not a stibine oxide with an Sb=O/Sb⁺-O^- bond.

Vanishing of the atomic form factor derivatives in non-spherical structural refinement - a key approximation scrutinized in the case of Hirshfeld atom refinement

When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-spherical? The assumption that this particular term is very close to zero is generally made in non-spherical refinements (for example, implementations of Hirshfeld atom refinement or transferable aspherical atom models), unless the form factors are refinable parameters (for example multipole modelling). To evaluate this general approximation for one specific method, a numerical differentiation was implemented within the NoSpherA2 framework to calculate the derivatives of the structure factors in a Hirshfeld atom refinement directly as accurately as possible, thus bypassing the approximation altogether. Comparing wR₂ factors and atomic parameters, along with their uncertainties from the approximate and numerically differentiating refinements, it turns out that the impact of this approximation on the final crystallographic model is indeed negligible.

SHG in a centrosymmetric crystal - can it be possible?

The present report lists selected publications on centrosymmetric compounds that manifest second harmonic generation responses in a laser, along with a few publications that dispute the laser outcomes. Two studies provide a plausible explanation for this apparent contradiction between second-order nonlinear susceptibility and inversion symmetry: the crystals are noncentrosymmetric and are twinned by inversion. If crystal structures of SHG-active compounds are presented in centrosymmetric settings, the authors of the publications may consider stipulating that the true space group is likely to be one of the noncentrosymmetric sub-space groups.

Effect of the nO → π*C═O Interaction on the Conformational Preference of 1,3-Diketones: A Case Study of Riolozatrione Derivatives

The cyclopropane ring-opening reaction of riolozatrione, a natural product obtained from Jatropha dioica, afforded a 2,2-disubstituted 1,3-cyclohexandione displaying an alkyl methyl ether group at position 5. The conformational analysis of this product showed a high preference for the trans-diaxial conformation in both solution and solid state. Such conformation was possible from the noncovalent intramolecular n_X → π*_C═O interactions (X = an element having an unshared electron pair), allowing the determination of the interaction energies. Since the n_X → π*_C═O interactions can be regarded as additive, the energy values ranged from 4.52 to 6.51 kcal mol^-1 for each carbonyl group with a strong dependency on the interatomic distances. The rigorous analysis of the electron density in the topological theory of atoms in molecules framework clearly shows that the origin of O-C═O interactions are through the n_O → π*_C═O electron transfer mechanism. Such interactions are slightly weaker than a canonical hydrogen bond but seemingly stronger than a van der Waals interaction. This interaction must be considered as a stereoelectronic effect due the electronic transfer between the interacting groups, which are limited by their relative stereochemistry and can be represented by a bond-no bond interaction, causing the pyramidalization of the carbonyl, which is the charge acceptor group.

The Effects of Chemical Bonding at Subatomic Resolution: A Case Study on α-Boron

Similar to classical asphericity shifts, aspherical deformations of the electron density in the atomic core region can result in core asphericity shifts in refinements using a Hansen-Coppens multipolar model (HCM), especially when highly precise experimental datasets with resolutions far beyond sin(θ)/λ ≤ 1.0 Å⁻¹ are employed. These shifts are about two orders of magnitude smaller than their counterparts caused by valence shell deformations, and their underlying deformations are mainly of dipolar character for 1st row atoms. Here, we analyze the resolution dependence of core asphericity shifts in α-boron. Based on theoretical structure factors, an appropriate Extended HCM (EHCM) is developed, which is tested against experimental high-resolution (sin(θ)/λ ≤ 1.6 Å⁻¹) single-crystal diffraction data. Bond length deviations due to core asphericity shifts of α-boron in the order of 4–6·10⁻⁴ Å are small but significant at this resolution and can be effectively compensated by an EHCM, although the correlation of the additional model parameters with positional parameters prevented a free refinement of all core model parameters. For high quality, high resolution data, a proper treatment with an EHCM or other equivalent methods is therefore highly recommended.

Establishing electron diffraction in chemical crystallography

The emerging field of 3D electron diffraction (3D ED) opens new opportunities for structure determination from sub-micrometre-sized crystals. Although the foundations of this technology emerged earlier, the past decade has seen developments in cryo-electron microscopy and (X-ray) crystallography that particularly enable the widespread use of 3D ED. This Perspective describes to chemists and chemical crystallographers just how similar electron and X-ray diffraction are and discusses their complementary aspects. We wish to establish 3D ED in the broader chemistry community, such that electron crystallography becomes a common part of the analytical chemistry toolkit. With a suitable instrument at their disposal, every skilled crystallographer can quickly learn to perform structure determinations using 3D ED.

Relativistic Hirshfeld atom refinement of an organo-gold(I) compound

The main goal of this study is the validation of relativistic Hirshfeld atom refinement (HAR) as implemented in Tonto for high-resolution X-ray diffraction datasets of an organo-gold(I) compound. The influence of the relativistic effects on statistical parameters, geometries and electron density properties was analyzed and compared with the influence of electron correlation and anharmonic atomic motions. Recent work in this field has indicated the importance of relativistic effects in the static electron density distribution of organo-mercury compounds. This study confirms that differences in electron density due to relativistic effects are also of significant magnitude for organo-gold compounds. Relativistic effects dominate not only the core region of the gold atom, but also influence the electron density in the valence and bonding region, which has measurable consequences for the HAR refinement model parameters. To study the effects of anharmonic motion on the electron density distribution, dynamic electron density difference maps were constructed. Unlike relativistic and electron correlation effects, the effects of anharmonic nuclear motion are mostly observed in the core area of the gold atom.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

lamaGOET: an interface for quantum crystallography

In quantum crystallography, theoretical calculations and crystallographic refinements are closely intertwined. This means that the employed software must be able to perform both quantum-mechanical calculations and crystallographic least-squares refinements. So far, the program Tonto is the only one able to do that. The lamaGOET interface described herein deals with this issue since it interfaces dedicated quantum-chemical software (the widely used Gaussian package and the specialized ELMOdb program) with the refinement capabilities of Tonto. Three different flavours of quantum-crystallographic refinements of the dipetide glycyl-l-threonine dihydrate are presented to showcase the capabilities of lamaGOET: Hirshfeld atom refinement (HAR), HAR-ELMO, namely HAR coupled with extremely localized molecular orbitals, and X-ray constrained wavefunction fitting.

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.

Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K

The experimental electron density distribution (EDD) of 1-methyluracil (1-MUR) was obtained by single crystal X-ray diffraction (XRD) experiments at 23 K. Four different structural models fitting an extensive set of XRD data to a resolution of (sinθ/λ)max = 1.143 Å-1 are compared. Two of the models include anharmonic temperature factors, whose inclusion is supported by the Hamilton test at a 99.95% level of confidence. Positive Fourier residuals up to 0.5 eÅ-3 in magnitude were found close to the methyl group and in the region of hydrogen bonds. Residual density analysis (RDA) and molecular dynamics simulations in the solid-state demonstrate that these residuals can be likely attributed to unresolved disorder, possibly dynamical and long-range in nature. Atomic volumes and charges, molecular moments up to hexadecapoles, as well as maps of the molecular electrostatic potential were obtained from distributed multipole analysis of the EDD. The derived electrostatic properties neither depend on the details of the multipole model, nor are significantly affected by the explicit inclusion of anharmonicity in the least-squares model. The distribution of atomic charges in 1-MUR is not affected by the crystal environment in a significant way. The quality of experimental findings is discussed in light of in-crystal and gas-phase quantum simulations.

A new family of decanuclear Ln7Cr3 clusters exhibiting a magnetocaloric effect

Two dimeric Ln–Cr clusters with formula {Ln(H₂O)₈[Ln₆Cr₃(L)₆(CH₃COO)₆(μ₃-OH)₁₂(H₂O)₁₂]}·(ClO₄)₆·xH₂O (Ln = Gd, x = 35 for 1 and Ln = Dy, x = 45 for 2, HL = 2-pyrazinecarboxylic acid) were obtained by a ligand-controlled hydrolytic method with a mixed ligand system (2-pyrazinecarboxylic acid and acetate). Single crystal structure analysis showed that two trigonal bipyramids of [Gd₃Cr₂(μ₃-OH)₆]⁹⁺ worked as building blocks in constructing the metal-oxo cluster core of [Gd₆Cr₃(μ₃-OH)₁₂]¹⁵⁺ by sharing a common top – a Cr³⁺ ion. Additionally, compound 1 forms a three-dimensional framework with a one-dimensional nanopore channel along the a-axis through a hydrogen-bond interaction between the cationic cluster core and the free mononuclear cation [Gd(H₂O)₈]³⁺ and the π-bond interactions of the pyrazine groups on the two cationic cluster cores. Magnetic calculations indicated a weak ferromagnetic coupling interaction for Gd⋯Gd and Gd⋯Cr in compound 1, with its magnetic entropy change (−ΔS_m) reaching 21.1 J kg⁻¹ K⁻¹ at 5 K, 7 T, while compound 2 displayed an obvious frequency-dependency at H_dc = 2000 Oe.

Two decanuclear Ln–Cr clusters Ln₇Cr₃ were obtained, which formed a three-dimensional framework with one-dimensional nanopore channel through hydrogen-bond and π-bond interactions. Gd₇Cr₃ had a magnetic entropy change of 21.1 J kg⁻¹ K⁻¹ at 5 K, 7 T.

Towards accurate and precise positions of hydrogen atoms bonded to heavy metal atoms

A comparison of five X-ray structures of transition-metal-bound hydride complexes, successfully refined using Hirshfeld Atom Refinement (HAR) against low resolution X-ray diffraction data (including the positions and ADPs of all hydrogen atoms), with neutron structures shows that using aspherical atomic scattering factors instead of spherical ones results in systematic elongation of metal-hydrogen bonds, which in the case of the highest-quality data leads to excellent agreement of the X-ray and the neutron-derived bond lengths.

Multipole electron densities and structural parameters from synchrotron powder X-ray diffraction data obtained with a MYTHEN detector system (OHGI)

Powder X-ray diffraction has some inherent advantages over traditional single-crystal X-ray diffraction in accurately determining electron densities and structural parameters due to the lower requirements for sample crystallinity, simpler corrections and measurement simultaneity. For some simple inorganic materials, it has been shown that these advantages can compensate for disadvantages such as peak overlap and error-prone background subtraction. Although it is challenging to extend powder X-ray diffraction-based electron-density studies to organic materials with significant peak overlap, previous results using a dedicated vacuum diffractometer with a large image-plate camera (AVID) demonstrated that it can be done. However, the vacuum setup with the off-line detector system was found to prohibit a widespread use. Fast microstrip detectors, which have been employed at a number of powder diffraction beamlines, have the potential to facilitate electron-density studies. Nevertheless, no electron-density studies even for materials with slight peak overlap have been performed with microstrip detectors. One of the most critical problems has been a difference in sensitivity between microstrip channels, which substantially defines the dynamic range of a detector. Recently, a robust approach to this problem has been developed and applied to a total scattering measurement system (OHGI) with 15 MYTHEN microstrip modules. In the present study, synchrotron powder X-ray diffraction data obtained with OHGI are evaulated in terms of multipole electron densities and structural parameters (atomic positions and displacement parameters). These results show that, even without a dedicated setup and perfect samples, electron-density modelling can be carried out on high-quality powder X-ray diffraction data. However, it was also found that the required prior information about the sample prohibits widespread use of the method. With the presently obtainable data quality, electron densities of molecular crystals in general are not reliably obtained from powder data, but it is an excellent, possibly superior, alternative to single-crystal measurements for small-unit-cell inorganic solids. If aspherical atomic scattering factors can be obtained from other means (multipole databases, theoretical calculations), then atomic positions (including for hydrogen) and anisotropic atomic displacement parameters (non-hydrogen atoms) of excellent accuracy can be refined from synchrotron powder X-ray diffraction data on organic crystals.

Climbing Jacob's Ladder of Structural Refinement: Introduction of a Localized Molecular Orbital-Based Embedding for Accurate X-ray Determinations of Hydrogen Atom Positions

The positions of hydrogen atoms in molecules are fundamental in many aspects of chemistry. Nevertheless, most molecular structures are obtained from refinements of X-ray data exploiting the independent atom model (IAM), which uses spherical atomic densities and provides bond lengths involving hydrogen atoms that are too short compared to the neutron reference values. To overcome the IAM shortcomings, the wave function-based Hirshfeld atom refinement (HAR) method has been recently proposed, emerging as a promising strategy able to give element-hydrogen bond distances in excellent agreement with the neutron ones in terms of accuracy and precision. In this Letter, we propose a significant improvement of HAR based on the idea of describing the crystal environment explicitly in the underlying wave function calculation through a quantum mechanical embedding strategy that exploits extremely localized molecular orbitals. Test-bed refinements on a crystal structure characterized by strong intermolecular interactions are also discussed.

Naphthalen-1-ylmethanol

Apart from the OH group, the molecule of the title compound, C11H10O, is almost planar with all carbon atoms located within 0.03 Å of their mean plane. In the crystal, the molecules are linked by O—H...O hydrogen bonds, generating infinite chains running parallel to the [100] direction.

A new look at two polymorphic crystal structures of dibenzoylmethane: relationship between the crystal packing and the hydrogen atom position revealed by quantum chemistry and quantum crystallography methods

Chalcones, including dibenzoylmethane, are an important subgroup of natural polyphenolic compounds that exhibit a wide spectrum of pharmacological and industrial applications. Dibenzoylmethane was isolated from Hottonia palustris L. (Primulaceae). The compound was crystallized in two polymorphic forms: in monoclinic space group P2₁/c and orthorhombic space group Pbca. Crystal structures of the polymorphs were solved and refined against diffraction data measured at 100 and 293 K. In both crystal structures, the chalcone occurs in its keto-enol tautomeric form with the hydroxyl H atom mutually bound by two oxygen atoms rather than covalently attached to a particular oxygen atom. To explain this phenomenon in more detail, density functional theory and quantum theory of atoms in molecules based quantum chemistry calculations were applied. Additionally, high-resolution experimental data of very high quality measured for the monoclinic and orthorhombic crystals at 100 K allowed the engagement of the quantum crystallography method, based on Hirshfeld atom refinement, to determine the position of each individual H atom. It is suggested that the presence of the particular tautomeric form of dibenzoylmethane with a centred H atom position results from the π-stacking interaction between the phenyl ring and the malondialdehyde quasi-ring causes delocalization of the electron density in the latter.

Accurate crystal structures and chemical properties from NoSpherA2

The relationship between the structure and the properties of a drug or material is a key concept of chemistry. Knowledge of the three-dimensional structure is considered to be of such importance that almost every report of a new chemical compound is accompanied by an X-ray crystal structure – at least since the 1970s when diffraction equipment became widely available. Crystallographic software of that time was restricted to very limited computing power, and therefore drastic simplifications had to be made. It is these simplifications that make the determination of the correct structure, especially when it comes to hydrogen atoms, virtually impossible. We have devised a robust and fast system where modern chemical structure models replace the old assumptions, leading to correct structures from the model refinement against standard in-house diffraction data using no more than widely available software and desktop computing power. We call this system NoSpherA2 (Non-Spherical Atoms in Olex2). We explain the theoretical background of this technique and demonstrate the far-reaching effects that the improved structure quality that is now routinely available can have on the interpretation of chemical problems exemplified by five selected examples.

NoSpherA2 brings quantum crystallography to routine structure determination and to the analysis of chemical properties for any class of materials.

Hirshfeld atom like refinement with alternative electron density partitions

Hirshfeld atom refinement is one of the most successful methods for the accurate determination of structural parameters for hydrogen atoms from X-ray diffraction data. This work introduces a generalization of the method [generalized atom refinement (GAR)], consisting of the application of various methods of partitioning electron density into atomic contributions. These were tested on three organic structures using the following partitions: Hirshfeld, iterative Hirshfeld, iterative stockholder, minimal basis iterative stockholder and Becke. The effects of partition choice were also compared with those caused by other factors such as quantum chemical methodology, basis set, representation of the crystal field and a combination of these factors. The differences between the partitions were small in terms of R factor (e.g. much smaller than for refinements with different quantum chemistry methods, i.e. Hartree-Fock and coupled cluster) and therefore no single partition was clearly the best in terms of experimental data reconstruction. In the case of structural parameters the differences between the partitions are comparable to those related to the choice of other factors. We have observed the systematic effects of the partition choice on bond lengths and ADP values of polar hydrogen atoms. The bond lengths were also systematically influenced by the choice of electron density calculation methodology. This suggests that GAR-derived structural parameters could be systematically improved by selecting an optimal combination of the partition and quantum chemistry method. The results of the refinements were compared with those of neutron diffraction experiments. This allowed a selection of the most promising partition methods for further optimization of GAR settings, namely the Hirshfeld, iterative stockholder and minimal basis iterative stockholder.

Crystal structures, Hirshfeld atom refinements and Hirshfeld surface analyses of tris-(4,5-di-hydro-furan-2-yl)methyl-silane and tris-(4,5-di-hydro-furan-2-yl)phenyl-silane

The title compounds, C13H18O3Si (1) and C18H20O3Si (2), represent functional-izable di-hydro-furan-ylsilanes, which permit substitution by a variety of nucleophiles. The crystal structures of 1 and 2 display weak inter-molecular C-H⋯O hydrogen-bonding inter-actions (qu-anti-fied by Hirshfeld surface analysis), leading to a two-dimensional supra-molecular network for 1 and a one-dimensional supra-molecular network for 2. The crystal structures of 1 and 2 were refined both on the basis of the independent atom model (IAM) and the Hirshfeld atom refinement (HAR) approach, and the results are comparatively discussed.

On the accuracy and precision of X-ray and neutron diffraction results as a function of resolution and the electron density model

X-ray diffraction is the main source of three-dimensional structural information. In total, more than 1.5 million crystal structures have been refined and deposited in structural databanks (PDB, CSD and ICSD) to date. Almost 99.7% of them were obtained by approximating atoms as spheres within the independent atom model (IAM) introduced over a century ago. In this study, X-ray datasets for single crystals of hydrated α-oxalic acid were refined using several alternative electron density models that abandon the crude spherical approximation: the multipole model (MM), the transferable aspherical atom model (TAAM) and the Hirshfeld atom refinement (HAR) model as a function of the resolution of X-ray data. The aspherical models (MM, TAAM, HAR) give far more accurate and precise single-crystal X-ray results than IAM, sometimes identical to results obtained from neutron diffraction and at low resolution. Hence, aspherical approaches open new routes for improving existing structural information collected over the last century.

Crystal structures of tolfenamic acid polymorphic forms I and II with precise hydrogen-atom positions for nuclear magnetic resonance studies

The structures of tolfenamic acid [TFA; 2-(3-chloro-2-methyl-anilino)benzoic acid, C14H12ClNO2] polymorph forms I and II have been redetermined [compare Andersen et al. (1989 ▸). J. Chem. Soc., Perkin Trans. 2, pp. 1443-1447] with improved precision using high-resolution X-ray diffraction data and Hirshfield atom refinement in order to better define both hydrogen-atom locations and their associated bond lengths. Covalent bond lengths to hydrogen were found to be significantly longer throughout both structures, especially for the anilino H atom, which is involved in an important intra-molecular N-H⋯O hydrogen bond to the carb-oxy-lic acid group. This hydrogen bond is shown to clearly perturb the electron density around both oxygen atoms in the latter group. The extended structures of both polymorphs feature carb-oxy-lic acid inversion dimers. These structures provide an improved foundation for nuclear magnetic resonance studies in both solution and the solid state.

A positive to negative uniaxial thermal expansion crossover in an organic benzothienobenzothiophene structure

Compound 6,6'-([1]benzothieno[3,2-b][1]benzothiophene-2,7-diyl)bis(butan-1-ol) (BTBT-C4OH) displays a continuous type 0 first-order isosymmetric phase transition at 200 K which is accompanied by a continuous change of the thermal expansion along the b axis from positive to negative. The equivalent isotropic atomic displacement parameters for all non-hydrogen atoms as well as all the eigenvalues of the anisotropic atomic displacement tensor show discontinuous behavior at the phase transition. The eigenvalues of the translational tensor in a rigid-body description of the molecule are all discontinuous at the phase transition, but the librational eigenvalues are discontinuous only in their temperature derivative. BTBT-C4OH displays a similar type of quasi-supercritical phase transition as bis(hydroxyhexyl)[1]benzothieno[3,2-b][1]benzothiophene (BTBT-C6OH), despite the difference in molecular packing and the very large difference in thermal expansion magnitudes.

Quantum Crystallography in the Last Decade: Developments and Outlooks

In this review article, we report on the recent progresses in the field of quantum crystallography that has witnessed a massive increase of production coupled with a broadening of the scope in the last decade. It is shown that the early thoughts about extracting quantum mechanical information from crystallographic experiments are becoming reality, although a century after prediction. While in the past the focus was mainly on electron density and related quantities, the attention is now shifting toward determination of wavefunction from experiments, which enables an exhaustive determination of the quantum mechanical functions and properties of a system. Nonetheless, methods based on electron density modelling have evolved and are nowadays able to reconstruct tiny polarizations of core electrons, coupling charge and spin models, or determining the quantum behaviour at extreme conditions. Far from being routine, these experimental and computational results should be regarded with special attention by scientists for the wealth of information on a system that they actually contain.

TAAM: a reliable and user friendly tool for hydrogen-atom location using routine X-ray diffraction data

Hydrogen is present in almost all of the molecules in living things. It is very reactive and forms bonds with most of the elements, terminating their valences and enhancing their chemistry. X-ray diffraction is the most common method for structure determination. It depends on scattering of X-rays from electron density, which means the single electron of hydrogen is difficult to detect. Generally, neutron diffraction data are used to determine the accurate position of hydrogen atoms. However, the requirement for good quality single crystals, costly maintenance and the limited number of neutron diffraction facilities means that these kind of results are rarely available. Here it is shown that the use of Transferable Aspherical Atom Model (TAAM) instead of Independent Atom Model (IAM) in routine structure refinement with X-ray data is another possible solution which largely improves the precision and accuracy of X-H bond lengths and makes them comparable to averaged neutron bond lengths. TAAM, built from a pseudoatom databank, was used to determine the X-H bond lengths on 75 data sets for organic molecule crystals. TAAM parametrizations available in the modified University of Buffalo Databank (UBDB) of pseudoatoms applied through the DiSCaMB software library were used. The averaged bond lengths determined by TAAM refinements with X-ray diffraction data of atomic resolution (d_min ≤ 0.83 Å) showed very good agreement with neutron data, mostly within one single sample standard deviation, much like Hirshfeld atom refinement (HAR). Atomic displacements for both hydrogen and non-hydrogen atoms obtained from the refinements systematically differed from IAM results. Overall TAAM gave better fits to experimental data of standard resolution compared to IAM. The research was accompanied with development of software aimed at providing user-friendly tools to use aspherical atom models in refinement of organic molecules at speeds comparable to routine refinements based on spherical atom model.

fragHAR: towards ab initio quantum-crystallographic X-ray structure refinement for polypeptides and proteins

The first ab initio aspherical structure refinement against experimental X-ray structure factors for polypeptides and proteins using a fragmentation approach to break up the protein into residues and solvent, thereby speeding up quantum-crystallographic Hirshfeld atom refinement (HAR) calculations, is described. It it found that the geometric and atomic displacement parameters from the new fragHAR method are essentially unchanged from a HAR on the complete unfragmented system when tested on dipeptides, tripeptides and hexapeptides. The largest changes are for the parameters describing H atoms involved in hydrogen-bond interactions, but it is shown that these discrepancies can be removed by including the interacting fragments as a single larger fragment in the fragmentation scheme. Significant speed-ups are observed for the larger systems. Using this approach, it is possible to perform a highly parallelized HAR in reasonable times for large systems. The method has been implemented in the TONTO software.

On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography

Modern methods of quantum crystallography are techniques firmly rooted in quantum chemistry and, as in many quantum chemical strategies, electron densities are expressed as two-centre expansions that involve basis functions centred on atomic nuclei. Therefore, the computation of the necessary structure factors requires the evaluation of Fourier transform integrals of basis function products. Since these functions are usually Cartesian Gaussians, in this communication it is shown that the Fourier integrals can be efficiently calculated by exploiting an extension of the Obara–Saika recurrence formulas, which are successfully used by quantum chemists in the computation of molecular integrals. Implementation and future perspectives of the technique are also discussed.

checkCIF validation ALERTS: what they mean and how to respond

Authors of a paper that includes a new crystal-structure determination are expected to not only report the structural results of inter-est and their inter-pretation, but are also expected to archive in computer-readable CIF format the experimental data on which the crystal-structure analysis is based. Additionally, an IUCr/checkCIF validation report will be required for the review of a submitted paper. Such a validation report, automatically created from the deposited CIF file, lists as ALERTS not only potential errors or unusual findings, but also suggestions for improvement along with inter-esting information on the structure at hand. Major ALERTS for issues are expected to have been acted on already before the submission for publication or discussed in the associated paper and/or commented on in the CIF file. In addition, referees, readers and users of the data should be able to make their own judgment and inter-pretation of the underlying experimental data or perform their own calculations with the archived data. All the above is consistent with the FAIR (findable, accessible, inter-operable, and reusable) initiative [Helliwell (2019 ▸). Struct. Dyn. 6, 05430]. Validation can also be helpful for less experienced authors in pointing to and avoiding of crystal-structure determination and inter-pretation pitfalls. The IUCr web-based checkCIF server provides such a validation report, based on data uploaded in CIF format. Alternatively, a locally installable checkCIF version is available to be used iteratively during the structure-determination process. ALERTS come mostly as short single-line messages. There is also a short explanation of the ALERTS available through the IUCr web server or with the locally installed PLATON/checkCIF version. This paper provides additional background information on the checkCIF procedure and additional details for a number of ALERTS along with options for how to act on them.

Fast energy minimization of the CCDC drug-subset structures by molecule-in-cluster computations allows independent structure validation and model completion

Optimizing structures with computations on clusters of molecules permits generation of structure-specific restraints for refinement and structure validation.

Two zinc coordination polymers with photochromic behaviors and photo-controlled luminescence properties

Two new coordination polymers, [Zn(3-NDI)_0.5(NDC)(DMF)]_n (1) and {[Zn_1.5(3-NDI)_0.5(BDC)_1.5]·2.5DMF}_n (2), were synthesized. Both complexes show photochromic behaviors and have obvious fluorescence quenching behaviors upon irradiation.