Yes, one can obtain better quality structures from routine X-ray data collection

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.

Aspherical atom refinements on X-ray data of diverse structures including disordered and covalent organic framework systems: a time-accuracy trade-off

Aspherical atom refinement is the key to achieving accurate structure models, displacement parameters, hydrogen-bond lengths and analysis of weak interactions, amongst other examples. There are various quantum crystallographic methods to perform aspherical atom refinement, including Hirshfeld atom refinement (HAR) and transferable aspherical atom model (TAAM) refinement. Both HAR and TAAM have their limitations and advantages, the former being more accurate and the latter being faster. With the advent of non-spherical atoms in Olex2 (NoSpherA2), it is now possible to overcome some limitations, like treating disorder, twinning and network structures, in aspherical refinements using HAR, TAAM or both together. TAAM refinement in NoSpherA2 showed significant improvement in refinement statistics compared with independent atom model (IAM) refinements on a diverse set of X-ray diffraction data. The sensitivity of TAAM towards poor data quality and disorder was observed in terms of higher refinement statistics for such structures. A comparison of IAM with TAAM and HAR in NoSpherA2 indicated that the time taken by TAAM refinements was of the same order of magnitude as that taken by IAM, while in HAR the time taken using a minimal basis set was 50 times higher than for IAM and rapidly increased with increasing size of the basis sets used. The displacement parameters for hydrogen and non-hydrogen atoms were very similar in both HAR and TAAM refinements. The hydrogen-bond lengths were slightly closer to neutron reference values in the case of HAR with higher basis sets than in TAAM. To benefit from the advantages of each method, a new hybrid refinement approach has been introduced, allowing a combination of IAM, HAR and TAAM in one structure refinement. Refinement of coordination complexes involving metal-organic compounds and network structures such as covalent organic frameworks and metal-organic frameworks is now possible in a hybrid mode such as IAM-TAAM or HAR-TAAM, where the metal atoms are treated via either the IAM or HAR method and the organic part via TAAM, thus reducing the computational costs without compromising the accuracy. Formal charges on the metal and ligand can also be introduced in hybrid-mode refinement.

Dominant changes in centre Fe atom of decamethyl-ferrocene from ferrocene in methylation

Staggered decamethyl-ferrocene (*Fc) becomes the lower energy conformer at low temperature, whereas the eclipsed conformer of ferrocene (Fc) is more stable. The powerful infrared (IR) spectroscopy which has remarkably provided signatures of ferrocene (Fc) in eclipsed and staggered conformers recently is employed to investigate methylation of Fc. The most significant consequences of the full methylation of Fc in the IR spectra are the blue shift of the band at ~ 800 cm−1 in Fc to ~ 1500 cm−1 in *Fc, and the enhancement of the C–H stretch band at ~ 3200 cm−1 region in *Fc. Further analysis reveals large impact of Fc methylation on core electron energies of the centre Fe atom (1s22s22p63s23p6). The Fe core electron energy changes can be as large as ~ 10 kcal mol−1 and are directional—the Fe 2pz and 3pz orbitals along the *Cp–Fe–*Cp axis (Cp centroids, vertical) change more strongly than other Fe core electrons in px and py orbitals. The directional inner shell energy changes are evidenced by larger inner shell reorganization energy. Energy decomposition analysis (EDA) indicates that methyl groups in *Fc apparently change the physical energy components with respect to Fc. The large steric energy of *Fc evidences that the closest hydrogens on adjacent methyl groups of the same *Cp ring in crystal structure are 0.2–0.4 Å closer than the hydrogens on nearest-neighbour methyl groups on opposing rings in *Fc. A significant increase in Pauli repulsive energy contributes to the large repulsive steric energy in *Fc.

Crystal structure of 2-{[5-amino-1-(phenyl-sulfon-yl)-1H-pyrazol-3-yl]-oxy}-1-(4-methyl-phen-yl)ethan-1-one

In the title compound, C18H17N3O4S, the pyrazole ring is planar, with the sulfur atom lying 0.558 (1) Å out of the ring plane. The NH2 group is involved in an intra-molecular hydrogen bond to a sulfonyl oxygen atom; its other hydrogen atom forms an asymmetric three-centre hydrogen bond to the two oxygen atoms of the -O-CH2-C=O- grouping, via the 21 screw axis, forming a ribbon structure parallel to the b axis. Translationally adjacent, coplanar ribbons form a layer parallel to (10).

On modelling disordered crystal structures through restraints from molecule-in-cluster computations, and distinguishing static and dynamic disorder

Distinguishing disorder into static and dynamic based on multi-temperature X-ray or neutron diffraction experiments is the current state of the art, but is only descriptive, not predictive. Here, several disordered structures are revisited from the Cambridge Crystallographic Data Center 'drug subset', the Cambridge Structural Database and own earlier work, where experimental intensities of Bragg diffraction data were available. Using the molecule-in-cluster approach, structures with distinguishable conformations were optimized separately, as extracted from available or generated disorder models of the respective disordered crystal structures. Re-combining these 'archetype structures' by restraining positional and constraining displacement parameters for conventional least-squares refinement, based on the optimized geometries, then often achieves a superior fit to the experimental diffraction data compared with relying on experimental information alone. It also simplifies and standardizes disorder refinement. Ten example structures were analysed. It is observed that energy differences between separate disorder conformations are usually within a small energy window of RT (T = crystallization temperature). Further computations classify disorder into static or dynamic, using single experiments performed at one single temperature, and this was achieved for propionamide.

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.

Towards triptycene functionalization and triptycene-linked porphyrin arrays

Herein, 9,10-diethynyltriptycene is investigated for its use as a rigid isolating unit in the synthesis of multichromophoric arrays. Sonogashira cross-coupling conditions are utilized to attach various porphyrins and boron dipyrromethenes (BODIPYs) to the triptycene scaffold. While there are previous examples of triptycene porphyrin complexes, this work reports the first example of a linearly connected porphyrin dimer, linked through the bridgehead carbons of triptycene. Symmetric and unsymmetric examples of these complexes are demonstrated and single crystal X-ray analysis of an unsymmetrically substituted porphyrin dimer highlights the evident linearity in these systems. Moreover, initial UV-vis and fluorescence studies show the promise of triptycene as a linker for electron transfer studies, showcasing its isolating nature.

Interplay between packing, dimer interaction energy and morphology in a series of tricyclic imide crystals

Crystal morphology is a very important feature in many industrial applications. Tricyclic imides, derivatives of 10-oxa-4-azatricyclo[5.2.1.0^2,6]dec-8-ene-3,5-dione with differing small hydrophobic groups (Me, Et), were studied and grouped based on Etter's rule. Using experimental X-ray studies, dimer energy calculations, framework analysis and periodic DFT-D calculations, it is shown that knowledge of the hydrogen-bond pattern can be used to determine the final crystal shape. Molecules forming a ring hydrogen-bond motif crystallize as plate crystals with the {100} facet as the slowest growing, whereas those molecules forming an infinite hydrogen-bond motif in the crystal structure crystallize as needles with the {101} facet having the largest surface area.

The borderline: exploring the structural landscape of triptycene in cocrystallization with ferrocene

When the effective packing of triptycene (TripH)–ferrocene chain oligomers in their cocrystal could not be achieved, we reached a borderline at the structural landscape of TripH, where the packing of TripH molecules reproduces the pattern in the native TripH crystal.

The role of multiple observations in small-molecule single-crystal service X-ray structure determination

In order to gain a better understanding of how to improve the quality of small-molecule single-crystal X-ray diffraction data achievable in a finite time, a study was carried out to investigate the effect of varying the multiplicity, acquisition time, detector binning, maximum resolution and completeness. The results suggest that, unless there are strong arguments for a different strategy, a good routine procedure might be to optimize the conditions necessary to get the best data from single scans, and then choose a multiplicity of observations (MoO) to utilize the available time fully. Different strategies may be required if the crystal is highly absorbing, is larger than the incident beam, is enclosed in a capillary tube or is unusual in some other way. The signal-to-noise ratio should be used with care, as collecting data for longer or at higher multiplicity appears to give a systematic underestimate of the intensity uncertainties. Further, the results demonstrate that including poor-quality data in a refinement may degrade the result and, in the general case, the accidental omission of reflections has a very small impact on the refinement as long as they are omitted at random. Systematic omission of reflections needs a convincing procedural justification.

X-ray diffraction data as a source of the vibrational free-energy contribution in polymorphic systems

In this contribution we attempt to answer a general question: can X-ray diffraction data combined with theoretical computations be a source of information about the thermodynamic properties of a given system? Newly collected sets of high-quality multi-temperature single-crystal X-ray diffraction data and complementary periodic DFT calculations of vibrational frequencies and normal mode vectors at the Γ point on the yellow and white polymorphs of di-methyl 3,6-di-chloro-2,5-di-hydroxy-terephthalate are combined using two different approaches, aiming to obtain thermodynamic properties for the two compounds. The first approach uses low-frequency normal modes extracted from multi-temperature X-ray diffraction data (normal coordinate analysis), while the other uses DFT-calculated low-frequency normal mode in the refinement of the same data (normal mode refinement). Thermodynamic data from the literature [Yang et al. (1989), Acta Cryst. B45, 312-323] and new periodic ab initio DFT supercell calculations are used as a reference point. Both approaches tested in this work capture the most essential features of the systems: the polymorphs are enantiotropically related, with the yellow form being the thermodynamically stable system at low temperature, and the white form at higher temperatures. However, the inferred phase transition temperature varies between different approaches. Thanks to the application of unconventional methods of X-ray data refinement and analysis, it was additionally found that, in the case of the yellow polymorph, anharmonicity is an important issue. By discussing contributions from low- and high-frequency modes to the vibrational entropy and enthalpy, the importance of high-frequency modes is highlighted. The analysis shows that larger anisotropic displacement parameters are not always related to the polymorph with the higher vibrational entropy contribution.

The upcoming subatomic resolution revolution

Subatomic resolution macromolecular crystallography has been revealing the most fascinating details of macromolecular structures for many years. This most extreme form of macromolecular crystallography is going through rapid changes. A new generation of superbrilliant X-ray sources and detectors is facilitating the rapid acquisition of high-quality datasets. Equally important, a new breed of methods and highly integrated advanced computational tools for structure refinement and analysis is poised to change the way we use subatomic resolution data and reposition high-resolution macromolecular crystallography in medicinal chemistry studies. Subatomic resolution macromolecular crystallography may soon be a routine source of detailed molecular information besides precise geometries, including binding energies and other chemical descriptors, opening new possibilities of application.

Nonconjugated Hydrocarbons as Rigid-Linear Motifs: Isosteres for Material Sciences and Bioorganic and Medicinal Chemistry

Nonconjugated hydrocarbons, like bicyclo[1.1.1]pentane, bicyclo[2.2.2]octane, triptycene, and cubane are a unique class of rigid linkers. Due to their similarity in size and shape they are useful mimics of classic benzene moieties in drugs, so-called bioisosteres. Moreover, they also fulfill an important role in material sciences as linear linkers, in order to arrange various functionalities in a defined spatial manner. In this Review article, recent developments and usages of these special, rectilinear systems are discussed. Furthermore, we focus on covalently linked, nonconjugated linear arrangements and discuss the physical and chemical properties and differences of individual linkers, as well as their application in material and medicinal sciences.

A new tool for validating theoretically derived anisotropic displacement parameters with experiment: directionality of prolate displacement ellipsoids

How well do anisotropic displacement parameters from theory match experiment? The orientation of prolate ellipsoids contributes to the answer!

Doxycycline hydrate and doxycycline hydrochloride dihydrate – crystal structure and charge density analysis

High-resolution low-temperature X-ray diffraction experiments for doxycycline monohydrate and hydrochloride dihydrate have been performed. Translation-Libration-Screw (TLS) analysis for both crystal forms as well as the data from neutron diffraction experiment for hydrochloride combined with the Hansen-Coppens formalism resulted in precise charge density distribution models for both the zwitterionic monohydrate and a protonated hydrochloride crystal forms. Their detailed topological analysis suggested that the electron structure of doxycycline’s amide moiety undergoes significant changes during protonation due to formation of a very strong resonance-assisted hydrogen bond. A notably increased participation of amide nitrogen atom and hydrogen-accepting oxygen atom in the resonance upon doxycycline protonation was observed. A comparison of TLS- and neutron data-derived hydrogen parameters confirmed the experimental neutron data to be vital for proper description of intra- and inter-molecular interactions in this compound. Finally, calculated lattice and interaction energies quantified repulsive Dox-Dox interactions in the protonated crystal form of the antibiotic, relating with a good solubility of doxycycline hydrochloride relative to its hydrate.

Predicting anisotropic thermal displacements for hydrogens from solid-state NMR: a study on hydrogen bonding in polymorphs of palmitic acid

The hydrogen-bonding environments at the COOH moiety in eight polycrystalline polymorphs of palmitic acid are explored using solid-state NMR. Although most phases have no previously reported crystal structure, measured 13C chemical shift tensors for COOH moieties, combined with DFT modeling establish that all phases crystallize with a cyclic dimer (R22(8)) hydrogen bonding arrangement. Phases A2, Bm and Em have localized OH hydrogens while phase C has a dynamically disordered OH hydrogen. The phase designated As is a mix of five forms, including 27.4% of Bm and four novel phases not fully characterized here due to insufficient sample mass. For phases A2, Bm, Em, and C the anisotropic uncertainties in the COOH hydrogen atom positions are established using a Monte Carlo sampling scheme. Sampled points are retained or rejected at the ±1σ level based upon agreement of DFT computed 13COOH tensors with experimental values. The collection of retained hydrogen positions bear a remarkable resemblance to the anisotropic displacement parameters (i.e. thermal ellipsoids) from diffraction studies. We posit that this similarity is no mere coincidence and that the two are fundamentally related. The volumes of NMR-derived anisotropic displacement ellipsoids for phases with localized OH hydrogens are 4.1 times smaller than those derived from single crystal X-ray diffraction and 1.8 times smaller than the volume of benchmark single crystal neutron diffraction values.

DiSCaMB: a software library for aspherical atom model X-ray scattering factor calculations with CPUs and GPUs

It has been recently established that the accuracy of structural parameters from X-ray refinement of crystal structures can be improved by using a bank of aspherical pseudoatoms instead of the classical spherical model of atomic form factors. This comes, however, at the cost of increased complexity of the underlying calculations. In order to facilitate the adoption of this more advanced electron density model by the broader community of crystallographers, a new software implementation called DiSCaMB, 'densities in structural chemistry and molecular biology', has been developed. It addresses the challenge of providing for high performance on modern computing architectures. With parallelization options for both multi-core processors and graphics processing units (using CUDA), the library features calculation of X-ray scattering factors and their derivatives with respect to structural parameters, gives access to intermediate steps of the scattering factor calculations (thus allowing for experimentation with modifications of the underlying electron density model), and provides tools for basic structural crystallographic operations. Permissively (MIT) licensed, DiSCaMB is an open-source C++ library that can be embedded in both academic and commercial tools for X-ray structure refinement.

Does the compound hexaaqua-zinc(ii)bis(hydrogensulfate)dihydrate, [Zn(H2O)6](HSO4·H2O)2, really exist?

A careful examination of the crystal structure of the hydrogensulfate compound [Zn(H₂O)₆](HSO₄·H₂O)₂ reported in this journal shows that the sample used for X-ray diffraction was almost certainly the Tutton salt [Zn(H₂O)₆](SO₄·NH₄)₂, isoelectronic with the former elusive compound (F₀₀₀ = 416, P2₁/c space group). Indeed, any chemistry involving ammonium and sulfate moieties in an aqueous medium containing a transition metal cation should afford the corresponding Tutton salt as a by-product. We redetermined the structure of [Zn(H₂O)₆](SO₄·NH₄)₂, on the basis of high-resolution X-ray data (d = 0.47 Å), with the purpose of illustrating that at such resolution, difference Fourier maps may be used to unambiguously differentiate between a sulfate and a hydrogensulfate ion. On the other hand, regardless of the data resolution, geometrical considerations may be enough to avoid misassignment of such small ions in crystal structures, providing that some knowledge about the average shape of these ions is available from curated crystallographic databases.

The structure published for the compound [Zn(H₂O)₆](HSO₄·H₂O)₂ is re-interpreted as being the Tutton double salt [Zn(H₂O)₆](SO₄·NH₄)₂, known for a long time.

Using invariom modelling to distinguish correct and incorrect central atoms in `duplicate structures' with neighbouring 3d elements

Modelling coordination compounds has been shown to be feasible using the invariom method; for the best fit to a given set of diffraction data, additional steps other than using lookup tables of scattering factors need to be carried out. Here such procedures are applied to a number of `duplicate structures', where structures of two or more supposedly different coordination complexes with identical ligand environments, but with different 3d metal ions, were published. However, only one metal atom can be plausibly correct in these structures, and other spectroscopic data are unavailable. Using aspherical scattering factors, a structure can be identified as correct from the deposited Bragg intensities alone and modelling only the ligand environment often suffices to make this distinction. This is not possible in classical refinements using the independent atom model. Quantum-chemical computations of the better model obtained after aspherical-atom refinement further confirm the assignment of the element in the respective figures of merit.

Invariom-model refinement and Hirshfeld surface analysis of well-ordered solvent-free dibenzo-21-crown-7

Crown ethers and their supramolecular derivatives are well-known chelators and scavengers for a variety of cations, most notably heavier alkali and alkaline-earth ions. Although they are widely used in synthetic chemistry, available crystal structures of uncoordinated and solvent-free crown ethers regularly suffer from disorder. In this study, we present the X-ray crystal structure analysis of well-ordered solvent-free crystals of dibenzo-21-crown-7 (systematic name: dibenzo[b,k]-1,4,7,10,13,16,19-heptaoxacycloheneicosa-2,11-diene, C₂₂H₂₈O₇). Because of the quality of the crystal and diffraction data, we have chosen invarioms, in addition to standard independent spherical atoms, for modelling and briefly discuss the different refinement results. The electrostatic potential, which is directly deducible from the invariom model, and the Hirshfeld surface are analysed and complemented with interaction-energy computations to characterize intermolecular contacts. The boat-like molecules stack along the a axis and are arranged as dimers of chains, which assemble as rows to form a three-dimensional structure. Dispersive C-H...H-C and C-H...π interactions dominate, but nonclassical hydrogen bonds are present and reflect the overall rather weak electrostatic influence. A fingerprint plot of the Hirshfeld surface summarizes and visualizes the intermolecular interactions. The insight gained into the crystal structure of dibenzo-21-crown-7 not only demonstrates the power of invariom refinement, Hirshfeld surface analysis and interaction-energy computation, but also hints at favourable conditions for crystallizing solvent-free crown ethers.

Transferable Aspherical Atom Modeling of Electron Density in Highly Symmetric Crystals: A Case Study of Alkali-Metal Nitrates

A comparative electron density study (from X-ray diffraction and periodic quantum chemistry) of sodium and potassium nitrates is performed to test the performance of a transferrable aspherical atom model, which is based on the invarioms, to describe chemical bonding features of ions occurring in sites of different symmetry typical of inorganic salts and in different crystal environments. Relying on tabulated entries for the isolated ions (although tailor-made to account for different site symmetries), it takes the same time to employ as the spherical atom model routinely used in X-ray diffraction studies but provides an electron density distribution that faithfully reveals all the interionic interactions-even the weakest ones (such as between the nitrate anions or a K···N interaction found in the metastable form of KNO₃) yet important for properties of inorganic materials-as if obtained from high-resolution X-ray diffraction data.

Invariom modeling of disordered structures: case studies on a dipeptide, an amino acid, and cefaclor, a cephalosporin antibiotic

Routines to facilitate the treatment of disorder in invariom modeling have been implemented in the open-source program MolecoolQt, a visualization program for charge-density work, and InvariomTool, a pre-processor program. Two published structures of an amino acid and a dipeptide and the new structure of cefaclor, a cephalosporin antibiotic, provide examples with increasing amounts of disorder, which can now be successfully modeled with invarioms. Like for ordered structures, these non-spherical scattering factors predicted by density functional theory significantly improve the structural model (figures of merit and standard deviations) also in these cases. Furthermore, they allow rapid calculation and comparison of the electrostatic potential and the molecular dipole moment for the different conformers present in the crystal structures.

Challenges in the structural science of materials

Articles published recently in IUCrJ continue to exemplify the developments and challenges in the structural science of materials.

Transferable aspherical atom model refinement of protein and DNA structures against ultrahigh-resolution X-ray data

In contrast to the independent-atom model (IAM), in which all atoms are assumed to be spherical and neutral, the transferable aspherical atom model (TAAM) takes into account the deformed valence charge density resulting from chemical bond formation and the presence of lone electron pairs. Both models can be used to refine small and large molecules, e.g. proteins and nucleic acids, against ultrahigh-resolution X-ray diffraction data. The University at Buffalo theoretical databank of aspherical pseudo-atoms has been used in the refinement of an oligopeptide, of Z-DNA hexamer and dodecamer duplexes, and of bovine trypsin. The application of the TAAM to these data improves the quality of the electron-density maps and the visibility of H atoms. It also lowers the conventional R factors and improves the atomic displacement parameters and the results of the Hirshfeld rigid-bond test. An additional advantage is that the transferred charge density allows the estimation of Coulombic interaction energy and electrostatic potential.

Anisotropic thermal motion in transition-metal carbonyls from experiments and ab initio theory

This proof-of-concept study extends the ab initio computation of anisotropic displacement parameters to complexes with transition metal centres.