Enhancing hydrogen positions in X-ray structures of transition metal hydride complexes with dynamic quantum crystallography

Hirshfeld atom refinement (HAR) is a method which enables the user to obtain more accurate positions of hydrogen atoms bonded to light chemical elements using X-ray data. When data quality permits, this method can be extended to hydrogen-bonded transition metals (TMs), as in hydride complexes. However, addressing hydrogen thermal motions with HAR, particularly in TM hydrides, presents a challenge. At the same time, proper description of thermal vibrations can be vital for determining hydrogen positions correctly. In this study, we employ tools such as SHADE3 and Normal Mode Refinement (NoMoRe) to estimate anisotropic displacement parameters (ADPs) for hydrogen atoms during HAR and IAM refinements performed for seven structures of TM (Fe, Ni, Cr, Nb, Rh and Os) and metalloid (Sb) hydride complexes for which both the neutron and the X-ray structures have been determined. A direct comparison between neutron and HAR/SHADE3/NoMoRe ADPs reveals that the similarity between neutron hydrogen ADPs and those estimated with NoMoRe or SHADE3 is significantly higher than when hydrogen ADPs are refined with HAR. Regarding TM-H bond lengths, traditional HAR exhibits a slight advantage over the other methods. However, combining NoMoRe/SHADE3 with HAR results in a minor decrease in agreement with neutron TM-H bond lengths. For the Cr complex, for which high-resolution X-ray data were collected, an investigation of resolution-related effects was possible.

Indium Kα radiation from a MetalJet X-ray source: comparison of the Eiger2 CdTe and Photon III detectors

The MetalJet source makes available new Kα radiation wavelengths for use in X-ray diffraction experiments. The purpose of this paper is to demonstrate the application of indium Kα radiation in independent-atom model refinement, as well as approaches using aspherical atomic form factors. The results vary greatly depending on the detector employed, as the energy cut-off of the Eiger2 CdTe provides a solution to a unique energy contamination problem of the MetalJet In radiation, which the Photon III detector cannot provide.

Elucidating the nature of chemical bonds in a coordination compound through quantum crystallographic techniques

Investigations simultaneously involving multiple techniques of quantum crystallography could be very useful to prove the consistency of obtained results or to highlight different facets of the same scientific phenomenon or problem. Pinto et al. [Acta Cryst. (2023), B79, 282-296] exploit three different quantum crystallographic techniques (Hansen & Coppens multipole model refinement, QTAIM analysis of the electron density, and Hirshfeld atom refinement) to characterize the nature of chemical bonds and of intra/intermolecular interactions in an organometallic compound.

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.

Accurate crystal structure of ice VI from X-ray diffraction with Hirshfeld atom refinement

Water is an essential chemical compound for living organisms, and twenty of its different crystal solid forms (ices) are known. Still, there are many fundamental problems with these structures such as establishing the correct positions and thermal motions of hydrogen atoms. The list of ice structures is not yet complete as DFT calculations have suggested the existence of additional and - to date - unknown phases. In many ice structures, neither neutron diffraction nor DFT calculations nor X-ray diffraction methods can easily solve the problem of hydrogen atom disorder or accurately determine their anisotropic displacement parameters (ADPs). Here, accurate crystal structures of H₂O, D₂O and mixed (50%H₂O/50%D₂O) ice VI obtained by Hirshfeld atom refinement (HAR) of high-pressure single-crystal synchrotron and laboratory X-ray diffraction data are presented. It was possible to obtain O-H/D bond lengths and ADPs for disordered hydrogen atoms which are in good agreement with the corresponding single-crystal neutron diffraction data. These results show that HAR combined with X-ray diffraction can compete with neutron diffraction in detailed studies of polymorphic forms of ice and crystals of other hydrogen-rich compounds. As neutron diffraction is relatively expensive, requires larger crystals which can be difficult to obtain and access to neutron facilities is restricted, cheaper and more accessible X-ray measurements combined with HAR can facilitate the verification of the existing ice polymorphs and the quest for new ones.

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.

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.

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.

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.

Further Validation of Quantum Crystallography Approaches

Quantum crystallography is a fast-developing multidisciplinary area of crystallography. In this work, we analyse the influence of different charge density models (i.e., the multipole model (MM), Hirshfeld atom refinement (HAR), and the transferable aspherical atom model (TAAM)), modelling of the thermal motion of hydrogen atoms (anisotropic, isotropic, and with the aid of SHADE or NoMoRe), and the type of radiation used (Mo Kα and Cu Kα) on the final results. To achieve this aim, we performed a series of refinements against X-ray diffraction data for three model compounds and compared their final structures, geometries, shapes of ADPs, and charge density distributions. Our results were also supported by theoretical calculations that enabled comparisons of the lattice energies of these structures. It appears that geometrical parameters are better described (closer to the neutron values) when HAR is used; however, bonds to H atoms more closely match neutron values after MM or TAAM refinement. Our analysis shows the superiority of the NoMoRe method in the description of H-atom ADPs. Moreover, the shapes of the ADPs of H atoms, as well as their electron density distributions, were better described with low-resolution Cu Kα data in comparison to low-resolution Mo Kα data.

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.

Crystal Structure and Non-Hydrostatic Stress-Induced Phase Transition of Urotropine Under High Pressure

High-pressure behavior of hexamethylenetetramine (urotropine) was studied in situ using angle-dispersive single-crystal synchrotron X-ray diffraction (XRD) and Fourier-transform infrared absorption (FTIR) spectroscopy. Experiments were conducted in various pressure-transmitting media to study the effect of deviatoric stress on phase transformations. Up to 4 GPa significant damping of molecular librations and atomic thermal motion was observed. A first-order phase transition to a tetragonal structure was observed with an onset at approximately 12.5 GPa and characterized by sluggish kinetics and considerable hysteresis upon decompression. However, it occurs only in non-hydrostatic conditions, induced by deviatoric or uniaxial stress in the sample. This behavior finds analogies in similar cubic crystals built of highly symmetric cage-like molecules and may be considered a common feature of such systems. DFT computations were performed to model urotropine equation of state and pressure dependence of vibrational modes. The first successful Hirshfeld atom refinements carried out for high-pressure diffraction data are reported. The refinements yielded more realistic C-H bond lengths than the independent atom model even though the high-pressure diffraction data are incomplete.

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.

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.

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.

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.

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

Hirshfeld atom refinement (HAR) is a novel X-ray structure refinement technique that employs aspherical atomic scattering factors obtained from stockholder partitioning of a theoretically determined tailor-made static electron density. HAR overcomes many of the known limitations of independent atom modelling (IAM), such as too short element-hydrogen distances, r(X-H), or too large atomic displacement parameters (ADPs). This study probes the accuracy and precision of anisotropic hydrogen and non-hydrogen ADPs and of r(X-H) values obtained from HAR. These quantities are compared and found to agree with those obtained from (i) accurate neutron diffraction data measured at the same temperatures as the X-ray data and (ii) multipole modelling (MM), an established alternative method for interpreting X-ray diffraction data with the help of aspherical atomic scattering factors. Results are presented for three chemically different systems: the aromatic hydro-carbon rubrene (orthorhombic 5,6,11,12-tetra-phenyl-tetracene), a co-crystal of zwitterionic betaine, imidazolium cations and picrate anions (BIPa), and the salt potassium hydrogen oxalate (KHOx). The non-hydrogen HAR-ADPs are as accurate and precise as the MM-ADPs. Both show excellent agreement with the neutron-based values and are superior to IAM-ADPs. The anisotropic hydrogen HAR-ADPs show a somewhat larger deviation from neutron-based values than the hydrogen SHADE-ADPs used in MM. Element-hydrogen bond lengths from HAR are in excellent agreement with those obtained from neutron diffraction experiments, although they are somewhat less precise. The residual density contour maps after HAR show fewer features than those after MM. Calculating the static electron density with the def2-TZVP basis set instead of the simpler def2-SVP one does not improve the refinement results significantly. All HARs were performed within the recently introduced HARt option implemented in the Olex2 program. They are easily launched inside its graphical user interface following a conventional IAM.

Hydrogen atoms can be located accurately and precisely by x-ray crystallography

Precise and accurate structural information on hydrogen atoms is crucial to the study of energies of interactions important for crystal engineering, materials science, medicine, and pharmacy, and to the estimation of physical and chemical properties in solids. However, hydrogen atoms only scatter x-radiation weakly, so x-rays have not been used routinely to locate them accurately. Textbooks and teaching classes still emphasize that hydrogen atoms cannot be located with x-rays close to heavy elements; instead, neutron diffraction is needed. We show that, contrary to widespread expectation, hydrogen atoms can be located very accurately using x-ray diffraction, yielding bond lengths involving hydrogen atoms (A-H) that are in agreement with results from neutron diffraction mostly within a single standard deviation. The precision of the determination is also comparable between x-ray and neutron diffraction results. This has been achieved at resolutions as low as 0.8 Å using Hirshfeld atom refinement (HAR). We have applied HAR to 81 crystal structures of organic molecules and compared the A-H bond lengths with those from neutron measurements for A-H bonds sorted into bonds of the same class. We further show in a selection of inorganic compounds that hydrogen atoms can be located in bridging positions and close to heavy transition metals accurately and precisely. We anticipate that, in the future, conventional x-radiation sources at in-house diffractometers can be used routinely for locating hydrogen atoms in small molecules accurately instead of large-scale facilities such as spallation sources or nuclear reactors.

Electron density, disorder and polymorphism: high-resolution diffraction studies of the highly polymorphic neuralgic drug carbamazepine

Analysis of neutron and high-resolution X-ray diffraction data on form (III) of carbamazepine at 100 K using the atoms in molecules (AIM) topological approach afforded excellent agreement between the experimental results and theoretical densities from the optimized gas-phase structure and from multipole modelling of static theoretical structure factors. The charge density analysis provides experimental confirmation of the partially localized π-bonding suggested by the conventional structural formula, but the evidence for any significant C-N π bonding is not strong. Hirshfeld atom refinement (HAR) gives H atom positional and anisotropic displacement parameters that agree very well with the neutron parameters. X-ray and neutron diffraction data on the dihydrate of carbemazepine strongly indicate a disordered orthorhombic crystal structure in the space group Cmca, rather than a monoclinic crystal structure in space group P2(1)/c. This disorder in the dihydrate structure has implications for both experimental and theoretical studies of polymorphism.

Accurate H-atom parameters from X-ray diffraction data

The difficulties in defining the positions and thermal parameters for hydrogen atoms using X-ray diffraction data alone are discussed.

Hirshfeld atom refinement for modelling strong hydrogen bonds

High-resolution low-temperature synchrotron X-ray diffraction data of the salt L-phenylalaninium hydrogen maleate are used to test the new automated iterative Hirshfeld atom refinement (HAR) procedure for the modelling of strong hydrogen bonds. The HAR models used present the first examples of Z' > 1 treatments in the framework of wavefunction-based refinement methods. L-Phenylalaninium hydrogen maleate exhibits several hydrogen bonds in its crystal structure, of which the shortest and the most challenging to model is the O-H...O intramolecular hydrogen bond present in the hydrogen maleate anion (O...O distance is about 2.41 Å). In particular, the reconstruction of the electron density in the hydrogen maleate moiety and the determination of hydrogen-atom properties [positions, bond distances and anisotropic displacement parameters (ADPs)] are the focus of the study. For comparison to the HAR results, different spherical (independent atom model, IAM) and aspherical (free multipole model, MM; transferable aspherical atom model, TAAM) X-ray refinement techniques as well as results from a low-temperature neutron-diffraction experiment are employed. Hydrogen-atom ADPs are furthermore compared to those derived from a TLS/rigid-body (SHADE) treatment of the X-ray structures. The reference neutron-diffraction experiment reveals a truly symmetric hydrogen bond in the hydrogen maleate anion. Only with HAR is it possible to freely refine hydrogen-atom positions and ADPs from the X-ray data, which leads to the best electron-density model and the closest agreement with the structural parameters derived from the neutron-diffraction experiment, e.g. the symmetric hydrogen position can be reproduced. The multipole-based refinement techniques (MM and TAAM) yield slightly asymmetric positions, whereas the IAM yields a significantly asymmetric position.

Hydrogen ADPs with Cu Kα data? Invariom and Hirshfeld atom modelling of fluconazole

For the structure of fluconazole [systematic name: 2-(2,4-difluorophenyl)-1,3-bis(1H-1,2,4-triazol-1-yl)propan-2-ol] monohydrate, C13H12F2N6O·H2O, a case study on different model refinements is reported, based on single-crystal X-ray diffraction data measured at 100 K with Cu Kα radiation to a resolution of sin θ/λ of 0.6 Å(-1). The structure, anisotropic displacement parameters (ADPs) and figures of merit from the independent atom model are compared to `invariom' and `Hirshfeld atom' refinements. Changing from a spherical to an aspherical atom model lowers the figures of merit and improves both the accuracy and the precision of the geometrical parameters. Differences between results from the two aspherical-atom refinements are small. However, a refinement of ADPs for H atoms is only possible with the Hirshfeld atom density model. It gives meaningful results even at a resolution of 0.6 Å(-1), but requires good low-order data.