Hirshfeld atom refinement

Levamisole Based Co(II) Single-Ion Magnet

A new Co(II) complex, [Co(NCS)2(L)2] (1) has been synthesized based on levamisole (L) as a new ligand. Single-crystal X-ray diffraction analyses confirm that the Co(II) ion is having a distorted tetrahedral coordination geometry in the complex. Notably strong intramolecular S⋅⋅⋅S and S⋅⋅⋅N interactions has been confirmed by employing Quantum Theory of Atoms in Molecules (QTAIM). These intramolecular interactions occur among the sulfur and nitrogen atoms of the levamisole ligands and also the nitrogen atoms of the thiocyanate. Direct current (dc) magnetic analyses reveal presence of zero field splitting (ZFS) and large magnetic anisotropy on Co(II). Detailed ab initio ligand field theory calculations quantitatively predicted the magnitude of ZFS. Prominent field-induced single-ion magnet (SIM) behavior was observed for 1 from dynamic magnetization measurements. Slow magnetic relaxation follows an Orbach mechanism with the effective energy barrier Ueff=29.6 (7) K and relaxation time τo=1.4 (4)×10-9 s.

Hirshfeld atom refinement and dynamical refinement of hexagonal ice structure from electron diffraction data

Reaching beyond the commonly used spherical atomic electron density model allows one to greatly improve the accuracy of hydrogen atom structural parameters derived from X-ray data. However, the effects of atomic asphericity are less explored for electron diffraction data. In this work, Hirshfeld atom refinement (HAR), a method that uses an accurate description of electron density by quantum mechanical calculation for a system of interest, was applied for the first time to the kinematical refinement of electron diffraction data. This approach was applied here to derive the structure of ordinary hexagonal ice (Ih). The effect of introducing HAR is much less noticeable than in the case of X-ray refinement and it is largely overshadowed by dynamical scattering effects. It led to only a slight change in the O-H bond lengths (shortening by 0.01 Å) compared with the independent atom model (IAM). The average absolute differences in O-H bond lengths between the kinematical refinements and the reference neutron structure were much larger: 0.044 for IAM and 0.046 Å for HAR. The refinement results changed considerably when dynamical scattering effects were modelled - with extinction correction or with dynamical refinement. The latter led to an improvement of the O-H bond length accuracy to 0.021 Å on average (with IAM refinement). Though there is a potential for deriving more accurate structures using HAR for electron diffraction, modelling of dynamical scattering effects seems to be a necessary step to achieve this. However, at present there is no software to support both HAR and dynamical refinement.

(5S)-5-Benzylswainsonines as potent and selective inhibitors of Golgi α-mannosidase II: synthesis, enzyme evaluation and molecular modelling

Development of novel anti-cancer therapeutics based on Golgi α-mannosidase II (GMII) inhibition is considerably impeded by an undesired co-inhibition of lysosomal α-mannosidase leading to severe side-effects. In this contribution, we describe a fully stereoselective synthesis of (5S)-5-[4-(halo)benzyl]swainsonines as highly potent and selective inhibitors of GMII. The synthesis starts from a previously reported aldehyde readily available from l-ribose, and the key features include an intramolecular reductive amination with substrate-controlled stereoselectivity and a late-stage derivatisation of the benzyl group via ipso-substitution. These novel swainsonine analogues were found to be nanomolar inhibitors of the Golgi-type α-mannosidase AMAN-2 (Ki = 23-75 nM) with excellent selectivity (selectivity index = 205-870) over the lysosomal-type Jack bean α-mannosidase. Finally, molecular docking and pKa calculations were performed to provide more insight into the structure of the inhibitor:enzyme complexes, and a pair interaction energy analysis (FMO-PIEDA) was carried out to rationalise the observed potency and selectivity of the inhibitors.

Current developments and trends in quantum crystallography

Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X-ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid-state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state-of-the-art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction-/density matrix-based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies.

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.

Chemistry and crystal engineering

Recent studies published in the Chemistry and crystal engineering section of IUCrJ emphasize developments both in methodology and techniques as well as the diverse range of classes of compounds being studied and of problems being tackled.

Exploring crystal structure-physical property relationships with pressure

From its conception, X-ray crystallography has provided a unique understanding of the structure, bonding and electronic state of materials, which, in turn, unlocks a means of examining the properties and function of crystalline systems. Using state-of-the-art single-crystal X-ray diffraction, along with UV-Vis spectroscopy and DFT calculations, Zwolenik et al. [(2024). IUCrJ, 11, 519-527] have provided a comprehensive study of the structure-optical property relationship of 1,3-diacetylpyrene with methodologies that are increasingly accessible to non-specialist laboratories.

Evolution of structure and spectroscopic properties of a new 1,3-diacetylpyrene polymorph with temperature and pressure

A new polymorph of 1,3-diacetylpyrene has been obtained from its melt and thoroughly characterized using single-crystal X-ray diffraction, steady-state UV-Vis spectroscopy and periodic density functional theory calculations. Experimental studies covered the temperature range from 90 to 390 K and the pressure range from atmospheric to 4.08 GPa. Optimal sample placement in a diamond anvil cell according to our previously presented methodology ensured over 80% data coverage up to 0.8 Å for a monoclinic sample. Unrestrained Hirshfeld atom refinement of the high-pressure crystal structures was successful and anharmonic behavior of carbonyl oxygen atoms was observed. Unlike the previously characterized polymorph, the structure of 2°AP-β is based on infinite π-stacks of antiparallel 2°AP molecules. 2°AP-β displays piezochromism and piezofluorochromism which are directly related to the variation in interplanar distances within the π-stacking. The importance of weak intermolecular interactions is reflected in the substantial negative thermal expansion coefficient of -55.8 (57) MK-1 in the direction of C-H...O interactions.

Photoswitchable hydrazones with pyridine-based rotors and halogen substituents

The Z,E-photoisomerization of pyridine-based hydrazone switches is typically suppressed due to the presence of pyridine-based rotors. The crystal structures of studied compounds were investigated using theoretical methods combining DFT and QT-AIM calculations to unveil the nature and properties of the intramolecular hydrogen bonding. In this study, we introduced a new series of pyridine-based hydrazones anchored with o-halogen substituents (2-X) and investigated their photoswitching abilities using 1H NMR and UV-Vis spectroscopy. The efficiency of the photoisomerization from initial 2-X-Z to the 2-X-E isomer varied, with the highest yield observed for 2-Cl-E (55%). Our findings, supported by DFT calculations, revealed the formation of a new diastereomer, 2-X-E*, upon back-photoisomerization. We demonstrated that hydrazones from the 2-X series can be reversibly photoswitched using irradiation from the UV-Vis range, and additionally, we explored the effect of the halogen atom on their switching capabilities and also on their thermodynamics and kinetics of photoswitching, determining their molecular solar thermal energy storage potential.

Probing the Isolobal Relation between Cp'''NiP3 and White Phosphorus by Experimental Charge Density Analysis

An in-depth analysis of the description of bonding within Cp'''Ni-cyclo-P3 (Cp'''=1,2,4-tri-tert-butylcyclopentadienyl, [Ni]P3) employing X-ray diffraction based multipolar modeling, density functional theory (DFT) as well as an "experimental wavefunction" obtained from X-ray restrained wavefunction (XRW) fitting is presented. The results are compared to DFT calculations on white phosphorus - an isolobal analogue to [Ni]P3. A complementary bonding analysis shows insights into the reactivity of [Ni]P3. The isolobal principle is reflected in every aspect of our analysis and the employed methods seamlessly predict the differences in reactivity of [Ni]P3 and P4. Crystallographic modeling, solid-state NMR, and DFT calculations describe the dynamic behavior of the cyclo-P3 unit in the title molecule.

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.

Persistence of atoms in molecules: there is room beyond electron densities

Evidence that the electronic structure of atoms persists in molecules to a much greater extent than has been usually admitted is presented. This is achieved by resorting to N-electron real-space descriptors instead of one- or at most two-particle projections like the electron or exchange-correlation densities. Here, the 3N-dimensional maxima of the square of the wavefunction, the so-called Born maxima, are used. Since this technique is relatively unknown to the crystallographic community, a case-based approach is taken, revisiting first the Born maxima of atoms in their ground state and then some of their excited states. It is shown how they survive in molecules and that, beyond any doubt, the distribution of electrons around an atom in a molecule can be recognized as that of its isolated, in many cases excited, counterpart, relating this fact with the concept of energetic promotion. Several other cases that exemplify the applicability of the technique to solve chemical bonding conflicts and to introduce predictability in real-space analyses are also examined.

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.

Influence of N-protonation on electronic properties of acridine derivatives by quantum crystallography

Applications of 9-aminoacridine (9aa) and its derivatives span fields such as chemistry, biology, and medicine, including anticancer and antimicrobial activities. Protonation of such molecules can alter their bioavailability as weakly basic drugs like aminoacridines exhibit reduced solubility at high pH levels potentially limiting their effectiveness in patients with elevated gastric pH. In this study, we analyse the influence of protonation on the electronic characteristics of the molecular organic crystals of 9-aminoacridine. The application of quantum crystallography, including aspherical atom refinement, has enriched the depiction of electron density in the studied systems and non-covalent interactions, providing more details than previous studies. Our experimental results, combined with a topological analysis of the electron density and its Laplacian, provided detailed descriptions of how protonation changes the electron density distribution around the amine group and water molecule, concurrently decreasing the electron density at bond critical points of N/O-H bonds. Protonation also alters the molecular architecture of the systems under investigation. This is reflected in different proportions of the N⋯H and O⋯H intermolecular contacts for the neutral and protonated forms. Periodic DFT calculations of the cohesive energies of the crystal lattice, as well as computed interaction energies between molecules in the crystal, confirm that protonation stabilises the crystal structure due to a positive synergy between strong halogen and hydrogen bonds. Our findings highlight the potential of quantum crystallography in predicting crystal structure properties and point to its possible applications in developing new formulations for poorly soluble drugs.

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.

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).

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.

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.

Molecular Alumo- and Gallosilicate Hydrides Functionalized with Terminal M(NR2)3 and Bridging M(NR2)2 (M = Ti, Zr, Hf; R = Me, Et) Moieties

A general synthetic strategy for the systematic synthesis of group 4 MIV heterometallic complexes LMIII(H)(μ-O)Si(μ-O)(OtBu)2}nMIV(NR2)4-n (L = {[HC{C(Me)N(2,6-iPr2C6H3)}2; MIII = Al or Ga; n = 1 or 2; MIV = Ti, Zr, Hf; R = Me, Et), based on alumo- or gallosilicate hydride ligands bearing a Si-OH moiety, is presented. The challenging isolation of these metalloligands involved two strategies. On the one hand, the acid-base reaction of LAlH2 with (HO)2Si(OtBu)2 yielded LAlH(μ-O)Si(OH)(OtBu)2 (1), while on the other hand, the oxidative addition of (HO)2Si(OtBu)2 to LGa produced the gallium analog (2). These metalloligands successfully stabilized two hydrogen atoms with different acid-base properties (MIII-H and SiO-H) in the same molecule. Reactivity studies between 1 and 2 and group 4 amides MIV(NR2)4 (MIV = Ti, Zr, Hf; R = Me, Et) and tuning the reactions conditions and stoichiometry led to isolation and structural characterization of heterometallic complexes 3-11 with a 1:1 or 2:1 metalloligand/MIV ratio. Notably, some of these molecular heterometallic silicate complexes stabilize for the first time terminal (O3Si-O-)MIV(NR2)3 moieties known from single-site silica-grafted species. Furthermore, the aluminum-containing heterometallic complexes possess Al-H vibrational energies similar to those reported for modified alumina surfaces, which makes them potentially suitable models for the proposed MIV species grafted onto silica/alumina surfaces with hydride and dihydride architectures.

Locating Interstitial Hydrides in MH2@Cu14 (M = Cu, Ag) Clusters by Single-Crystal X-ray Diffraction

Two structures, [Cu15H2(S2CNnBu2)6(C≡CPh)6][CuCl2] (1) and [AgH2Cu14{S2P(OiPr)2}6(C≡CPh)6][PF6] (2), are characterized by X-ray crystallography with high-quality single crystals. The position of interstitial hydrides can be accurately located. In addition, the refinement of the hydrides with anisotropic displacement parameters (ADPs) was successful. The distances between the central atom and copper atoms, as well as the distances within the metal cages surrounding the hydrides, are analyzed and compared with similar MH2@Cu14 (M = Cu, Ag, Pd) compounds. This work provides a thoughtful and accurate assessment of the considerations and challenges associated with anisotropic refinement for H atoms, particularly in X-ray data collection.

Experimental charge density and topological analysis of tetraaquabis(hydrogenmaleato)nickel(II): a comparison with Hirshfeld atom refinement

Experimental charge density analysis is conducted on the coordination compound tetraaquabis(hydrogenmaleato)nickel(II), which exhibits a short intramolecular hydrogen bond. Through topological analysis, the nature of Ni-O bonds is concluded to be intermediate between ionic and covalent, but mainly presenting an ionic character, while the short hydrogen bond is classified as covalent in nature. The compound was also analysed after Hirshfeld atom refinement performed using NoSpherA2. A topological analysis was conducted on the molecular wavefunction and the results are compared with those obtained from experiment. In general, there is good agreement between the refinements, and the chemical bonds involving H atoms are in better agreement with what is expected from neutron data after HAR than they are after multipole refinement.

A Polymorph of Dipeptide Halide Glycyl-L-Alanine Hydroiodide Monohydrate: Crystal Structure, Optical Second Harmonic Generation, Piezoelectricity and Pyroelectricity

A polymorph of glycyl-L-alanine HI.H₂O is synthesized from chiral cyclo-glycyl-L-alanine dipeptide. The dipeptide is known to show molecular flexibility in different environments, which leads to polymorphism. The crystal structure of the glycyl-L-alanine HI.H₂O polymorph is determined at room temperature and indicates that the space group is polar (P2₁), with two molecules per unit cell and unit cell parameters a = 7.747 Å, b = 6.435 Å, c = 10.941 Å, α = 90°, β = 107.53(3)°, γ = 90° and V = 520.1(7) ų. Crystallization in the polar point group 2, with one polar axis parallel to the b axis, allows pyroelectricity and optical second harmonic generation. Thermal melting of the glycyl-L-alanine HI.H₂O polymorph starts at 533 K, close to the melting temperature reported for cyclo-glycyl-L-alanine (531 K) and 32 K lower than that reported for linear glycyl-L-alanine dipeptide (563 K), suggesting that although the dipeptide, when crystallized in the polymorphic form, is not anymore in its cyclic form, it keeps a memory of its initial closed chain and therefore shows a thermal memory effect. Here, we report a pyroelectric coefficient as high as 45 µC/m²K occurring at 345 K, one order of magnitude smaller than that of semi-organic ferroelectric triglycine sulphate (TGS) crystal. Moreover, the glycyl-L-alanine HI.H₂O polymorph displays a nonlinear optical effective coefficient of 0.14 pm/V, around 14 times smaller than the value from a phase-matched inorganic barium borate (BBO) single crystal. The new polymorph displays an effective piezoelectric coefficient equal to deff=280 pCN-1, when embedded into electrospun polymer fibers, indicating its suitability as an active system for energy harvesting.

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.

Reversing the Bond Length Alternation Order in Conjugated Polyenes by Substituent Effects

We have synthesised several push-pull substituted conjugated polyenes and determined their accurate C-C bond lengths and charge-density distributions by utilising quantum crystallographic techniques. In a series of alkene, dienes, and triene bearing two (trifluoromethyl)sulfonyl (triflyl) groups on the terminal carbon atom, unique reversal of the bond-length alternation (BLA) order has been observed. This is a pronounced aberration from the molecular structure predicted by the Lewis-structure-based neutral resonance structure. Such reversal of BLA order has not been observed in push-pull compounds bearing conventional electron-withdrawing groups such as carbonyl and cyano groups instead of triflyl groups. Bonding behaviour of both normal and reversed bond length alternating systems has been revealed by complementary bonding analysis using several bond descriptors based on the experimentally fitted wavefunctions.

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.

How do density functionals affect the Hirshfeld atom refinement?

In this work, the effect of mixing different amounts of Hartree-Fock (HF) exchange with hybrid density functionals applied to the Hirshfeld atom refinement (HAR) of urea and oxalic acid dihydrate is explored. Together, the influence of using different basis sets, methods (including MP2 and HF) and cluster sizes (to model bulk effects) is studied. The results show that changing the amount of HF exchange, no matter the level of theory, has an impact almost exclusively on the H atom refinement parameters. Contrary to pure quantum mechanical calculations where good geometries are obtained with intermediate HF exchange mixtures, in the HAR the best match with neutron diffraction reference values is not necessarily found for these admixtures. While the non-hydrogen covalent bond lengths are insensitive to the combination of method or basis set employed, the X-H bond lengths always increase proportionally to the HF exchange for the analysed systems. This outcome is opposite to what is normally observed from geometry optimisations, i.e., shorter bonds are obtained with greater HF exchange. Additionally, the thermal ellipsoids tend to shrink with larger HF exchange, especially for the H atoms involved in strong hydrogen bonding. Thus, it may be the case that the development of density functionals or basis sets suitable for quantum crystallography should take a different path than those fitted for quantum chemistry calculations.

Introduction of a weighting scheme for the X-ray restrained wavefunction approach: advantages and drawbacks

In a quite recent study [Genoni et al. (2017). IUCrJ, 4, 136-146], it was observed that the X-ray restrained wavefunction (XRW) approach allows a more efficient and larger capture of electron correlation effects on the electron density if high-angle reflections are not considered in the calculations. This is due to the occurrence of two concomitant effects when one uses theoretical X-ray diffraction data corresponding to a single-molecule electron density in a large unit cell: (i) the high-angle reflections are generally much more numerous than the low- and medium-angle ones, and (ii) they are already very well described at unrestrained level. Nevertheless, since high-angle data also contain important information that should not be disregarded, it is not advisable to neglect them completely. For this reason, based on the results of the previous investigation, this work introduces a weighting scheme for XRW calculations to up-weight the contribution of low- and medium-angle reflections, and, at the same time, to reasonably down-weight the importance of the high-angle data. The proposed strategy was tested through XRW computations with both theoretical and experimental structure-factor amplitudes. The tests have shown that the new weighting scheme works optimally if it is applied with theoretically generated X-ray diffraction data, while it is not advantageous when traditional experimental X-ray diffraction data (even of very high resolution) are employed. This also led to the conclusion that the use of a specific external parameter λ_J for each resolution range might not be a suitable strategy to adopt in XRW calculations exploiting experimental X-ray data as restraints.

3,4-Bis-O-propargyl-1,2:5,6-di-O-isopropylidene-D-mannitol: a study of multiple weak hydrogen bonds in the solid state

The title homochiral compound, C18H26O6, 1, was examined by single-crystal X-ray crystallography in order to understand its potential as a synthetic building block, particularly in inter- and intramolecular cyclocondensation reactions. It has also proven to be an excellent model for understanding multiple weak donor-acceptor D-H...A interactions involving terminal acetylenes as donors and as acceptors. The asymmetric unit of 1 comprises three almost identical independent molecules, each with the mannitol 2R,3R,4R,5R configuration and different conformations. Like independent molecules align in strands through acetylenic donor C-H...O contacts with equivalent dioxolanyl acceptor groups. Two of the strands are aligned unidirectionally, in parallel, while the third strand aligns perpendicular to the first two, to give interwoven layers in the supramolecular structure. A detailed study of the interdigitation of the second propargyl group from each independent molecule between strands, and of other short interstrand C-H...O contacts, provides new insight into the application of weak hydrogen-bond theory within the context of a conformationally flexible symmetrical molecule. Analyses of the Cambridge Structural Database using Crystal Packing Features and ConQuest search motifs support the importance of the D...A distance parameter, demonstrate the different influences of donor and acceptor types, and reveal the interplay between H...A and D...A contributions in different contact types.

Synchrotron X-ray Electron Density Analysis of Chemical Bonding in the Graphitic Carbon Nitride Precursor Melamine

Melamine is a precursor and building block for graphitic carbon nitride (g-CN) materials, a group of layered materials showing great promise for catalytic applications. The synthetic pathway to g-CN includes a polycondensation reaction of melamine by evaporation of ammonia. Melamine molecules in the crystal organize into wave-like planes with an interlayer distance of 3.3 Å similar to that of g-CN. Here we present an extensive investigation of the experimental electron density of melamine obtained from modelling of synchrotron radiation X-ray single-crystal diffraction data measured at 25 K with special focus on the molecular geometry and intermolecular interactions. Both intra- and interlayer structures are dominated by hydrogen bonding and π-interactions. Theoretical gas-phase optimizations of the experimental molecular geometry show that bond lengths and angles for atoms in the same chemical environment (C-N bonds in the ring, amine groups) differ significantly more for the experimental geometry than for the gas-phase-optimized geometries, indicating that intermolecular interactions in the crystal affects the molecular geometry. In the experimental crystal geometry, one amine group has significantly more sp3 -like character than the others, hinting at a possible formation mechanism of g-CN. Topological analysis and energy frameworks show that the nitrogen atom in this amine group participates in weak intralayer hydrogen bonding. We hypothesize that melamine condenses to g-CN within the layers and that the unique amine group plays a key role in the condensation process.

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.

Refinement of anomalous dispersion correction parameters in single-crystal structure determinations

Correcting for anomalous dispersion is part of any refinement of an X-ray dif-fraction crystal structure determination. The procedure takes the inelastic scattering in the diffraction experiment into account. This X-ray absorption effect is specific to each chemical compound and is particularly sensitive to radiation energies in the region of the absorption edges of the elements in the compound. Therefore, the widely used tabulated values for these corrections can only be approximations as they are based on calculations for isolated atoms. Features of the unique spatial and electronic environment that are directly related to the anomalous dispersion are ignored, although these can be observed spectroscopically. This significantly affects the fit between the crystallographic model and the measured intensities when the excitation wavelength in an X-ray diffraction experiment is close to an element's absorption edge. Herein, we report on synchrotron multi-wavelength single-crystal X-ray diffraction, as well as X-ray absorption spectroscopy experiments which we performed on the mol-ecular compound Mo(CO)6 at energies around the molybdenum K edge. The dispersive (f') and absorptive (f'') terms of the anomalous dispersion can be refined as independent parameters in the full-matrix least-squares refinement. This procedure has been implemented as a new feature in the well-established OLEX2 software suite. These refined parameters are in good agreement with the independently recorded X-ray absorption spectrum. The resulting crystallographic models show significant improvement compared to those employing tabulated values.

Structural and Molecular Packing study of Three New Amidophosphoric Acid Esters and Assessment of Their Inhibiting Activity Against SARS-CoV-2 by Molecular Docking

Three new compounds of amidophosphoric acid esters with a [OCH2C(CH3)2CH2O]P(O)[X] segment (where X=cyclopentylamido (1), 2-aminopyridinyl (2) and pyrrolidinyl (3)) were synthesized and studied using FT-IR and 31P/13C/1H NMR spectroscopies and single-crystal X-ray diffraction analysis. The compounds crystallize in the triclinic space groups P 1 ‾ for 1 and 3 and in the orthorhombic space group Pca21 for 2, where the asymmetric unit consists of three symmetrically-independent molecules for 1 and one molecule for 2 and 3. The intermolecular interactions and supramolecular assemblies are assessed by Hirshfeld surface analysis and enrichment ratios. The results reveal that the substituent effect plays an important role in directing the supramolecular structures. The presence of the aromatic substituent aminopyridine in 2 providing the C-H…π interactions leads to a larger variety in interactions including H…H, H…O/O…H, H…C/C…H and H…N/N…H contacts, whereas the packings of the compounds 1 and 3 bearing aliphatic substituents only include H…H and H…O/O…H contacts. The enrichment ratios affirm the importance of O…H/H…O contacts reflecting the hydrogen bond N-H…O interactions to be the enriched contacts. Compounds 1-3 were also investigated along with five similar reported structures with a [OCH2C(CH3)2CH2O]P(O) segment for their inhibitory behavior against SARS-CoV-2. The molecular docking results illustrate that the presence of the aromatic amido substituent versus the aliphatic type provides a more favorable condition for their biological activities.

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.

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.

Crystal structures

A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X-ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry.

Remarks on X-ray constrained/restrained wavefunction fitting

X-ray constrained/restrained wavefunctions (XCWs/XRWs) result from a combination of theory and experiment and are therefore affected by experimental errors and model uncertainties. The present XCW/XRW procedure does not take this into account, thus limiting the meaning and significance of the obtained wavefunctions.

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.

Four-Coordinate Monoboron Complexes with 8-Hydroxyquinolin-5-Sulfonate: Synthesis, Crystal Structures, Theoretical Studies, and Luminescence Properties

8-Hydroxyquinolin-5-sulfonic acid (8HQSA) was combined with 3-pyridineboronic acid (3PBA) or 4-pyridineboronic acid (4PBA) to give two zwitterionic monoboron complexes in crystalline form. The compounds were characterized by elemental analysis, single-crystal X-ray diffraction studies, and IR, 1H NMR, UV-Visible, and luminescence spectroscopy. The analyses revealed compounds with boron atoms adopting tetrahedral geometry. In the solid state, the molecular components are linked by charge-assisted (B)(O-H···−O(S) and N+-H···O(S) hydrogen bonds aside from C-H···O contacts and π···π interactions, as shown by Hirshfeld surface analyses and 2D fingerprint plots. The luminescence properties were characterized in terms of the emission behavior in solution and the solid state, showing emission in the bluish-green region in solution and large positive solvatofluorochromism, caused by intramolecular charge transfer. According to TD-DFT calculations at the M06-2X/6-31G(d) level of theory simulating an ethanol solvent environment, the emission properties are originated from π-π * and n-π * HOMO-LUMO transitions.

The benefits of Cu Kβ radiation for the single-crystal X-ray structure determination of crystalline sponges

The crystalline sponge method facilitates the X-ray structure determination of samples that do not crystallize or are too sparsely available to afford viable crystallization. By including these materials in a metal-organic framework, the structure of the guest molecules can be determined. Some of the inherent difficulties of this method are discussed and the use of Cu Kβ radiation is presented as a simple and effective means to improve the quality of the diffraction data that can be obtained from a sponge crystal.

Benzene and Borazine, so Different, yet so Similar: Insight from Experimental Charge Density Analysis

Although benzene and borazine are isoelectronic and isostructural, they have very different electronic structures, mainly due to the polar nature of the B-N bond. Herein, we present an experimental study of the charge density distribution obtained from the multipole model formalism and Hirshfeld atom refinement (HAR) based on high-resolution X-ray diffraction data of borazine B₃N₃H₆ (1) and B,B',B″-trichloroborazine (2) crystals. These data are compared to those obtained from HAR for benzene (4) and 1,3,5-trichlorobenzene (5) and further compared with values obtained from density functional theory calculations in the gas phase, where N,N',N″-trichloroborazine (3) was also included. The results confirm that, unlike benzene, borazines are only weakly aromatic with an island-like electronic delocalization within the B₃N₃ ring involving only the nitrogen atoms. Furthermore, delocalization indices and interacting quantum atom energy for bonded and non-bonded atoms were found to be highly suitable indicators capable of describing the origin of the discrepancies observed when the degree of aromaticity in 2 and 3 is evaluated using common aromaticity indices. Additionally, analysis of intermolecular interactions in the crystals brings further evidence of a weakly aromatic character of the borazines as it reveals surprising similarities between the crystal packing of borazine and benzene and also between B,B',B″-trichloroborazine and 1,3,5-trichlorobenzene.

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

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