Atomic Refinement Research Articles

Hirshfeld Atom Refinement (HAR) and Complementary Bonding Analysis of Lithium m-Terphenylhydridoborates Containing B-H···Li Linkages.

The synthesis and characterization of the lithium m-terphenylhydridoborates [Li(2,6-Mes2C6H3)BH3]2 (1), Li(2,6-Mes2C6H3)2BH2 (2) and Li(OEt2)(2,6-Mes2C6H3)2BH2 (3) are reported. Hirshfeld Atom Refinement (HAR) of the experimentally obtained molecular structures by single-crystal X-ray crystallography allowed the determination of the exact positions of the hydrogen atoms. The bond situations of the various B-H···Li linkages were investigated by a complementary bonding analysis using various methods including atoms in molecules (AIM), electron localizability indicator (ELI-D), non-covalent interaction (NCI) index and the compliance matrix.

Further evaluation of the shape of atomic Hirshfeld surfaces: M...H contacts and homoatomic bonds.

It is well known that Hirshfeld surfaces provide an easy and straightforward way of analysing intermolecular interactions in the crystal environment. The use of atomic Hirshfeld surfaces has also demonstrated that such surfaces carry information related to chemical bonds which allow a deeper evaluation of the structures. Here we briefly summarize the approach of atomic Hirshfeld surfaces while further evaluating the kind of information that can be retrieved from them. We show that the analysis of the metal-centre Hirshfeld surfaces from structures refined via Hirshfeld Atom Refinement (HAR) allow accurate evaluation of contacts of type M...H, and that such contacts can be related to the overall shape of the surfaces. The compounds analysed were tetraaquabis(3-carboxypropionato)metal(II), [M(C4H3O4)2(H2O)4], for metal(II)/M= manganese/Mn, cobalt/Co, nickel/Ni and zinc/Zn. We also evaluate the sensitivity of the surfaces by an investigation of seemingly flat surfaces through analysis of the curvature functions in the direction of C-C bonds. The obtained values not only demonstrate variations in curvature but also show a correlation with the hybridization of the C atoms involved in the bond.

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.

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.

Influence of the steric bulk of a trityl group in the formation of molecular metallosilicates

The molecular silanol (Ph3CO)(iPrO)2Si(OH) was designed to evaluate the degree of steric bulk the trityl moiety imposes on the Si–OH group. The reactivity of the silanol was evaluated by the formation of three metallosilicates with lithium, aluminum, and gallium, and their molecular structures and the degree of association were determined. Hirshfeld atom refinement or DFT calculation, and QTAIM analysis of the electron density in all compounds were used to analyze the bonding situation in the metallosilicate moieties and determine the strength of the intermolecular hydrogen bonds formed by the silanol. Finally, ring-opening polymerization of ε-caprolactone was used as another criterion for the evaluation of the steric bulk imposed by the trityl group.

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.

Redetermination of germacrone type II based on single-crystal X-ray data.

The extraction and purification procedures, crystallization and crystal structure refinement (single-crystal X-ray data) of germacrone type II, C15H22O, are presented. The structural results are compared with a previous powder X-ray synchrotron study [Kaduk et al. (2022 ▸). Powder Diffr. 37, 98-104], revealing significant improvements in terms of accuracy and precision. Hirshfeld atom refinement (HAR), as well as Hirshfeld surface analysis, give insight into the inter-molecular inter-actions of germacrone type II.

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.

Spectroscopic properties, crystal structure, Hirshfeld surface analysis and DFT study of a new Cu(II) complex based on quinazolinone O,N,O-donor ligand

A quinazolinone-based Schiff base ligand 3-[(2‑hydroxy-5-methoxybenzylidene)amino]-2-(2‑hydroxy-5-methoxyphenyl)-2,3-dihydroquinazolin-4-one (L1) and its new mononuclear copper(II) complex [Cu(L1)Cl(H2O)] (1) were synthesised and fully characterised by various spectroscopic techniques (NMR, FTIR, UV–Vis) and single-crystal X-ray diffraction study. The aspherical model of the crystal structure of the ligand L1 as well as of the copper(II) complex 1 was refined by the Hirshfeld Atom Refinement method. The crystal structure of the copper(II) complex shows the existence of a substitution disorder at the position of the water molecule, which represents two different complex molecules [Cu(L1)Cl(H2O)] (1a) and [Cu(L1)Cl] (1b) with different coordination polyhedra around the copper atom. The majority of the mononuclear complex [Cu(L1)Cl(H2O)] (1a) in the crystal structure contains a coordinated water molecule, but the minority in the crystal structure contains a mononuclear complex [Cu(L1)Cl] (1b) and a water molecule is outside the coordination sphere around the copper atom. The crystal structure of complex 1 showed a penta-coordinated (1a) or tetra-coordinated (1b) Cu atom in the shape of a tetragonal pyramid (1a) or square planar (1b) formed by a chloride atom in the equatorial plane, and a Schiff base bound as an O,N,O-tridentate ligand, and an additional water molecule in the axial position (only 1a). A detailed analysis of the intermolecular interactions was investigated using three-dimensional 3D Hirshfeld surfaces and their associated two-dimensional 2D fingerprint plots. Hirshfeld surface analysis was performed for both crystal structures. Furthermore, theoretical DFT analysis has been performed in order to interpret the experimental data. In order to obtain high quality DFT data, we present here a new basis set B1MH, which is an extension of the LanL2DZ basis with incorporated polarisation and diffusion functions for heavy atoms (C, N, O, Cl and Cu) and added ECPs for Cl and Cu atoms. The presented B1MH basis set allowed us to obtain better theoretical results than those previously published.

Cryo-EM structure and B-factor refinement with ensemble representation

Cryo-EM experiments produce images of macromolecular assemblies that are combined to produce three-dimensional density maps. Typically, atomic models of the constituent molecules are fitted into these maps, followed by a density-guided refinement. We introduce TEMPy-ReFF, a method for atomic structure refinement in cryo-EM density maps. Our method represents atomic positions as components of a Gaussian mixture model, utilising their variances as B-factors, which are used to derive an ensemble description. Extensively tested on a substantial dataset of 229 cryo-EM maps from EMDB ranging in resolution from 2.1-4.9 Å with corresponding PDB and CERES atomic models, our results demonstrate that TEMPy-ReFF ensembles provide a superior representation of cryo-EM maps. On a single-model basis, it performs similarly to the CERES re-refinement protocol, although there are cases where it provides a better fit to the map. Furthermore, our method enables the creation of composite maps free of boundary artefacts. TEMPy-ReFF is useful for better interpretation of flexible structures, such as those involving RNA, DNA or ligands.

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.

Hydrogen atom restraints and disorder treatment in Hirshfeld atom refinement of polypeptides

Hydrogen atom restraints and disorder treatment in Hirshfeld atom refinement of polypeptides

Accurate crystal structures of ices from X-ray and ED with Hirshfeld atom refinement

Accurate crystal structures of ices from X-ray and ED with Hirshfeld atom refinement

A periodic calculation for a periodic system: using projector-augmented wave densities as a basis for Hirshfeld atom refinement

A periodic calculation for a periodic system: using projector-augmented wave densities as a basis for Hirshfeld atom refinement

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.

Overall protein structure quality assessment using hydrogen-bonding parameters.

Atomic model refinement at low resolution is often a challenging task. This ismostly because the experimental data are not sufficiently detailed to be described by atomic models. To make refinement practical and ensure that a refined atomic model is geometrically meaningful, additional information needs to be used such as restraints on Ramachandran plot distributions or residue side-chain rotameric states. However, using Ramachandran plots or rotameric states as refinement targets diminishes the validating power of these tools. Therefore, finding additional model-validation criteria that are not used or are difficult to use as refinement goals is desirable. Hydrogen bonds are one of the important noncovalent interactions that shape and maintain protein structure. These interactions can be characterized by a specific geometry of hydrogen donor and acceptor atoms. Systematic analysis of these geometries performed for quality-filtered high-resolution models of proteins from the Protein Data Bank shows that they have a distinct and a conserved distribution. Here, it is demonstrated how this information can be used for atomic model validation.

Accurate crystal structures of ices from X-ray and ED with Hirshfeld atom refinement

Accurate crystal structures of ices from X-ray and ED with Hirshfeld atom refinement

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.

Synthesis, Hirshfeld atom refinement of crystal structure, and Hirshfeld surface analysis of 5-ethoxycarbonyl-6-methyl-4-(2-(trifluoromethyl)phenyl)-3,4-dihydropyrimidin-2-(1H)-one formic acid monosolvate

We report the cyanamide-based multicomponent synthesis and crystal structure of the title compound, 5-ethoxycarbonyl-6-methyl-4-(2-(trifluoromethyl)phenyl)-3,4-dihydropyrimidin-2-(1H)-one which crystallized as a binary cocrystal with formic acid, C15H15F3N2O3·HCO2H (DHPM···FA). The molecular structure of the DHPM···FA heterosynthon was unequivocally confirmed using X-ray single crystal diffraction techniques and spectroscopic methods. X-ray diffraction analysis shows that this cocrystalline material crystallizes in the monoclinic space group P21/n, Z = 4 with the 3,4-dihydropyrimidin-2-(1H)-one ring in a twist-boat form attached to the ester and phenyl group in an s−cis/s−cis and sp−conformation, respectively. The molecular structure and crystalline packing are stabilized by intermolecular N2–H2∙∙∙O1, N1–H1∙∙∙O5, O4–H4A∙∙∙O1, C4–H4∙∙∙O5, C6–H6∙∙∙O3 and C16–H16∙∙∙O3 hydrogen bonds into a 3D supramolecular network R22(8). Furthermore, the Hirshfeld surface analysis confirms that the most important contributions for the crystal packing are the H∙∙∙O/O∙∙∙H (58.7%), C − H···C (17.8%), H∙∙∙H (30.4%) and H∙∙∙F/F∙∙∙H (18.3%) surface contacts.