Charge Density Analysis of an Organic Ferroelectric. Croconic Acid: an Experimental and Theoretical Study

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

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

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.

Direct air capture of CO-2 - topological analysis of the experimental electron density (QTAIM) of the highly insoluble carbonate salt of a 2,6-pyridine-bis(iminoguanidine), (PyBIGH2)(CO3)(H2O)4

Chemical bonding and all intermolecular interactions in the highly insoluble carbonate salt of a 2,6-pyridine-bis(iminoguanidine), (PyBIGH2)(CO3)(H2O)4, recently employed in the direct air capture of CO2 via crystallization, have been analyzed within the framework of the quantum theory of atoms in molecules (QTAIM) based on the experimental electron density derived from X-ray diffraction data obtained at 20 K. Accurate hydrogen positions were included based on an analogous neutron diffraction study at 100 K. Topological features of the covalent bonds demonstrate the presence of multiple bonds of various orders within the PyBIGH2 2+ cation. Strong hydrogen bonds define ribbons comprising carbonate anions and water molecules. These ribbons are linked to stacks of essentially planar dications via hydrogen bonds from the guanidinium moieties and an additional one to the pyridine nitro-gen. The linking hydrogen bonds are approximately perpendicular to the anion-water ribbons. The observation of these putative interactions provided motivation to characterize them by topological analysis of the total electron density. Thus, all hydrogen bonds have been characterized by the properties of their (3,-1) bond critical points. Weaker interactions between the PyBIGH2 2+ cations have similarly been characterized. Integrated atomic charges are also reported. A small amount of cocrystallized hydroxide ion (∼2%) was also detected in both the X-ray and neutron data, and included in the multipole model for the electron-density refinement. The small amount of additional H+ required for charge balance was not detected in either the X-ray or the neutron data. The results are discussed in the context of the unusually low aqueous solubility of (PyBIGH2)(CO3)(H2O)4 and its ability to sequester atmospheric CO2.

Intermolecular head-to-head interaction of carbonyl groups in bicyclic hydrogen-bonded synthon based on β-hydroxy ketones

In this study, we report a counterintuitive carbonyl–carbonyl interaction explored for crystalline (2RS,3RS)-1-aryl-2-bromo-3-hydroxy-3-(2-nitrophenyl)-propan-1-ones.

QTAIM Assessment of the Intra- and Intermolecular Bonding in a Bis(nitramido-oxadiazolate) Energetic Ionic Salt at 20 K

Accurate experimental determination of the electron density distribution for the energetic ionic salt bis(ammonium) 2,2'-dinitramido-5,5'-bis(1-oxa-3,4-diazolate) dihydrate (1) is obtained from multipole modeling of single-crystal X-ray diffraction data collected at 20 K. The intra- and intermolecular bonding is assessed in terms of the quantum theory of atoms in molecules (QTAIM) with a view to better understanding the physicochemical properties in relation to chemical bonding. Topological analysis reveals stronger bonding for the N-NO₂ bond relative to energetic nitramines RDX and HMX and the indication of a trend between this and impact sensitivity of nitro-containing energetic materials is noted. The intermolecular bonding of 1 is dominated by classical H-bonds but includes multiple π-bonding interactions and interactions between H-bond donor and acceptor atoms where bond paths are deflected by H atoms. There also exists a weak O···O interaction between end-on nitro groups, as well as an intramolecular ring-forming 1,5-type interaction. An anharmonic description of thermal motion was required to obtain the best fitting model, despite the low temperature of the study. The experimental study was complemented by periodic boundary DFT calculations at the experimental geometry as well as gas phase calculations on the isolated dianion.

Mechanism of enhancement of ferroelectricity of croconic acid with temperature

A detailed study of the thermal behaviour of atomic motions in the organic ferroelectric croconic acid is presented in the temperature range 5-300 K. Using high-resolution inelastic neutron scattering and first-principles electronic-structure calculations within the framework of density functional theory and a quasiharmonic phonon description of the material, we find that the frequencies of the well defined doublet in inelastic neutron scattering spectra associated with out-of-plane motions of hydrogen-bonded protons decrease monotonically with temperature indicating weakening of these bonding motifs and enhancement of proton motions. Theoretical mean-square displacements for these proton motions are within 5% of experimental values. A detailed analysis of this observable shows that it is unlikely that there is a facile proton transfer along the direction of ferroelectric polarization in the absence of an applied electric field. Calculations predict constrained thermal motion of proton along crystallographic lattice direction c retaining the hydrogen bond motif of the crystal at high temperature. Using the Berry-phase method, we have also calculated the spontaneous polarization of temperature dependent cell structures, and find that our computational model provides a satisfactory description of the anomalous and so far unexplained rise in bulk electric polarization with temperature. Correlating the thermal motion induced lattice strain with temperature dependent spontaneous polarizations, we conclude that increasing thermal strain with temperatures combined with constrained thermal motion along the hydrogen bond motif are responsible of this increase in ferroelectricity at high temperature.

Validation of X-ray Wavefunction Refinement

In this work, the quality of the electron density in crystals reconstructed by the multipolar model (MM) and by X-ray wavefunction refinement (XWR) is tested on a set of high-resolution X-ray diffraction data sets of four amino acids and six tripeptides. It results in the first thorough validation of XWR. Agreement statistics, figures of merit, residual- and deformation-density maps, as well as atomic displacement parameters are used to measure the quality of the reconstruction relative to the measured structure factors. Topological analysis of the reconstructed density is carried out to obtain atomic and bond-topological properties, which are subsequently compared to the values derived from benchmarking periodic DFT geometry optimizations. XWR is simultaneously in better agreement than the MM with both benchmarking theory and the measured diffraction pattern. In particular, the obvious problems with the description of polar bonds in the MM are significantly reduced by using XWR. Similarly, modeling of electron density in the vicinity of hydrogen atoms with XWR is visibly improved.

Experimental Charge-Density Study of the Intra- and Intermolecular Bonding in TKX-50

The intra- and intermolecular bonding in the known phase of dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate, TKX-50, has been analyzed on the basis of the experimentally determined charge density distribution from high-resolution X-ray diffraction data obtained at 20 K. This was compared to the charge density obtained from DFT calculations with periodic boundary conditions using both direct calculations and derived structure factors. Results of topological analysis of the electron density corroborate that TKX-50 is best described as a layered structure linked primarily by a number of hydrogen bonds as well as by a variety of other interactions. Additional bonding interactions were identified, including a pair of equivalent 1,5-type intramolecular closed-shell interactions in the dianion. Refinement of anharmonic motion was shown to be essential for obtaining an adequate model, despite the low temperature of the study. Although generally unusual, the implementation of anharmonic refinement provided a significant improvement compared to harmonic refinement of both traditional and split-core multipole models.

Revisiting the charge density analysis of 2,5-dichloro-1,4-benzoquinone at 20 K

A high-resolution X-ray diffraction measurement of 2,5-dichloro-1,4-benzoquinone (DCBQ) at 20 K was carried out. The experimental charge density was modeled using the Hansen-Coppens multipolar expansion and the topology of the electron density was analyzed in terms of the quantum theory of atoms in molecules (QTAIM). Two different multipole models, predominantly differentiated by the treatment of the chlorine atom, were obtained. The experimental results have been compared to theoretical results in the form of a multipolar refinement against theoretical structure factors and through direct topological analysis of the electron density obtained from the optimized periodic wavefunction. The similarity of the properties of the total electron density in all cases demonstrates the robustness of the Hansen-Coppens formalism. All intra- and intermolecular interactions have been characterized.

Experimental charge-density studies: data reduction and model quality: the more the better?

In this review, recent developments concerning data and model quality in experimental charge-density investigations from a personal view-point are described. Data quality is not only achieved by the high resolution, high I/σ(I) values, low merging R values and high multiplicity. The quality of the innermost reflections especially is crucial for mapping the density distribution of the outermost valence electrons and can be monitored by (I/σ)^asymptotic. New detector technologies seem to be promising improvements. Empirical corrections to correct for low-energy contamination of mirror-focused X-ray data and for resolution- and temperature-dependent errors caused by factors such as thermal diffuse scattering are described. Shashlik-like residual density patterns can indicate the need for an anharmonic description of the thermal motion of individual atoms. The physical reliability of the derived model must be thoroughly analysed. The derived probability density functions for the mean-squared atomic vibrational displacements especially should have only small negative values. The treatment of H atoms has been improved by methods to estimate anisotropic thermal motion. For very high resolution data, the polarization of the core density cannot be neglected. Several tools to detect systematic errors are described. A validation tool is presented that easily detects when the refinement of additional parameters yields a real improvement in the model or simply overfits the given data. In all investigated structures, it is proved that the multipole parameters of atoms with a comparable chemical environment should be constrained to be identical. The use of restraints could be a promising alternative.

Multi-temperature study of potassium uridine-5'-monophosphate: electron density distribution and anharmonic motion modelling

Uridine, a nucleoside formed of a uracil fragment attached to a ribose ring via a β-N1-glycosidic bond, is one of the four basic components of ribonucleic acid. Here a new anhydrous structure and experimental charge density distribution analysis of a uridine-5'-monophosphate potassium salt, K(UMPH), is reported. The studied case constitutes the very first structure of a 5'-nucleotide potassium salt according to the Cambridge Structural Database. The excellent crystal quality allowed the collection of charge density data at various temperatures, i.e. 10, 100, 200 and 300 K on one single crystal. Crystal structure and charge density data were analysed thoroughly in the context of related literature-reported examples. Detailed analysis of the charge density distribution revealed elevated anharmonic motion of part of the uracil ring moiety relatively weakly interacting with the neighbouring species. The effect was manifested by alternate positive and negative residual density patterns observed for these atoms, which `disappear' at low temperature. It also occurred that the potassium cation, quite uniformly coordinated by seven O atoms from all molecular fragments of the UMPH^- anion, including the O atom from the ribofuranose ring, can be treated as spherical in the charge density model which was supported by theoretical calculations. Apart from the predominant electrostatic interactions, four relatively strong hydrogen bond types further support the stability of the crystal structure. This results in a compact and quite uniform structure (in all directions) of the studied crystal, as opposed to similar cases with layered architecture reported in the literature.

Charge Density and Electrostatic Potential Study of 16α,17β-Estriol and the Binding of Estrogen Molecules to the Estrogen Receptors ERα and ERβ

An accurate X-ray diffraction study at 20 K combined with DFT theoretical calculations has been performed for the estriol crystal with two conformationally different molecules in the asymmetric unit. The electron density has been modeled via a multipole expansion, using both experimental and theoretical structure factors, and a topological analysis has been performed. The experimental molecular geometry, hydrogen bonding, atomic charges, dipole moments, and other topological characteristics are compared with those calculated theoretically. In particular, the molecular electrostatic potential has been extracted and compared with those reported for other estrogen molecules exhibiting different binding affinities to the estrogen receptors (ERα and ERβ).

Contemporary X-ray electron-density studies using synchrotron radiation

Synchrotron radiation has many compelling advantages over conventional radiation sources in the measurement of accurate Bragg diffraction data. The variable photon energy and much higher flux may help to minimize critical systematic effects such as absorption, extinction and anomalous scattering. Based on a survey of selected published results from the last decade, the benefits of using synchrotron radiation in the determination of X-ray electron densities are discussed, and possible future directions of this field are examined.

Hirshfeld atom refinement

Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly-l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree-Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints - even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu's), all other structural parameters agree within less than 2 csu's. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Å for temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å(2) as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements - an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.

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.

Experimental determination of core electron deformation in diamond

Synchrotron powder X-ray diffraction data are used to determine the core electron deformation of diamond. Core shell contraction inherently linked to covalent bond formation is observed in close correspondence with theoretical predictions. Accordingly, a precise and physically sound reconstruction of the electron density in diamond necessitates the use of an extended multipolar model, which abandons the assumption of an inert core. The present investigation is facilitated by negligible model bias in the extraction of structure factors, which is accomplished by simultaneous multipolar and Rietveld refinement accurately determining an atomic displacement parameter (ADP) of 0.00181 (1) Å(2). The deconvolution of thermal motion is a critical step in experimental core electron polarization studies, and for diamond it is imperative to exploit the monatomic crystal structure by implementing Wilson plots in determination of the ADP. This empowers the electron-density analysis to precisely administer both the deconvolution of thermal motion and the employment of the extended multipolar model on an experimental basis.

Topology of the electron density of d0 transition metal compounds at subatomic resolution

Accurate X-ray diffraction experiments allow for a reconstruction of the electron density distribution of solids and molecules in a crystal. The basis for the reconstruction of the electron density is in many cases a multipolar expansion of the X-ray scattering factors in terms of spherical harmonics, a so-called multipolar model. This commonly used ansatz splits the total electron density of each pseudoatom in the crystal into (i) a spherical core, (ii) a spherical valence, and (iii) a nonspherical valence contribution. Previous studies, for example, on diamond and α-silicon have already shown that this approximation is no longer valid when ultrahigh-resolution diffraction data is taken into account. We report here the results of an analysis of the calculated electron density distribution in the d(0) transition metal compounds [TMCH3](2+) (TM = Sc, Y, and La) at subatomic resolution. By a detailed molecular orbital analysis, it is demonstrated that due to the radial nodal structure of the 3d, 4d, and 5d orbitals involved in the TM-C bond formation a significant polarization of the electron density in the inner electronic shells of the TM atoms is observed. We further show that these polarizations have to be taken into account by an extended multipolar model in order to recover accurate electron density distributions from high-resolution structure factors calculated for the title compounds.